Poster 1 - Poster 9
Poster 10 - Poster 18
Poster 19 - Poster 26
Francisco López González; Ana María Herrera González; Fernando Donado Pérez
Instituto de Ciencias Basicas e Ingenieria de la Universidad Autonoma del Estado de Hidalgo-AACTyM;Instituto de Ciencias Basicas e Ingenieria de la Universidad Autonoma del Estado de Hidalgo-AACTyM;Instituto de Ciencias Basicas e Ingenieria de la Universidad Autonoma del Estado de Hidalgo-AAFyM
A bidimensional tilted, vibrated and sheared granular system is presented herein as a mechanism to simulate glass to crystal annealings. Sinusoidal vibratory waves, fixed in amplitude and frequency, supply a constant temperature. The particles are inclosed in a deformable boundary that provides one-dimensional shear through cyclic rhomboid deformations. The tilt provides a slightly attractive field that causes sedimentation. This kind of excitation drives the system, initially in random closed packed (RCP) state modeling an amorphous solid, into a mono crystal. Two type of granular particles are used: millimetric hard spheres and cubes. In the hard sphere, hexagonal order is reached whereas in the hard cube the tetraic one. We measured the temporal evolution of the sixth and fourth order by means of the sixth and fourth bond orientational order parameters ’6 and’4, respectively, and found order correlations with the amplitude, acceleration and shape of the shearing boundary.
Jose Enrique Robles-Soto (1), Monica Ledesma-Motolinia (2), Luis Rojas-Ochoa (3), Catalina Haro-Perez (4)
Departamento de Ciencias Básicas, UAM-Azcapotzalco (1, 2, 4); Departamento de Física, Cinvestav (3)
Nanogels based on dispersions of media-permeable particles of pNIPAM (poli-N-isopropyl-acrilamide) can be used as model for behavior prediction of similar materials. Rheologic performance of them depends on interaction potential, which is profoundly correlated with electrostatic potential of the particles as themselves, coming from both, permanent electrostatic groups present in polymeric chains as well as the counterions and coions inside and surrounding the particles since they are disolved in media and modify the apparent electrostatic charge density of particles. To study the effect that permanent electrostatic groups density has on interaction potential of particles and finally on collectivity behavior refflected on rheologic performance, set of particles were synthesized using different amounts of polimerization initiator sodium persulfate (KPS) and characterized using Dynamic Light Scattering, Static Light Scattering, Electrophoretic measurements and Conductimetric titrations to finally conduct rheological behavior measurements. Results show a decrease of hydrodynamic radii when higher dose level of KPS is used. Conductimetric titration was conducted to evaluate number of permanent electrostatic groups present in chains coming from each sulfate group that was used as chain initiator. Rheologic performance to be evaluated on further analysis.
H. Hernández-Saldaña
Universidad Autónoma Metropolitana at Azcapotzalco
Statistical properties of Mexican data bases of federal elections have been analyzed from a phenomenological point of view during at last three lustra. Several models for voters and elections inspired in statistical mechanics appeared in the last decades, included in the so called sociophysics. Unfortunately validation of models and enrichment of them using the Mexican Data is limited. Here we discuss briefly some of the efforts to use both models and data in the Mexican context. In particular, we analyze a model based in a modified Boltzmann equation on geographical distributions of electoral participation. The model has been discussed for a wide number of election in western democracies, including Mexico [1]. Here, we discuss some posible modifications based on a better understanding of the electoral data in Mexico [2] in order to introduce asymmetrical distributions for the solutions in the Boltzmann-like equation proposed in [1].
[1]C. Borghesi and J.-P. Bouchaud. Eur. Phys. J. B, 75 (2010) 395-404.
