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XXXVI Winter Meeting on
Statistical Physics

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The XXXVI edition of the Winter Meeting on Statistical Physics

will take place in Taxco, Guerrero (Mexico) from the 9^th to the 12^th January, 2007. Home

The XXXVI edition of the Winter Meeting on Statistical Physics will take place in Taxco, Guerrero (Mexico) from the 9^th to the 12^th January, 2007.

This event is the most important meeting on statistical physics in Mexico and it has been taking place yearly for the last thirty four years with high scientific level. The purpose of the meeting is to discuss frontier problems in basic statistical physics and its applications to technological, chemical and biological research, among others, as well as to get knowledge of hot topics in these fields. Therefore, to succeed in this, the meeting is bringing together international qualified experts from different research groups providing an excellent occasion for academic exchange between local and foreign colleagues in a pleasant informal environment. The main program consists only of plenary lectures given by selected invited speakers who share, in a general way, relevant results from their research, and of a poster session presented mainly by graduate students.

Speakers (click on name for avaibable titles and abstracts) Home

1.- Jan Sengers (Institute for Physical Science and Technology - University of Maryland, USA)

2.- Elisabeth Schöll-Paschinger (Institut für Experimentalphysik der Universität Wien, Austria)

3.- Agustí Perez-Madrid (Departament de Física Fonamental, Universitat de Barcelona, Spain)

4.- Nitant Kenkre (University of New Mexico, USA)

5.- Tomás Alarcón (Mathematical Institute, University of Oxford, England)

6.- Emmanuel Trizac (Laboratoire de Physique Théorique et Modèles Statistiques, Université de Paris-Sud, France)

7.- Peter Vekilov (Department of Chemical and Biomolecular Engineering, University of Houston, USA)

8.- Fernando Oliveira (Insituto de Física e Centro Internacional de Física da Matéria Condensada, Universidade de Brasilia, Brazil)

(NOTE: Due to problems with mexican visa, Profr. Oliveira is not coming to the conference this time).

9.- Jure Dobnikar (Jozef Stefan Institute, Ljubljana, Slovenia)

10.- Jesús Santana Solano (Cinvestav-Monterrey, Mexico)

11.- Moisés Santillán Zerón (Cinvestav-Monterrey, Mexico)

12.- Minerva González Melchor (Universidad Autónoma de Puebla, Mexico)

13.- Orlando Guzmán (Universidad Autónoma Metropolitana-Iztapalapa, Mexico)

14.- Hernán Larralde (Centro de Ciencias Físicas, Mexico)

15.- Victor Romero Rochín (Instituto de Física - UNAM, Mexico)

16.- Jaime Ruiz García (Instituto de Física-UASLP, Mexico)

Program Home

	Tuesday 9	Wednesday 10	Thursday 11	Friday 12
7:00 – 9:00		Breakfast	Breakfast	Breakfast
8:45 – 9:00		Opening ceremony
9:00 – 10:00		Sengers	Pérez-Madrid	Ruiz
10:00 – 11:00		Guzmán	Larralde	Alarcón
11:00 – 11:30		Coffee / Posters	Coffee / Posters	Coffee / Posters
11:30 – 12:30		Santana	To be announced	Santillán
12:30 – 13:30		González-Melchor	Vekilov	Kenkre
13:30 – 14:30		Posters	Trizac
14:30 – 16:00		Lunch	Lunch	Lunch
16:00 – 17:00	Registration	Romero-Rochín	Organizing meeting
17:00 – 18:00	Registration	Dobnikar	Free
18:00 – 18:30	Posters	Coffee	Afternoon
18:30 – 19:30	Posters	Schöll-Paschinger
19:15 – 20:15	Welcome cocktail
20:00	Dinner	Dinner	Dinner

Talks Home

Thermal Fluctuations in Nonequilibrium Thermodynamics

Jan V. Sengers

Institute for Physical Science and Technology, University of Maryland, College Park, MD, U.S.A.

The lecture will address the following three principles concerning fluctuations in fluids and fluid mixtures that are in not in thermodynamic equilibrium:

1. The principle of local thermodynamic equilibrium in nonequilibrium thermodynamics is valid for the thermodynamic properties, but not for the fluctuations of these properties.

2. Fluctuations in fluids in stationary nonequilibrium states are always long ranged, even far away from any hydrodynamic instability.

3. Traditional hydrodynamic instability analysis does not yield a correct

description of fluctuations near instabilities.

These principles will be illustrated by theoretical and experimental studies of fluctuations in liquid and liquid mixtures subjected to a stationary temperature gradient.

A Self-Consistent Liquid-State Theory

Elisabeth Schöll-Paschinger

Institut für Experimentalphysik der Universität Wien, Austria

I will present the self-consistent Ornstein-Zernike approximation (SCOZA), an advanced microscopic liquid-state theory that was developed by Hoye and Stell and is known to give remarkably accurate results for the liquid-vapour coexistence curves of simple fluids and remains successful even in the critical region. After introducing the theoretical concept, I will discuss several applications of this theory to various discrete and continuum systems. Hard-core Yukawa fluids, Ise-Sogami fluids, fullerenes, and square well fluids will be studied in detail. Furthermore, I will present the phase behavior of systems with explicitly density-dependent potentials that exhibit the phenomenon of double criticality. The accuracy of the SCOZA for binary symmetric fluid mixtures, which show a much richer phase behavior, will be demonstrated by comparison with Monte Carlo simulations. Finally, I discuss possible extensions of the theory to soft-core fluids.

On the Law of Increase of Entropy for Nonequilibrium Systems

Agustí Pérez Madrid

Departament de Física Fonamental, Universitat de Barcelona, Spain

In this contribution we prove that the nonequilibrium entropy of an N-body isolated system possesses a lower bound and therefoere can not decrease and the entropy production should be non-negative. Under the assumption of a smooth full phase-space distribution function we define the nonequilibrium entropy as a functional of the set of reduced distribution functions (distribution vector). As an application we obtain a generalization of the BGK (Bhatnagar-Gross-Krook) relaxational model in addition to the Boltzmann kinetic equation. We also establish the relation between our theory and Clausius' formulation of the second law.

Patterns, Confinement of Random Walkers, and Wavefront Propagation in Population Dynamics

V. M. Kenkre

Consortium of the Americas for Interdisciplinary Science, University of New Mexico, Albuquerque, NM 87131, USA

Recent work carried out in our group in the description of random walks and wavefront propagation in the subject of mathematical ecology will be presented. Specifically three issues will be discussed: patterns that arise as a result of spatially nonlocal competition interactions, effect of confinement on measurements of motion parameters, and transient effects in wavefront propagation from nonlinear population dynamics equations. The work is supported by the NSF, the NIH and DARPA.