[2] H. Hernández-Saldaña. Front. App. Math. Stat. 7 (2021) 518371
H. Hernández-Saldaña
Universidad Autónoma Metropolitana at Azcapotzalco
The conditions that lead to thermalization processes in many-body quantum systems have long been studied and have received renewed interest in recent years. The role played by the eigenfunctions of the Hamiltonian operator of a closed system of anharmonic oscillators with chaotic classical analog is explored from the perspective of its semi-classical equivalent. This equivalent corresponds to the intersection of the energy shells of the Hamiltonian under consideration and the non-perturbed Hamiltonian in which the values of the eigenfunctions are calculated. As a measure of the thermalization of the system, the expected value of the quantum operator of the occupation number of the fermionic states is calculated and its decay rate is associated with the Boltzmann factor. The result is consistent with the semi-classical and near to the equipartition energy approach.
A. Escobar, F. Donado
Instituto de Ciencias Básicas e Ingeniería de la Universidad Autónoma del Estado de Hidalgo-AAMF, Pachuca 42184, Pachuca, México
This work studies the crystallization process in a two-dimensional system of magnetic particles placed on a concave surface under an oscillating magnetic field. The time-dependent field fluidizes particles, and its amplitude controls effective temperature. The system exhibits a gas-like behavior when the effective temperature is high. By decreasing the effective temperature, the particles' dynamics become lower until they reach an arrested configuration. Previously, we have shown that when the temperature drops slowly in an almost linear cooling, the particles acquire a crystalline arrangement. We studied at particle detail level the nucleus's birth and growth. This work focuses on finding the optimal conditions to crystallize the system more quickly. For this, we substituted the linear cooling route with a staggered one, with decreases in temperature in giant steps. In each step, the temperature was kept constant for a particular time. We determine the minimum time for each temperature stage to allow particles to find their energy minimum configuration. We found that crystallization time was notably reduced when we used this method.
Fernando Donado Pérez, María de los Ángeles Escobar López
Universidad Autónoma del Estado de Hidalgo
We study the crystallization process in a 2D-dimensional magnetic granular system based on millimetric steel beads [1]. Particles are on a concave surface and under a sinusoidal magnetic field. Random particle motions are driven by the magnetic field, showing some similarities with the motions of atoms and molecules in a glass or a crystal-forming fluid. The effective temperature decreases when decreasing the magnetic field, and diffusive particle motion slows until it ceases. For slow cooling rates, we observe crystallization, where the particles organize into a hexagonal lattice. We study the crystalline nucleus's birth and the crystal's subsequent growth at a particle detail level. Our observations support non-classical theories of crystal formation. Initially, a dense amorphous aggregate of particles forms, and then in a second stage, this aggregate rearranges internally to form the crystalline nucleus. As the aggregate grows, the crystal grows in its interior. After a certain size, all the aggregated particles are part of the crystal, and after that, crystal growth follows the classical theory for crystal growth.
[1] Direct observation of crystal nucleation and growth in a quasi-two-dimensional nonvibrating granular system, Escobar, F. Donado, R. E. Moctezuma, and Eric R. Weeks, Rev. E 104, 044904 (2021)
Jaime Martínez-Rivera and Ramón Castañeda-Priego
División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato. Loma del Bosque 103, Colonia Lomas del Campestre, 37150 León, Guanajuato, México.
In recent years, much effort has been done to understand the physical mechanisms that lead to colloidal gelation. Some groups claim that the frustration of the spinodal decomposition might be understood as a kind of universal route for the formation of colloidal gels in short-ranged attractive colloids [1]. However, recent experimental evidence [2] pointed out that such route may be a consequence of the competition between gravitational forces and the attractive ones between colloidal particles. Furthermore, it was found that there is a critical and effective gravitational Péclet number that clearly indicates the onset of phase separation-induced gelation. Nevertheless, this important observation has not been studied in detail at the molecular level. Then, to have a better understanding of the gravitational effects on the formation of colloidal gels, in this contribution, we have performed extensive Monte Carlo computer simulations of sticky particles under the influence of a gravitational field. The Asakura-Oosawa potential, which describes the depletion-induced attraction between colloids immersed in a bath of non-adsorbing polymers, was used to model the forces between colloidal particles [3]. We systematically analyze the effects that gravity has on the percolation, the cluster size distribution and the fractal dimension of the resulting aggregates. From this analysis and from the determination of those states where the critical gravitational Péclet number occurs, we have built a state diagram in terms of the strength of the attractive forces and the bare Péclet number. We thus report the boundary where the onset of gelation might be associated to gravity.
Keywords: Gelation, Péclet number, colloidal dispersions.
[1] P. J. Lu, E. Zaccarelli, F. Ciulla, A. B. Schofield, F. Sciortino and D. A. Weitz. Nature, 453, 449 (2008).
[2] J. M. Kim, J. Fang, A. P. R. Eberle, R. Castañeda-Priego and N. J. Wagner. Phys. Rev. Lett., 110, 208302 (2013).
[3] J. K. Whitmer and E. Luijten. J. Chem. Phys., 134, 034510 (2011).
Sol María Hernández Hernández, Norma Palmero-Cruz and Erick Sarmiento Gómez
Benemérita Universidad Autónoma de Puebla, Universidad de Guanajuato and Universidad de Guanajuato
The purpose of the current study is to model the dynamics of tracer brownian particles in complex fluids, such as interpenetrating polymer network hydrogels and wormlike micelles, using random walkers confined in a two-dimensional box of several sizes. The ensemble of different sizes was established using right skewed distribution and the mobility of the walkers was limited by confinement conditions in the walls of the boxes. We found that the width of the distribution of cage sizes produces a smooth transition between the dynamical regimes usually found in confined brownian particles. This effect has been reported in microrheological experiments, and our results give an insight of its origin, finding that the distribution of cages for a wide distribution resembles the experimental distribution of mesh sizes.
Kevin R. Arriola-González, Alejandro Gil-Villegas, Susana Figueroa-Gerstenmaier
Division of Sciences and Engineering, University of Guanajuato, León, Mexico
Syndiotactic polystyrene is a semicrystalline stereoregular polymer (30-50% degree of crystallinity) which is easily crystallizable with high melting point presenting a very complex polymorphic behavior. There are two semicrystalline phases with trans-planar chains (α and β) and three with helical s(2/1)2 chains (γ, δ, and ε). Two of the helical semicrystalline phases (δ and ε) present nanopores, being able to absorb, even from diluted solutions, low-molecular-mass guest molecules in cavities of their structures, eventually leading to the formation of host-guest semicrystalline phases. Due to their flexible nature, these cavities (δ phase) and channels (ε phase) are modified, in such a way, the structure better fits the guest molecules. The δ phase presents two identical cavities and eight styrene monomeric units per unit cell, while the ε phase, with 4 chains per unitary cell, exhibits channels parallel to the chain axes. The nanoporous semicrystalline phase δ has been extensively investigated but the ε phase is still almost unexplored. In this work, we present results using a geometrical method to obtain the size and shape of the channels inside the material in terms of the size of guest molecules for the semicrystalline ε phase. Diffusion behavior of light guest molecules inside of the matrix was also analyzed using molecular dynamics.
Roger Iván Ramírez Kantun, Gabriel Guillermo Pérez Ángel
CINVESTAV Unidad Mérida
Colloidal systems have a broad spectrum of technological applications, thus understanding the different dynamical processes that occur in this kind of systems, especially close to the glass transition, is a fundamental and open task. The glass transition occurs when the system is cooled or compressed fast enough to avoid the crystallization, i.e., the system is not allowed to get to an equilibrium state. For the last years there has been a big number of publications using computational methods like Molecular Dynamics and Dynamic Monte Carlo (DMC) to study in detail the glass-forming systems under certain thermodynamic conditions.