Multiphysics Biological Modelling

Tomás Alarcón

Mathematical Institute, University of Oxford, England

As advances in biological sciences occur, it becomes clearer that a thorough understanding of biological phenomena will require theoretical, quantitative frameworks. However the complexity of such processes poses an extraordinary challenge to physical scientists. The multiscale nature of biological processes in which phenomena occuring at time and spatial scales ranging from tissue to gene are strongly coupled overcomes most of the traditional modelling approaches and, therefore, new ones are needed. An attempt to fill this gap consists of formulating multiphysics models. In these models, each scale of interest is analysed in terms of the different physical description. These different models are eventually integrated in one single model which couple them all. In this talk, I will introduce and motivate from a biological point of view this type of model and give some examples of applications in the study of the growth and treatment of solid tumours.

From Painleve classification to Manning counter-ion condensation : new results for the physical properties of bio-polymers

Emmanuel Trizac

Laboratoire de Physique Théorique et Modèles Statistiques, Université de Paris-Sud, France

Onsager-Manning condensation is a manifestation of the long range character of the Coulombic potential in 2D geometry. This phenomenon is the cornerstone of our understanding of bio-polymers. Beyond a charge density threshold, counterions "condensate" onto the charged polymer. With salt (added electrolyte), which is the experimentally relevant situation, the phenomenon is more complex and has received little attention. We will show that recent mathematical advances allow to obtain analytical results in a large range of salt content. We will in particular discuss the implications of this work for the Coulombic elasticity of bio-polymers through their persistence length.

Many-body interactions in colloidal systems

Jure Dobnikar

Jožef Stefan Institute, Jamova 39, 1000 Ljubljana

The colloid-colloid interactions in charge stabilized colloidal suspensions are mediated via microions (electrolyte) and are therefore inherently many-body in nature and simplified descriptions in terms of pairwise additive effective interactions are not always appropriate. In recent years a number of experimental and theoretical studies showed that understanding the many-body effects is essential for complete understanding of colloidal interactions.

I will present our numerical studies based on solving the nonlinear Poisson-Boltzmann equation in three dimensions.

The method has been applied to study the following problems:

· Coupling the Poisson-Boltzmann solver to the Brownian dynamics simulations, we have studied the solid-liquid phase transition and showed that many body interactions lead to a macroscopic effect, i.e., the deviation of the melting line from the predictions based on the pairwise additive interactions.

· Three-body interactions have been directly measured (experimentally) and calculated and a qualitative agreement has been obtained.

· The forces on each colloid in a system of 6000 colloids have been evaluated by solving the nonlinear Poisson-Boltzmann equation and compared to the sum of the effective forces derived from the cell model and Jellium model approximations. A reasonable agreement has been observed, again with deviations only explainable by many-body interactions.

The elastic constants have been measured and numerically calculated in 3-D colloidal fcc crystals and the Cauchy relation has been shown to be violated, which is a fingerprint of non pairwise additive potentials.

Physicochemical mechanisms of sickle cell anemia

Peter Vekilov

Department of Chemical and Biomolecular Engineering, University of Houston, USA

Sickle cell anemia is a debilitating genetic disease, which affects hundreds of thousands babies born each year worldwide. Its primary pathogenic event is the polymerization of a mutant, sickle cell, hemoglobin (HbS) and this is one of a line of diseases (Alzheimer's, Huntington's, prion, etc.) in which nucleation initiates pathophysiology. We show that the homogeneous nucleation of HbS polymers follows a two-step mechanism with metastable dense liquid clusters serving as precursor to the to the ordered nuclei of the HbS polymer. The evidence comes from data on: the rates of fiber nucleation and growth, and nucleation delay times; the interaction of fibers with polarized light; and mesoscopic metastable HbS clusters in solution. The presence of a precursor in the HbS nucleation mechanism potentially allows low-concentration solution components to strongly affect the nucleation kinetics. The variations of these concentrations in patients might account for the high variability of the disease in genetically identical patients. In addition, these components can potentially be utilized for control of HbS polymerization and treatment of the disease.

Direct Measurement of Colloidal Particle Rotation and Field Dependence in Alternating Current Electrohydrodynamic Flows

Jesús Santana Solano

Cinvestav-Monterrey, Mexico

We have measured the influence of both applied alernating current (AC) field strenght and frequency on the electrohydrodynamic (EH) flows present in colloidal systems near an electrode surface. The effect of the flows is visualized by the rotation of the colloids, fluorescently labeled by a novel technique involving EH-driven aggregation of smaller tracer colloids to the surface of the larger colloids. Our results shows an E^2 dependence of these flows, consistent with an induced charge mechanism for effective colloidal interactions. We have also observed a crossover in frequency that suggests a change in the origin of the induced charge, consistent with predictions from available theory. The EH flows appear to be hydrodynamically screened inside clusters, as evidenced by the lack of rotation of interior colloids and the cluster-size independent rotation rate of colloids on the boundary.

Jesus Santana-Solano, David T. Wu, and David W. M. Marr, Langmuir, 2006, 22, 5932-5936.

Origin of Bistability in the Lactose Operon

Moisés Santillán

Cinvestav-Monterrey, Mexico

Multistability is an emergent dynamic property that has been invoked to explain multiple co-existing biological states. In this, work we investigate the origin of bistability in the lac operon. To do this, we develop a mathematical model for the regulatory pathway in this system and compare the model predictions with the experimental results of Ozbudak et al. (Nature 427, 737-740, 2004), in which a non-metabolizable inducer was employed. We investigate the effect of lactose metabolism using this model, and show that it greatly modifies the bistable region in the external lactose (Le) vs. external glucose (Ge) parameter space. The model also predicts that lactose metabolism can cause bistability to disappear for very low Ge. We have also carried out stochastic numerical simulations of the model, for several values of Ge and Le, to analyze the effects of intrinsic noise due to small numbers of regulatory molecules. Our results indicate that bistability is an efficient way to guarantee that E. coli consumes glucose and lactose in the most efficient possible way. Namely, the lac operon is induced only when there is almost no glucose in the growing medium, but if Le is high, the operon induction level increases abruptly when the bacterial culture is virtually depleted of glucose. We demonstrate that this behavior could not be obtained without bistability if the stability of the induced and uninduced states is to be preserved. Finally, we wish to point out that the present methods and results may be useful to study the emergence of multistability in biological systems other than the lac operon.