In this work we show our first results obtained from computational simulations of a monodisperse patchy colloid system, consisting in 8192 particles whose interactions are short ranged and depend on the relative orientation between the patches on their surfaces. The calculations are Monte Carlo on it's Dynamic variant and the codes are written in the C language. The radial distribution function g(r) plots, the energy per particle and the mean squared displacement (MSD) curves for the rotational and translational movements, are discussed. All of these results showed correspond to a packing fraction of Ф = 0.45 and temperature of T = 0.02, and they allow us to determine whether if the dynamical arrest is present in the system or not. Finally, the rescaled MSD plots give us well defined time scales for the dynamical arrest, something that in principle is only possible with Molecular or Brownian Dynamics.
José Luis Godínez Pastor; Minerva González Melchor
Instituto de Física, Benemérita Universidad Autónoma de Puebla
Since the discovery of fullerenes in 1985, there have been studies under different conditions and the use of these molecules as lubricants has been proposed, given their composition and their approximately spherical shape, in photolithography due to the optical properties they present and the response under the action of ultraviolet light, while in biomedicine their use to scavenge radical and antioxidant, can be used to cleave DNA. For biomedical applications it is of fundamental interest to know the behavior of fullerenes in aqueous medium and therefore it is relevant to determine thermodynamic and transport properties of fullerenes in liquid phase and in phase coexistence. In this work we study the liquid phase and the liquid-vapor coexistence of the fullerene/water mixture considering the concentrations of 0.0378, 0.3065, 0.6948 mol/kg. In the liquid phase, we determine the radial distribution function that provides information on the average structure and distribution of the molecules, in addition to the equation of state at high pressures and 373 K. Additionally, we study the liquid-vapor coexistence curve and the associated surface tension to this interface.
Norma Caridad Palmero Cruz, Beatriz Morales Cruzado, Ramón Castañeda Priego, Erick Sarmiento Gómez
Division of Sciences and Engineering, University of Guanajuato, Mexico 2 Faculty of Engineering, University of San Luis Potosi, Mexico
In this work we report experimental results corresponding to a direct measurement of hydrodynamic interactions of two microscopic Brownian particles separated a given distance and trapped in optical tweezers. Using the positions of the two beads, we computed the cross-correlation function of displacements for different laser powers. The experimental results were compared with a theoretical model, finding a good agreement with our experiments.
Mónica Ledesma Motolinía, Fernando Donado Pérez, José Luis Carrillo Estrada
Instituto de Física "Ing. Luis Rivera Terrazas" de la Benemérita Universidad Autónoma de Puebla, Instituto de Ciencias Básicas e Ingeniería de la Universidad Autónoma del Estado de Hidalgo-AACTyM, Instituto de Física "Ing. Luis Rivera Terrazas" de la Benemérita Universidad Autónoma de Puebla
A methodical study of the dynamics and order parameters as a function of effective temperature was carried out for a 2D nonvibrating magnetic granular system to analyze the aggregate formation process. Specifically, the degree of order and growth of the aggregates formed as a function of time and effective temperature were studied. The system used has the particularity that the effective temperature is proportional to the amplitude of the applied magnetic field. The order parameters used are sensitive to the detection of small aggregates. The results on the dynamics of the system indicate that there are three distinct regions in the effective temperature: low, medium, and high. Structures formed in the medium temperature region have the highest degree order.
Néstor M. de los Santos-López, Gabriel Pérez-Ángel, Ramón Castaneda-Priego, José M. Méndez-Alcaraz
Departamento de Física Aplicada, Cinvestav-Mérida; División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato; Departamento de Física, Cinvestav-Zacatenco.
In this work, we present a theoretical study of the depletion forces in three-dimensional binary and ternary mixtures, in which we have one depleted species with one or two depletor species. For this, we introduce a general physical formalism that allows us to uniquely obtain the effective interactions by a process of contraction of the nude forces, even in highly concentrated systems. Such a formalism we tested by studying the depletion forces in mixtures with a total packing fraction up to 55%. With our result we can say that it is possible to find an efficient way to determine the effective interactions at finite concentrations, having a useful tool even in thermodynamic conditions near to non-equilibrium states.