Electrostatic Interactions in Dissipative Particle Dynamics

Minerva González-Melchor

Universidad Autónoma de Puebla, Mexico

A new proposal to calculate electrostatic interactions in dissipative particle dynamics is presented. These interactions are calculated using the Ewald Sums method combined with charge distributions on DPD particles. The method is applied to study bulk electrolytes and polyelectrolyte/surfactant solutions. This proposal is also applied to calculate the radius of gyration of a polyelectrolyte in a salt solution. The radius of gyration shows good agreement with the trend found in static light scattering experiments.

Liquid crystal-based biosensors: principles, simulations, and experiments

Orlando Guzmán
Departamento de Física, UAM-Iztapalapa

A thin film of liquid crystal can be used to detect subtle changes on the interfaces that confine it. By careful control over interfacial chemistry and topography, one can build LC-based biosensors. Typically, polarized light patterns are used to signal the detection of adsorbed analyte. In this talk we will: (a) describe recent experimental LC-based biosensors and discuss the principles for their operation, (b) show that, by using multiple methods, computer simulation has provided insights about the observed patterns and the dynamical behavior of the LC, and (c) present a way to enhance the sensitivity of these devices by quantifying the gradual modification of a surface, as a function of concentration of analyte, in terms of the liquid crystal’s anchoring energy.

Flux statistics

Hernán Larralde, Centro de Ciencias Físicas, Mexico

Out of equilibrium systems are characterized by the presence of fluxes. This is obvious in time dependent systems, but it is also the case in non equilibrium steady states, which are ditinguished from equilibrium by the fact that there is a non zero mean flux of some quantity through the system. The above statement requires the recognition that fluxes are stochastic variables and, perhaps, that their statistics beyond the mean, can provide insight into the description of out of equilibrium phenomena. Indeed, from Onsager to the fluctuation theorem, there has been a great deal of work trying to relate the statistics of flux to entropy production. In this talk I will present results from ongoing research on the statistical properties of mass, energy and coupled fluxes in some simple stochastic systems.

Glasses and Deformed Crystals: Equilibrium States?

Victor Romero-Rochín

Instituto de Física, UNAM, México

It is an accepted fact that glasses and deformed crystals are not states of equilibrium; they are assumed to be metaestable states. Without challenging directly such an assertion but based on the experimental evidence that those states may be extremely long lived, and thus be considered for those times as "stable", we present a consistent thermodynamic theory (based on well known results of the theory of elasticity) that can describe those solid states. We make a description of the equilibrium states by means of the metric or strain tensor and the pressure tensor of the body. We discuss our results aided by Molecular Dynamics Simulation of a Lennard-Jones system.

Trapping and Condensing DNA at the Air/Water Interface

Jaime Ruiz García, Instituto de Física, Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, San Luis Potosí, Mexico.

DNA is a highly charged polyelectrolite and as such it is considered to be completely soluble in pure water. Surprisingly, we found that DNA can be trapped at the air/water interface and does not go back into a pure water subphase. We show that DNA is trapped in a minimum energy at the interface, much bigger that KT, that does not permit its return to the bulk. Once at the interface, DNA molecules condense to form different two-dimensional mesostructures such as foams, giant rings, disks and rods at low density. This condensation occurs without the presence of multivalent cationic ions, as it is required in bulk, for example in condensing DNA toroids. However, we show that monovalent and divalent cations do not change this behavior, but trivalent cations does. At high density, the molecules form a remarkable monomolecular network. At the interface, DNA is only partially immersed in water, which originates that the chains get only partially charged, but the charges are of the same sign. Therefore, this can be considered another case of like-charge attraction, similar to those found in colloids trapped at the air/water interface. However, the origin of the attractive part of the interaction potential is unknown. In addition, we found that DNA at the air/water interface can form 2D smectic-like domains tens of microns in size. Both, the DNA monomolecular networks and the smectic-like domains are interesting from theoretical and application standpoints.

Posters Home

1.- A comparative study of the complex transcription-factor gene regulatory networks of E. coli and S. cerevisiae

L. Guzmán-Vargas¹, Moisés Santillán^2,3 and Albert Díaz-Guilera⁴

1) Unidad Profesional interdisciplinaria en Ingeniería y Tecnologías Avanzadas, Instituto Politécnico Nacional, Av. IPN No. 2580, México D.F. 07340, México

2) Centro de Investigaci_on y Estudios Avazados del IPN, Unidad Monterrey, Av. Cerro de las Mitras No. 2565, Col. Obispado, 064060, Monterrey, Nuevo Le_on, M_exico.

3) Centre for Nonlinear Dynamics in Physiology and Medicine, McGill University, McIntyre Medical Sciences Building, 655 Promenade Sir William Osler, H3G1Y6 Montreal QC, Canada.

4) Dept. Física Fonamental, Facultat de Física, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain.

In this work we present a comparative analysis of two dfferent transcriptional regulatory networks: one for the bacterium Escherichia coli, and one for the budding yeast Saccharomyces cerevisiae. First, we measure several network properties for the bipartite networks (with unidirectional links from the transcription factors to the regulated genes), as well as for the networks projected to the transcription factors and to the regulated genes. These measurements include the clustering coefficient, the degree distribution, and a coefficient measuring to what degree the nodes with most links in the network are connected among them. Later, we construct random networks with the same degree distributions as those of E. coli and S. cerevisiae, and carry out the same measurements to compare with the original networks. Finally, we tested network robustness by subjecting the original and randomized networks to removal of the most connected nodes, and evaluating the changes.

2.- Test of an universality ansatz fo the contact values of the radial distribution functions of hard-spheres mixtures near a hard wall

Mariano López de Haro¹, Santos B. Yuste² and Andrés Santos²

1.- Centro de Investigación en Energía, UNAM, Temixco, Morelos 62580, Mexico.

2.- Departamento de Física, Universidad de Extremadura, Badajoz, E-06071, Spain.

Recent Monte Carlo simulation results for the contact values of polydisperse hard-sphere mixtures at a hard planar wall are considered in the light of a universality assumption made in approximate theoretical approaches. It is found that the data seem to fulfill the universality ansatz reasonably well, thus opening up the possibility of inferring properties of complicated systems from the study of simpler ones.

3.- Structural Properties of a Seven-Dimensional Hard-Sphere Fluid

Miguel Robles¹, Mariano López de Haro¹ and Andrés Santos²

(1) Centro de Investigación en Energía, UNAM, Temixco, Morelos 62580, Mexico.

(2) Departamento de Física, Universidad de Extremadura, E-06071 Badajos, Spain.

The direct correlation function and the (static) structure factor for a seven-dimensional hard-sphere fluid are considered. Analytical results for these quantities are derived within the Percus-Yevick approximation.

4.- Monte Carlo Simulations of the Liquid-Vapour Interface of Lennard-Jones Diatomics for the Direct Determination of the Interfacial Tension using the Test-Area Method

José Guillermo Sampayo-Hernández, Erich A. Müller and George Jackson

Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK

We have performed Metropolis constant volume Monte-Carlo simulation (MC-NVT) to examine the vapour-liquid interface of systems of diatomic Lennard-Jones molecules. The recently developed test-area method (TA) [Gloor et al., J. Chem. Phys., 123, 134703 (2005)] is used to determine the interfacial tension; the TA method involves a thermodynamic (free energy perturbation) route to the tension rather than the more common mechanical (virial) relation of Kirkwood and Buff. Simulation data is reported for diatomics with different bond lengths L where the site-site Lennard-Jones potential is spherically truncated (ST) at 6s. Bond lengths of, 0.505, 0.6, 0.63, 0.67, 0.793 and 1.0 are examined. The surface tension obtained with the TA method for the Lennard-Jones diatomics with are compared with values obtained with the mechanical relation. The simulated vapour-liquid interfacial tensions for systems with values of the parameters chosen to represent real fluids (e.g., nitrogen and ethane) are satisfactory agreement with the experimental data. The density profiles, saturation densities in the vapour and liquid phases, and the interfacial thickness are also obtained for each system showing a good

agreement with previously published results where available.

5.- Behavior and Characterisation of Liquid Crystals Phases: a Molecular Dynamics Simulation Study

Enrique Cañeda Guzmán, José Antonio Moreno Razo and Enrique Díaz Herrera

Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, Mexico.

In this study we report results of Molecular Dynamics simulation of liquid crystals for ellipsoidal shape particles using a Gay-Berne (GB) potential. The phase diagram is calculated with parameters GB (k = 3; k’ = 5; m = 1; n = 3), it had been discussed a little in the literature and is of interest to study the orientacional behavior of the equilibrio liquid-crystal in the coexistence at low temperature. We give a detailed discussion of the structure of the liquid crystalline phases exhibited by ellipsoidal shaped mesogenic molecules. On the other hand, results of molecular dynamics simulations for binary mixtures of fuids confined Lennard-Jones type are presented, like initial stage in the development of a numerical code, in a future work we would study in more detail the effect of confinement of these systems, that has been few discussed. We will extend these study to binary liquid crystal mixtures.

6.- De la mariposa de Hofstadter a la de Fibonacci

Gerardo García Naumis and Francisco J. López Rodríguez

Instituto de Física, UNAM. Apartado POstal 20-364, 01000, México D.F., México.

En este trabajo se muestra que es posible escribir los potenciales ergódicos que resultan de considerar el movimiento de un electrón en una red bajo un campo magnético o en un cuasicristal, como un potencial genérico de tipo trigonométrico. De este modo, las propiedades de conducción y el espectro de energías de ambos sistemas pueden estudiarse mediante las funciones de correlación estadística del potencial, observandose una transición de estados extendidos a críticos (fractales). Como resultaod, el presente trabajo plantea la posibilidad de construir motores cuánticos de tipo matraca usando campos magnéticos modulados en el espacio.

7.- Title not available

José Antonio Climent Hernández

Facultad de Ciencias, UNAM. (Circuito interior S/N Facultad de Ciencias, Edificio de Ciencias Experimentales y Docencia "Tlahuizcalpan".

Analysis of the Cox, Ross & Rubinstein y Black & Scholes methods to develop an information system to value American and European Call and Put option prices on American dollar and the state of the contracts until their maturity. This development is performed in terms of a Fokker-Plank equation using the Itô and Stratonovich calculus.

8.- Microrheology of viscoelastic fluids containing light scattering inclusions

Catalina Haro-Pérez¹, Efrén Andablo-Reyes¹, Pedro Díaz-Leyva¹, and José Luis Arauz-Lara^1,2

(1) Instituto de Física "Manuel Sandoval Vallarta", Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, 78000 San Luis Potosí, México

(2) Departamento de Física, CINVESTAV, Avenida IPN 2508, Colonia Zacatenco, 07360 México D. F., México.

The microrheology of viscoelastic fluids containing inclusions with high scattering power is measured by depolarized dynamic light scattering (DDLS) from optically anisotropic spherical colloidal probes. The anisotropy of the probes allows us to measure both their translational and the rotational mean squared displacements simultaneously, whereas DDLS allows us to suppress the light scattered from the inclusions. The storage and loss moduli are determined from both mean squared displacements and the results compared with mechanical measurements.

9.- Polarization-Diffusion Effect on the Dispersion of N- and alpha- Dielectric Relaxation Modes

S. I. Hernández and L. F. del Castillo

Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, P.O Box 70-360, 04510 México, D.F., Mexico

In this work, the contribution of polarization diffusion on the dispersion of the electric susceptibility in polymeric materials, that exhibits normal (N-) relaxation at low frequencies and segmental or alpha relaxation at high frequencies, is studied. Polarization diffusion is locally established when the viscoelastic relaxation couples to the relaxation of a dipolar system. In order to formulate this diffusion process, it was proposed a physical description based on a system of two coupled equations to express the viscoelastic and dielectric relaxations, and the coupling between them is introduced by considering spatial inhomogeneities. The complex polarization-diffusion coefficient and the wave number as frequency function are obtained considering two parameters, which were evaluated considering a diffusive model for the N- and alpha dielectric modes respectively, for two polymeric systems.

10.- Structure and Diffusion of Colloidal Dumbbells

Andrés García-Castillo and José Luis Arauz-Lara

Instituto de Física, Universidad Autónoma de San Luis Potosí, San Luis Potosí, SLP, México

The static structure and diffusion of colloidal dumbbells in water, confined in quasi-two-dimensional geometries is measured by optical microscopy. Colloidal dumbbells are fabricated by inducing colloidal aggregation followed by sintering. The particles are confined between two parallel plates in order to form a quasi-two-dimensional system. Measurements of the structure of the suspension and the mean squared displacements, rotational and translational of the particles are presented.

11.- Thermodynamical Formalism of symbolic systems: An application to DNA sequence of Phage fX174

José Rubén Luévano

Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana-Azcapotzalco, 02200 México, DF, México.

In this work we give a straightforward application of thermodynamical formalism to DNA sequence of the bacteriophage fX174. That DNA sequence was the first one decoded, and its simplicity allows us to test the applicability of our thermodynamic approach. We introduce a formal canonical partition function, hence we compute the free energy and the generalized entropies. Also, we compute the Lempel-Ziv complexity of the symbolic system induced by the corresponding genetic sequence.

12.- Combining Rules for Mixtures of Elongated Molecules

José Alfredo González-Calderón and Fernando del Río

Apartado Postal 55-534, México 0934, Distrito Federal, México.