Javier A. S. Gallegos, Román Perdomo-Pérez, Néstor Enrique Valadez-Pérez, Ramón Castañeda-Priego
División de Ciencias e Ingenierías, Universidad de Guanajuato
By means of Monte Carlo computer simulations, we studythe structure and the coordination number in colloidal dis-persions composed of particles interacting with the Kern-Frenkel interaction potential. We mainly focus on the mech-anisms of gelation in patchy colloidal systems and, in par-ticular, we study the relationship between physical gelationand rigidity percolation, which here is assumed to occurwhen the coordination number takes the value〈nb〉= 2.4.
Juan Donaldo Dueñas Pérez, Gustavo Basurto-Islas and Susana Figueroa-Gerstenmaier
División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, León, Gto. México.
Alzheimer’s disease is the most common and fatal form of dementia, characterized by the aggregation and deposition of Amyloid-Beta(Aβ) oligomers in the brain of patients. There exists two main Aβ variants; Aβ1-42 and Aβ1-40 which constitute Aβplaques and fibrils generated as a result from it’s the aggregation process. Nevertheless, recent studies have demonstrated that a subset of different N-truncated variants (Aβ2-42, AβpE3–42, Aβ4-42, Aβ-5-42 and Aβ11-42)could present a greater aggregative propensity hence producing more deleterious effects in the nervous system. The experimentalattempts to identify and describe the underlying mechanism by which these new variants misfold and ensemble to form oligomers and fibrils are not conclusive. There are inherent limitations to what can be established based on observational data. It is challenging to relatemacroscopic experimental findings to nanoscale molecular events, given the intrinsic disorderly nature ofAβ peptides and the difference in timescales between empirical relevant milliseconds and molecular conformational changes in nanoseconds. Within this context, computational approaches such as Molecular Dynamics Simulations (MD) represent a powerful tool to connect these two approaches. In the present work we currently study the process of oligomer formation of AβX-42 (X = 2, pE3, 4, 5 and 11)in water and under physiological conditions using MD. Our objective therefore is to identify the conformational dynamics of these variants while the aggregation process occurs.
Viridiana Ramírez Carpio, Alejandro Gil-Villegas Montiel, Amparo Galindo
División de Ciencias e Ingenierías, Campus León. Universidad de Guanajuato. División de Ciencias e Ingenierías, Campus León. Universidad de Guanajuato. Department of Chemical Engineering, Faculty of Engineering, Imperial College London.
We present a study of the solid-fluid phase equilibrium of fully flexible linear Lennard-Jones chains to reproduce the global phase diagram of a set of n-alkanes, based on the extension of Wertheim’s first order thermodynamic perturbation theory (TPT1) to study solid-liquid coexistence, developed by Vega et al.[C. Vega , J. Chem. Phys. 116, 17 (2002)]. In the original treatment of this system, the number of segments m of the chain molecule is taken with the same value in the solid and liquid phases. In this work we present an alternative approach, where the chain molecules in the solid phase have an effective temperature-dependent parameter m, whereas in the liquid phase this quantity is constant. The former parameter was determined through a minimization between theoretical and liquid-solid experimental data. The liquid phase parameter mf and the LJ monomer potential parameters σ and ε were obtained from reported values in the literature. Vapor-liquid, solid-liquid and solid-vapor equilibrium are predicted accurately, including the location of the triple point.
Daniela Cywiak, Alejandro Gil-Villegas and Alessandro Patti
Universidad de Guanajuato, Universidad de Guanajuato and University of Manchester
Understanding the relaxation dynamics of colloidal suspensions is crucial to identify the elements that influence the mobility of their constituents, assess their macroscopic response across the relevant time and length scales, and thus disclose the fundamentals underpinning their exploitation in formulation engineering. In this work, we specifically assess the impact of long-ranged ordering on the relaxation dynamics of suspensions of soft-repulsive rod-like particles, which are able to self-organise into nematic and smectic liquid-crystalline phases. By performing Dynamic Monte Carlo simulations, we analyse the effect of translational and orientational order on the diffusion of the rods along the relevant directions imposed by the morphology of the background phases. To provide a clear picture of the resulting dynamics, we assess their dependence on temperature, which can dramatically determine the response time of the system relaxation and the self-diffusion coefficients of the rods. The computation of the van Hove correlation functions allows us to identify the existence of rods that diffuse significantly faster than the average and whose concentration can be accurately adjusted by a suitable choice of temperature.