We show that Approximate Non-Conformal (ANC) theory is reliable for describing the mixed second virial coefficient of mixtures of elongated molecules (n-alkanes) and also mixtures of elongated with quasi-spherical molecules. We analyzed systems with low dipole moments molecules such as n-methane, n-ethane,...., and n-octane, together with Ar, N2, and O2. The research was done using Lorentz-Berthelot, Fender-Halsey-Lorentz and Kong combining rules. Whe show that Lorentz-Berthelot combining rules are appropiate for describing the experimental data of second virial coefficient of the mixture while the other do not represent correctly the data when the mixture has components of very different sizes or energies.

13.- Optimised Equation of State of Square-Well Fluids of Variable Range

Rodolfo EspÃíndola-Heredia and Fernando del Río

Apartado Postal 55-534, México 0934, Distrito Federal, México.

A optimised equation of state (EOS) of particles interacting with a square-well (SW) potential of variable width 1.1 < Î» < 3.0 is presented. The equation was built following the perturbation procedure used in previous EOS. The SW perturbation terms were calculated up to fourth order by MC simulation of hard-sphere systems and comparated for consistency in the thermodinamic limit with the internal energy of the SW fluid obtained by NVT Monte Carlo simulations. Internal energies, pressures, chemical potentials and specific heats agree with results of simulations and compare farvourably with those of recent SW EOS.

14.- Prediction of Excess Properties and Phase Equilibrium in Liquids Mixtures from Effective Potentials

Benjamín Ibarra-Tandi and Fernando del Río

Apartado Postal 55-534, México 0934, Distrito Federal, México.

We calculate thermodynamic properties of mixtures using the Approximate Non-Conformal, ANC, theory of fluids. This theory introduces a family of intermolecular potentials characterized by the usual molecular parameters for size Î´m and energy Îµ, plus an extra parameter, account for the profile of the potential: The softness s. We predict excess volumes and vapour-liquid coexistence of mixtures of Ar, Kr and other simple liquids at low temperatures. Very good agreement with experiment is obtained by using the ANC interactions, previously determined from gas-phase properties, supplemented with a two-body effective term that models the Axilrod-Teller-Muto three-body potential.

15.- Virial coefficients and effective potentials of linear molecules

Adrián Rocha-Ichante and Fernando del Río

Apartado Postal 55-534, México 0934, Distrito Federal, México.

We test the applicability of the ANC theory to a diversity of nonspherical model molecules: Non-Spherical Square Wells (NSSW) and Non-Spherical Kihara (NSK). Effective volumes, virial coefficients are calculated analytically. Effective potentials are also determined explicitly for all cases. As a main qualitative results it is found that molecules look harder when they are more elongated. This behaviour has been observed in n-alkanes and perfluoro-alkanes.

16.- Motion in washboard potentials: Dimer versus monomer

E. Heinsalu and M. Patriarca

Institute of Theoretical Physics, Faculty of Chemistry and Physics, Tartu University, Tähe 4, 51010 Tartu, Estonia

We study the system of two interacting particles forming a dimer and moving in a one-dimensional periodic potential. The system is under the influence of a constant external force and the interaction between the particles is assumed to be harmonic. We study the diffusive motion and the mobility of the dimer in the parameter space of the system. The results are compared to those of a monomer.

17.- Recent results on fractional diffusion in space- and time-periodic force-fields

E. Heinsalu, M. Patriarca, I. Goychuk, G. Schmid and P. Hänggi,

Institute of Theoretical Physics, Faculty of Chemistry and Physics, Tartu University, Tähe 4, 51010 Tartu, Estonia

Recent novel results on fractional diffusion are presented. Anomalous transport is investigated within the framework of the fractional Fokker-Planck equation (FFPE) and the underlying continuous time random walk (CTRW). Our research addresses both, the time-independent as well as the time-dependent force fields. In the first case, we derive from FFPE some intriguing results for anomalous transport and anomalous diffusion in washboard and periodic potentials [1,2,3]. The results are confirmed by stochastic simulations of the underlying CTRW. Considering the time-dependent fields, we present new features for anomalous transport under the influence of a time-periodic symmetric dichotomous force. Our results prove that the standard FFPE in time-dependent fields is flawed. The results are, however, consistent with a modified version of the FFPE, which can be derived rigorously for this particular case under study.

[1] I. Goychuk, E. Heinsalu, M. Patriarca, G. Schmid, and P. Hänggi, Current and universal scaling in anomalous transport, Phys. Rev. E *73*, 020101 (2006), Rapid Communication.

[2] E. Heinsalu, M. Patriarca, I. Goychuk, G. Schmid, and P. Hänggi, Fractional Fokker-Planck dynamics: Numerical algorithm and simulations, Phys. Rev. E *73*, 046133 (2006).

[3] E. Heinsalu, M. Patriarca, I. Goychuk, and P. Hänggi, Fractional diffusion in periodic potentials, J. Phys. – Condensed Matter (2007), in press, [arXiv:cond-mat/0604269]

18.- Finite-size effects in microrheology

I. Santamaria-Holek and J.M. Rubi

We propose a model to explain finite-size effects in intracellular microrheology observed in experiments. The constrained dynamics of the particles in the intracellular medium, treated as a viscoelastic medium, is described by means of a diffusion equation in which interactions of the particles with the cytoskeleton are modelled by a harmonic force. The model reproduces the observed power-law behavior of the mean-square displacement in which the exponent depends on the ratio between particle-to-cytoskeleton-network sizes.

19.- Phases obtained by shear in a solution of flexible cylindrical micelles

Jorge Delgado¹, Pavlik Lettinga² and Rolando Castillo¹

(1) Instituto de Física at UNAM, Mexico and ⁽²⁾Forschungszentrum Jülich, Germany.

Semidilute and dilute regimes of viscoelastic CTAB/NaSal systems are studied under stationary and non-stationary shear flow conditions. In the diluted regime, we could observe and explain the formation of shear-induced structures (SIS) from fast strain thixotropic loops that decouple the stress coming from non-deforming material (the solvent) and the stress coming from SIS formation. Furthermore, the maximum quantity of SIS at every shear rate is obtained from ramping-down curves. These curves are independent of the deformation history and can be related with a typical time of SIS formation. In contrast with the dilute regime, where SIS span the fluid; in the semidilute regime the formation of bands in the fluid is common. Using different rheometers and from flow velocity profiles, we obtained the flow properties of different bands in the fluid. We can describe a real interface between bands and an initial hydrodynamic nature of stress oscillations under stationary flow conditions. We found that stress oscillations, typical from a coupling between concentration and flow, are associated with a single band in the fluid.

Finally we discuss the idea of a phase transition under shear in the semidilute regime.

20.- Purification and characterization of multi-wall carbon nanotubes produced by chemical vapor deposition (CVD) method

J.L. Hernández-López,¹ E.R. Alvizo-Páez,¹ J. Ruiz-García¹, J.M. Romo-Herrera,² M. Terrones² and H. Terrones²

(1) Instituto de Física, Departamento de Fisicoquímica y Física Estadística, Dr. Manuel Nava Martínez No. 6, Zona Universitaria, Universidad Autónoma de San Luis Potosí, San Luis Potosí, 78290 México.

(2) Instituto Potosino de Investigación Científica y Tecnológica, A.C., Camino a la Presa San José s/n, Lomas 4ª Sección, San Luis Potosí, 78231 México.

A purification procedure for multi-wall carbon nanotubes (MWCNTs) and nitrogen-containing carbon nanotubes (CN_x MWCNTs) is presented in this work. The methodology incorporates a hydrothermal/ultrasonic treatment along with other treatments such as extraction of polyaromatic compounds, dissolution of metal particles and mechanical separations by means of isopycnic centrifugation based-techniques. The effects of each treatment in the purification process are also discussed by characterizing the intermediate products using SEM, STEM, XRD, DRFTIR-spectroscopy and TGA.

21.- Morphology Transitions in Langmuir Monolayer Domains

Andrea Gutiérrez-Campos, Karen Volke and Rolando Castillo

Instituto de Física, UNAM.

In recent experiments, morphology transitions in Langmuir monolayer domains have been observed. In the present work related to my PhD research investigation, the mechanisms behind such morphology transitions will be studied. In the first part, pattern formation and growth from fluid to condensed phases will be studied for four different monolayers: Nervonic Acid, DODA, Methyl Palmitate and DMPE. With an appropriate Langmuir trough and a Brewster angle microscope (BAM), we will observe morphology transitions and relate them to a possible orientation change of the amphiphillic chains. This orientation change is related to the anisotropy in line tension of the interface between condensed and fluid phases. In the second part of this work, we will formulate a hydrodynamic model to understand the domain growth analyzing the interface instability. Finally, we propose an experimental setup which will allow us to trap one single monolayer domain with the aid of PMMA microspheres attached to the domains, using optical tweezers. With this experimental setup, we will be able to modify the thermodynamic variables involved in the morphology transitions and with the BAM we will observe the domain evolution.

22.- Concept of Caging in the Freezing of Hard Disk

Adrián Huerta¹, Andrij Trokhymchuk and Douglas Henderson

(1) Departamento de Física No lineal del Instituto de Ciencias Físicas, UNAM.

As density in the system of hard disks progressively increases towards freezing transition, the number of nearest neighbors of each disk saturates at the level of six neighbors and system as whole shows enhanced tendency for hexagonal ordering. An unoccupied area, that still is in disposal, is distributed uniformly over the entire system that results in the interparticle gap width of ~0.152¦Ò . This value of the gap correlates well with the estimates using independent sources from the literature. In the present report we show that hexagonal ordering with spacing of 0.152¦Ò initiates the caging of the central particle by the alternative nearest-neighbors and can be crucial in the understanding of the freezing transition in a hard-disk system.

23.- A Molecular Dynamics Study of Interfacial Behavior of Discotic Molecules

Cienega Cacerez Octavio, J Antonio Moreno-Razo and E. Díaz-Herrera

Universidad Autónomoa Metropolitana Iztapalapa, Av. San Rafael Atlixco 186, Colonia Vicentina, C.P. 09340, México D.F., México.

The Gay-Berne potential anisotropic of interaction has been employed extensively in simulation studies of rod-like liquid-crystals. However, the potential can be used also to study discotic liquid crystals, that is, compounds whose molecules are flattened or disc-shaped. Here we used a suitable parametrization for Gay-Berne discs with GB(k=0.345 k’=0.2 m=1 n=2) for pure systems. We report results of computacional simulations of molecular dynamics in the ensemble NPT and NVT for a system of 2000 particles. We calculated the phase diagram of this system and studied the behavior of the interface tension like function of the temperature for the coexistence curve. We calculated the pair radial distribution function g(r) and the orientational G(r) like part of the structural information of the homogeneus (Isotropic, Nematic, Columnar).

24.- Structure and Dynamics of Interacting Brownian Particles in One-Dimensional Channels on Periodic Laser-Fields

Salvador Herrera-Velarde and Ramón Castañeda-Priego

Instituto de Física, Universidad de Guanajuato, Loma del Bosque 103, Col. Loma del Campestre, 37150 León, Guanajuato, México.

We systematically study both structural and dynamic properties of one-dimensional charged colloids on periodic laser-fields by means of browian dynamics and Monte Carlo computer simulations, as well as by integral equations theory. The latter one, which is solved within the Rogers-Young approximation, describes quantitatively the structure in the fluid phase without applied laser-field. In such case, we find that the structure of the suspension possesses basically the properties shown by two- and three- dimensional open systems, i.e., the characteristic length scale of the system is given by the mean interparticle distance. We also find that the mean-square displacement (MSD), W(t), shows the typical crossover from normal diffusion at short-times to sub-diffusion at long-times in which W(t) ~ t^1/2, as theoretically predicted for colloidal and atomic systems. Nevertheless, when the laser-field is activated, a competition between its periodicity and the natural length scale of the suspension is observed and therefore a gradual structural transition is found. Moreover, at small potential strengths the MSD preserves its well-known sub-diffusive behaviour. However, at higher potential strengths the colloids are, on average, placed at the laser-potential minima, but one can also observe particle configurations in which two colloids are closer or further than the distance between two consecutive minima. Thus, the dynamics of the system is determined by the collective diffusion of such particle distributions along the channel modifying the t^1/2diffusion law at long times.

25.- Directing the Spectroscopies States of CdS Nanoparticles by Chemical Surface Modification

M. Quintana¹, F. Méndez² and E. Pérez¹

(1) IF-Universidad Autónoma de San Luis Potosí, Manuel Nava 6, Zona Universitaria, CP 78290, San Luis Potosí, SLP.

(2) Universidad Autónoma Metropolitana-Iztapalapa, México DF

Size-tunable optical properties in nanoscales derive primarily from the physical size and shape of the materials. In II-VI semiconductor nanoparticles the size-tuning is attributed to the confinement of the exciton in a nanocrystal significantly smaller than the bulk exciton. That interest the chemist because excitons can be engineered in a material according to structure. Interesting spectroscopic properties are governing by the size, including the band gap and the exciton binding energy which are often minuscules in bulk materials, and are greatly accentuated in nanometer sized materials. In this work we present a surface chemical modification of CdS nanoparticles by different Lewis bases. The spectroscopy studies reveal details of the collective excited states that capture and redistributed the excitation causing a blue shift and fluorescence enhancement depending on the adsorbed molecules. The experimental results are explained by a theoretical DFT calculation.