Jason Peña, Leonardo Dagdug
Universidad Autónoma Metropolitana CDMX, México, Universidad Autónoma Metropolitana CDMX México/National Institutes of Health Shriver National Institute of Child Health and Human Development Bethesda, MD 20892, U.S
Models of molecules transport through diffusion offer an important insight into the description of microscopic phenomena in nature. In the research, we focused on some models of chemoreception, from the perfect spherical absorbent, the use of Weber’s disk, and the development of Berg and Purcell approach, to Zwanzig and Szabo generalized solution where interference effect and partially absorbing receptors are considered. Afterwards, we extrapolate Dudko’s solution using a dimensional comparison for rate constant diffusion to receptors of arbitrary shape on a spherical cell, and contrast the absorption effectiveness on circular and elliptical chemoreceptors, using as reference the perfect spherical absorbent. During this process we looked to an important property related with the structure of chemoreceptors, their geometry. Is there a preferential setting that allows more particles to be absorbed in an ever smaller area? We found that the elliptical geometry offers a plausible model in cellular anatomy, a result that could explain the structure variation on chemoreceptors and the observed physiological changes on cells.
Ivan Pompa-García / Leonardo Dagdug
Universidad Autónoma Metropolitana - Iztapalapa. Ciudad de México, México / Universidad Autónoma Metropolitana - Iztapalapa. Ciudad de México, México, National Institutes of Health, Shriver National Institute of Child Health and Human Development. MD, U.S.
Using the projection method by Kalinay and Percus [J. Chem. Phys. 122, 204701 (2005)], we derive an effective diffusion coefficient for narrow channels that generalizes previously reported results. This is, a position-dependant diffusion coefficient for two-dimensional asymmetric channels under a transverse gravitational external field is obtained. The main result contains the well-known previous results for symmetric channels with external gravitational force presented by Kalinay [Phys. Rev. E 84, 011118 (2011)], as well as asymmetrical cases where the transverse field goes to zero. We also found a coefficient that can be be approximately written as an interpolation formula as proposed initially by Reguera and Rubi [Phys. Rev. E 64, 061106 (2001)], and could be used to recover preceding results as well. Finally, an excellent agreement of found equations with Brownian dynamics simulations is shown.
David Hernández León, Dr. Pablo Padilla Longoria, Dr. Leonardo Dagdug Lima
UAM-I, UNAM, UAM-I
The current COVID-19 pandemic has motivated the development of epidemiological models that are able to effectively describe the dynamics of an infectious disease, as well as to assist in decision-making for the implementation of public health policies. This paper shows the dynamics that follow an infectious disease when implementing in the population two containment measures: social distancing and optimal control of vaccination. In addition, given the difficulty that exists on the part of the authorities in implementing the containment measures since the beginning of an epidemic outbreak, the effect on the dynamics of the infection of the introduction of these measures at different times from the initial one is analyzed. To this end we focus on a SEIR model, using the optimal control theory, an optimization problem arises, whose objective is to determine the percentage of susceptible individuals that must be vaccinated in order to obtain the maximum number of the recovered population, while minimizing both the susceptible and infected population and the costs associated with vaccination campaigns. The results show a marked reduction in the exposed and infected population, as well as a temporary displacement of the peak of infected individuals, results that directly benefit a country’s public health infrastructure.
Luciano Robert-Jimenez (a), Gustavo Basurto-Islas (b), Susana Figueroa-Gerstenmaier (b), Salvador Herrera-Velarde (a)
(a) Subdirección de Posgrado e Investigación, Tecnológico Nacional de México / Instituto Tecnológico Superior de Xalapa, Xalapa, Ver., México. (b) División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, León, Gto. México.