26.- Study of the dynamic of Brownian non spherical particles

José Guillermo Méndez Bermúdez^a, Minerva González Melchor^a, Iván Santamaría Holek^b

^a Instituto de Física “Luis Rivera Terrazas” BUAP. C.P. 72570. Av. San Claudio y 18 sur, San Manuel. Puebla, México.

^b Facultad de Ciencias, Universidad Nacional Autónoma de México, Circuito exterior de Ciudad Universitaria, 04510 DF, México

In this work we analize the behavior of non-spherical particles inmersed in a heat bath at temperatura T. This system execute translational an rotacional Brownian motion. This study is being carried out with theory and computer simulation. In the theorical study we use the mesoscopic non equilibrium thermodynamics, base on the existente of local equilibrium in phase space. For this case, we derive the equation of state. In the second part, we use the Gay-Berne potencial to model the interaction of non spherical particles. The translational and rotacional equations of motion are solved numerically using the Leap-Frog algorithm. The implementation of this part of the work is in progress.

27.- The approximate entropy as a measure of the complexity in time series

A. Ramírez-Rojas

Área de Física de Procesos Irreversibles Departamento de Ciencias

Básicas, Universidad Autónoma Metropolitana-Azcapotzalco, 02200, México.

The approximate entropy (ApEn) was introduced by Pincus [1] to quantify the creation of information in a time series. A low value of the entropy indicates that the time series is deterministic; a high value indicates complexity. We calculate the ApEn for an electroseismic time series and, we observed an important decreasing behavior of the ApEn, indicating low complexity of the signal a few hours before a great earthquake. In fact, we consider that this methodology could be a good estimator in order to describe the complexity of a time series. Particularly ApEn seems to be as a possible indicator precursory behaviour before of a great seism.

1. S. M. Pincus. Approximate entropy as a measure of system complexity.

Proc. Natl. Acad. Sci. USA. 88, 2297 - 2301, 1991.

28.- Metastability in the kinetic Ising model

David P. Sanders, Hernan Larralde & Francois Leyvraz

Insituto de Ciencias Fisicas, Universidad Nacional Autónoma de México,

Apartado postal 48-3, C.P. 62551, Cuernavaca, Morelos, Mexico

Many physical systems have metastable states, i.e. states far from equilibrium, where a system remains for a long time before a sudden decay to equilibrium occurs. We sketch a theory [1,2] describing metastable states in Markov processes, assuming that the evolution operator has a small eigenvalue, i.e. a long time-scale. The corresponding eigenvector contains information about the structure of the metastable state.

We test this theory numerically [2] in the kinetic Ising model, i.e. the standard Ising model (spins on a lattice modelling a ferromagnet) with external field and Metropolis spin-flip dynamics, finding very good agreement. In particular, we use the Wang-Landau algorithm to show that the coarse-grained metastable distribution is proportional to the equilibrium distribution, as has commonly been assumed, and that the coarse-grained eigenvectors contain information about free energies, hysteresis loops, and the probability of reaching the metastable and equilibrium states from given initial conditions.

[1] H. Larralde and F. Leyvraz (2005), Metastability for Markov processes with detailed balance, Phys. Rev. Lett. 94, 160201.

29.- Computational studies of dilute systems with electrostatic interactions between particles

Edgar Nuñez Rojas and Hector Dominguez Castro

Instituto de Investigaciones en Materiales, UNAM, Circuito exterior s/n. México, D. F., C. P. 04500

In this work Dynamic Molecular simulations of dilute systems of particles electrostatically charged were carried out using the Soft Primitive Model. Simulations were performed at diferent desinsities within a given interval of temperatures. After, temperature was set up and simulations were carried out varying density of the system. In some of these systems, it was noticed the formation of aggregate structures with different number of particles; such systems are being studied to determine the main factors involved in its aggregation. Electrostatic system shows a metastable behaviour when temperature varies within the interval of temperature chosen. Results showed that there is a region within the interval of density chosen in which the cluster formation shows a metastable behaviour. On the other hand, after this region electrostatic system shows an homogeneous behaviour without formation of aggregate structures.

30.- Rheology and Micro-rheology of slow relaxing fluids

Julian M. Galvan-Miyoshi and Rolando Castillo

We have studied the rheology and microrheology behavior of a microemulsion made of hexadecyltrimethylammonium bromide (CTAB) / sodium salicylate (NaSal)/ water, which forms very long and flexible cylindrical worm-micelles. The viscoelastic behavior of this mixtures depends on the CTAB molar concentration, on the molecular ratio between CTAB and NaSal, R=[NaSal]/[CTAB], and on temperature. We have probed the viscoelastic properties of the mixture with a light scattering technique (diffusion wave spectroscopy), through measuring the average motion of microspheres dispersed in the microemulsion. We obtained G'(w) and G''(w), prior obtaining the mean square displacement of the microspheres, showing that the microemulsion is a Maxwellian fluid at low frequencies. We obtained the Cole-Cole diagram and the Maxwell fluid constants. Also, measurements of the intensity correlation function were made on the polyacrylamide gel during the sol-gel transition. Results shows a plateau appearing and growing as the gel is forming.

31.- Atomic Force Microscopy images of Lyotropic Lamellar Phases

C. Garza , L. T. Thieghi and R. Castillo

Instituto de Física. UNAM P.O. Box. 20-364, D.F. México, 01000, México.

For the very first time, atomic force microscope images of lamellar phases were observed combined with a freeze fracture technique that does not involve the use of replicas. Samples are rapidly frozen, fractured, and scanned directly with atomic force microscopy, at liquid nitrogen temperature and in high vacuum. This procedure can be used to investigate micro-structured liquids. The lamellar phases in AOT/water and in C12E5/water systems were used to asses this new technique. Our observations were compared with X-ray diffraction measurements and with other freeze fracture methods reported in the literature. Our results show that this technique is useful to image lyotropic lamellar phases and the estimated lamellar periodicities are consistent with those obtained by X-ray diffraction.

32.- Polystyrene Nanoparticles Covered with a Thermically Cross-linked PAH/PAA Film

Rosa Mayela Romero-Gómez¹, Ma. de Lourdes González-González², Ferdinando Tristán³, Elías Pérez²

(1)Facultad de Ciencias, (2)Instituto de Física, (3)Centro de Investigación y Estudios de Posgrado, Universidad Autónoma de San Luis Potosí, San Luis Potosí, S.L.P., México

Polyelectrolyte Layer-by-Layer (LbL) self-assembling is a well known method used to obtain very thin films on different surfaces based on the adsorption of the polymers by coulombic forces. This work is focused on the surface of negatively charged polystyrene [PS] colloidal particles. These colloidal particles are covered by a self-assembled film made with five bilayers of two weak polyelectrolytes: positive poly(allyl amine) [PAH] and negative poly(acrylic acid) [PAA]. In order to maximize their adsorption on the colloidal particles PAH is adsorbed on the surface using a pH value of 4 while the PAA is adsorbed at pH value of 7.5. Once the self-assembled film was formed on the PS colloidal particles, they are heated above 120 ºC to allow the cross-linking of the film. PS particles are characterized through all the process using Attenuated Total Reflectance Fourier Transform Infrared Spectroscopy [ATR-FTIR], Atomic Force Microscopy [AFM] and Dynamic Light Scattering [DLS].

33.- A markovian model for the G-protein voltage-sensitive modulation of N-type calcium channels

Santiago Rebolledo-Antúnezand David García-Díaz

Departamento de Fisiología, Facultad de Medicina, Universidad Nacional Autónoma de México, Av. Universidad 3000 México D.F. 04510, México

Neurotransmitters modulate N-type calcium channels via G protein-coupled receptors in both voltage-sensitive and insensitive modes. It has been suggested that voltage-sensitive modulation modifies gating of these channels involving changes at the level of voltage-sensitive transitions before the channel opens. Eyring theory implies that the rate constants for these transitions must consist of two components: one, is voltage-sensitive (with charge transferring) and the other, is voltage-insensitive (enthalpic and entropic factors). In this work we present a markovian model for the gating kinetics of the G-protein voltage-sensitive modulation of N-type calcium channels. This model suggests that this type of modulation occurs in the voltage-insensitive component at the rate constant transitions level where there is not charge transferring.

34.- Parametric adjustment of a model of coherent scattering of light to the optical reflectance of a flat surface with adsorbed particles

F. Alarcón-Oseguera², M.-C. Peña-Gomar¹, Augusto García², Francisco Castillo³ and E. Pérez³

(1) Facultad de Ciencias Físico-Matemáticas de la Universidad Michoacana de San Nicolás de Hidalgo, Edificio B, Ciudad Universitaria, C.P. 58030, Morelia, Michoacán, México.

(2) Centro de Ciencias Aplicadas y Desarrollo Tecnológico, Universidad Nacional Autónoma de México, Ciudad Universitaria, A.P. 70-168, México D.F. 04510.

(3) Instituto de Física, Universidad Autónoma de San Luis Potosí, Alvaro Obregón 64, C.P. 78000, San Luis Potosí, SLP, México.

In order to obtain the parameters and limits of a theoretical model of the reflectance produced by particles adsorbed in a flat surface an adjustment methodology is designed in where the experimental datas are taken into account. The quality of the fitting is moderate by a c² distribution. The adjustment is essentially, a method of least square that is solved by Newton-Raphson, where the matrix is inverted by singular values decomposition. This method allows a careful analysis of the fit parameters and it allows us to have criteria to validate the theoretical model.

35.- Statics and dynamics properties of a neutral complex made by a polymer and two spheres

A. Vargas-Calderón, N. Bagatella-Flores

Facultad de Física e Inteligencia Artificial, Universidad Veracruzana

Our main motivation is a biological system made by the nucleosome, which is the smallest entity of the chromatine and consist in a DNA chain and the histone, being it a octamer proteins and a linker protein. The DNA chain attach the histone almost two turns, and then attach other histone.

In this work we want to investigate the equilibrium configuration and the statics and dynamic properties of complex made by a polymer chain with two spheres via Brownian Molecular Dynamics simulations. We are looking for the equilibrium configuration of the complex made by the chain and the two spheres in which its energy is minimized. We ask which equilibrium configuration is preffered, to be the two big spheres together or separated, together in the middle of the chain or in one end, which end. For other hand, since the length chain is longer than the persistence length of the chain, we expect to see big loops, from them we want to count its size and preffered position to appear. We expect to see small loops but they must desapear faster because they cost big energy.

For the dynamic properties we need to determine the mean square displacement of the center monomer attatched to each sphere, then it is possible determine the resulting diffusion coefficient of each central monomer as a function of friction coefficient, chain length, persistence length l_p and absortion energy k^a. From this information we can describe the motion mechanism of the chain, which could be any of two situations, sliding or reptating (attach or detach monomers).

36.- Statics and dynamics properties of a set of polymers

J.H. Zamora-Navarrete, N. Bagatella-Flores

Facultad de Física e Inteligencia Artificial, Universidad Veracruzana

Our main motivation is a biological system like DNA, which is a chain with negative charge polyelectrolyte. The human cell contains more than two meters of DNA packaged into the molecules of dimensions from 5 to 20 micrometers of diameter. Then the chromosomic molecules of DNA are thousand of times larger than the nuclear diameter, for that reason the DNA must be packaged in a very efficient way, in order to protect the genetic information, along the cellular cycle. In the present work, using Brownian Molecular Dynamics simulation we want to understand the static and dynamic properties of a set of short polymers. Their equilibrium configuration as a function of their persistence length, those must be toroidal, bundle or globular configuration, and should looks like DNA real configurations.

37.- Polymeric Phase Diagrams

N. Bagatella-Flores,^*,1 S.A. Orozco-Fuentes¹, Z. Dominguez²

¹Facultad de Física e Inteligencia Artificial, Universidad Veracruzana, Apartado Postal 475. Xalapa, Veracruz., MEXICO

²Unidad de Servicios de Apoyo en Resolucion Analitica, Universidad Veracruzana., Apartado Postal 575, Xalapa, Ver., MEXICO

We investigate the equilibrium configurations and the dynamic and static properties of a polymer chain via Brownian Molecular Dynamics simulations. We start by calculating the dynamics of the polymer in one and three dimensions. Specifically, we determine the mean square displacement of the center of mass and the resulting diffusion coefficient of the chain as a function of friction coefficient, chain length, and persistence length. We observe that the diffusion value for a chain with fixed number of monomers and friction coefficient is almost the same in one or three dimensions. Our results reproduce the Einstein relation. Since the polymer is at equilibrium configuration in which its energy is minimized, the chain moves as a whole object, and the position of the center of mass is almost invariant with respect to the positions of all the monomers of the chain. Thus, we do not observe any noticeable change in the diffusion coefficient as a function of the persistence length. We also establish the dependence of the equilibrium configuration with respect to the chain length and the persistence length. From the equilibrium configurations we extract the length and position distribution of thermally excited loop defects. Finally, a polymeric phase diagram is obtained for a polymer in three dimensions as a function of the chain length.

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