Currently in the world there are about 50 million people with Alzheimer's disease (AD), this is the most common form of dementia and there is no cure. In AD, tau protein is altered, promoting its polymerization forming fibrils and neurofibrillary tangles, leading to the onset of the disease. The few and no satisfactory treatments have conducted to the scientific community to focus their efforts on the study and analysis of tau, however, tau is an intrinsically disordered protein, making its experimental characterization a challenge. One technique that has been proven effective to study this kind of protein is molecular dynamics. Nevertheless, modeling large biomolecular systems is a difficult task because of the high computational cost required, especially when using all-atom force fields. To identify the molecular mechanism of the tau assembly, we characterize the interaction and conformational changes of two full-length tau monomers in an explicit aqueous solution with ions using the coarse-grained force field: SIRAH. Two systems were built: the first, two tau proteins in water solution and the second, two tau proteins in water and ions solution. We performed simulations until we reached a trajectory for around 1 μs each. According to the available experimental data our results showed that the coarse-grained model predicts the performance of a disordered protein with no evidence of aggregation under these conditions. The analysis of the obtained trajectory contributes to understand the experimental results, and promote a better comprehension of the conformational space and interaction of two tau proteins.
Aramis de Icaza Astiz and Atahualpa S. Kraemer
Physics department, Faculty of Science, Universidad Nacional Autónoma de México
We introduce the concept of dynamic neighbors. This concept in turn serves to define an order parameter with which phase transitions and jamming can be detected in fluids of hard-spheres, without taking into account orientational or translational symmetry. It also gives a method to estimate the entropy of the system. Using molecular dynamics simulations we measure the number of dynamic neighbors. With this it is possible to detect three phases in $2$-dimensional system and two phases in the $3$-dimensional version. In the hard disk system these regions correspond to the fluid, hexatic and solid phases, while in the $3$-dimensional case they correspond to the solid and fluid phase. We observe continuous transition in the $2$-dimensional system, and a first order transition in the $3$-dimensional case. We also observe only two ``states'' in the case of binary mixtures and for hard-spheres with a fast compression speed. These two states correspond to fluid and jammed states.
Román Perdomo-Pérez, Ramón Castañeda-Priego
División de Ciencias e Ingenierías, Universidad de Guanajuato
The dynamical properties of particles in porous materials are affected by the complex morphology of the confinement and the distribution of the accessible volume leading to anomalous diffusion, ⟨∆r² (t)⟩ ∝ t^α. Recently, many efforts have been made in order to relate the anomalous diffusion with the fractal dimension of the porous matrix. In this context, we investigate the diffusion of a tracer particle of diameter σ immersed in a fractal porous environment by using Brownian dynamics simulations. The fractal matrix is made up by an array of percolating clusters with a well defined and controlled fractal dimension Df and a specific correlation length ξ. Our findings show that tracers exhibit anomalous diffusion at ⟨∆r²(t)⟩ < ξ²/6 and becomes diffusive (α = 1) when ⟨∆r² (t)⟩ > ξ²/6 . Later we show that increasing the diameter of the tracer particle the effect of the fractal dimension remains in the range of ξ/σ corroborating the concept of self-similarity typical of fractal-like structures.
J.A. SANTIAGO
Universidad Autónoma Metropolitana Cuajimalpa
The mechanical effects of membrane compositional inhomogeneities are analyzed in a process of vesicle shape transformation analogous to the discocyte-to-stomatocyte transformation of red blood cells. We cast on the Canham-Helfrich model of fluid membranes with both the spontaneous curvature and the surface tension being non-homogeneous functions along the cell membrane. In this work, the inhomogeneous distribution are determined by the equilibrium mechanical equations as the driving force the process of vesicle shape transformations from the symmetric discocyte to the stomatocyte configuration with a broken symmetry. The generalized concept of inhomogeneous membrane elasticity is proposed as a basic organization principle for the shape regulation of asymmetric vesicle organelles in real cells.