arXiv subjects

R. L. C. Vink

Publications and source records attributed to R. L. C. Vink.

At least 19 recordsLinked to original sources

arXiv2023

Dissipation in solids under oscillatory shear: Role of damping scheme and sample thickness

We study dissipation as a function of sample thickness in solids under global oscillatory shear applied to the top layer of the sample. Two types of damping mechanism are considered: Langevin and Dissipative Particle Dynamics (DPD). In the regime of low driving frequency, and under strain-controlled conditions, we observe that for Langevin damping, dissipation increases with sample thickness, while for DPD damping, it decreases. Under force-controlled conditions, dissipation increases with sample thickness for both damping schemes. These results can be physically understood by treating the solid as a one-dimensional harmonic chain in the quasi-static limit, for which explicit equations (scaling relations) describing dissipation as a function of chain length (sample thickness) are provided. The consequences of these results, in particular regarding the choice of damping scheme in computer simulations, are discussed.

cond-mat.mtrl-sci↗

arXiv2020

Friction on incommensurate substrates: Role of anharmonicity and defects

We present Molecular Dynamics simulations of one- and two-dimensional bead-spring models sliding on incommensurate substrates. We investigate how sliding friction is affected by interaction anharmonicity and structural defects. In their absence, we confirm earlier findings, namely, that at special resonance sliding velocities, friction is maximal. When sliding off-resonance, partially thermalized states are possible, whereby only a small number of vibrational modes becomes excited, but whose kinetic energies are already Maxwell-Boltzmann distributed. Anharmonicity and defects typically destroy partial thermalization, and instead lead to full thermalization, implying much higher friction. For sliders with periodic boundaries, thermalization begins with vibrational modes whose spatial modulation is compatible with the incommensurate lattice. For a disc-shaped slider, modes corresponding to modulations compatible with the slider radius are initially the most dominant. By tuning the mechanical properties of the slider's edge, this effect can be controlled, resulting in significant changes in the sliding distance covered.

cond-mat.mtrl-sci↗

arXiv2012

The main transition in the Pink membrane model: finite-size scaling and the influence of surface roughness

We consider the main transition in single-component membranes using computer simulations of the Pink model [D. Pink {\it et al.}, Biochemistry {\bf 19}, 349 (1980)]. We first show that the accepted parameters of the Pink model yield a main transition temperature that is systematically below experimental values. This resolves an issue that was first pointed out by Corvera and co-workers [Phys. Rev. E {\bf 47}, 696 (1993)]. In order to yield the correct transition temperature, the strength of the van der Waals coupling in the Pink model must be increased; by using finite-size scaling, a set of optimal values is proposed. We also provide finite-size scaling evidence that the Pink model belongs to the universality class of the two-dimensional Ising model. This finding holds irrespective of the number of conformational states. Finally, we address the main transition in the presence of quenched disorder, which may arise in situations where the membrane is deposited on a rough support. In this case, we observe a stable multi-domain structure of gel and fluid domains, and the absence of a sharp transition in the thermodynamic limit.

cond-mat.soft↗

arXiv2010

Domain formation in membranes with quenched protein obstacles: Lateral heterogeneity and the connection to universality classes

We show that lateral fluidity in membranes containing quenched protein obstacles belongs to the universality class of the two-dimensional random-field Ising model. The main feature of this class is the absence of a phase transition: there is no critical point, and macroscopic domain formation does not occur. Instead, there is only one phase. This phase is highly heterogeneous, with a structure consisting of micro-domains. The presence of quenched protein obstacles thus provides a mechanism to stabilize lipid rafts in equilibrium. Crucial for two-dimensional random-field Ising universality is that the obstacles are randomly distributed, and have a preferred affinity to one of the lipid species. When these conditions are not met, standard Ising or diluted Ising universality apply. In these cases, a critical point does exist, marking the onset toward macroscopic demixing.

cond-mat.soft↗

arXiv2010

Fluids with quenched disorder: Scaling of the free energy barrier near critical points

In the context of Monte Carlo simulations, the analysis of the probability distribution $P_L(m)$ of the order parameter $m$, as obtained in simulation boxes of finite linear extension $L$, allows for an easy estimation of the location of the critical point and the critical exponents. For Ising-like systems without quenched disorder, $P_L(m)$ becomes scale invariant at the critical point, where it assumes a characteristic bimodal shape featuring two overlapping peaks. In particular, the ratio between the value of $P_L(m)$ at the peaks ($P_{L, max}$) and the value at the minimum in-between ($P_{L, min}$) becomes $L$-independent at criticality. However, for Ising-like systems with quenched random fields, we argue that instead $ΔF_L := \ln (P_{L, max} / P_{L, min}) \propto L^θ$ should be observed, where $θ>0$ is the "violation of hyperscaling" exponent. Since $θ$ is substantially non-zero, the scaling of $ΔF_L$ with system size should be easily detectable in simulations. For two fluid models with quenched disorder, $ΔF_L$ versus $L$ was measured, and the expected scaling was confirmed. This provides further evidence that fluids with quenched disorder belong to the universality class of the random-field Ising model.

cond-mat.soft↗

arXiv2010

Nematics with quenched disorder : violation of self-averaging

We consider the isotropic-to-nematic transition in liquid crystals confined to aerogel hosts, and assume that the aerogel acts as a random field. We generally find that self-averaging is violated. For a bulk transition that is weakly first-order, the violation of self-averaging is so severe, even the correlation length becomes non-self-averaging: no phase transition remains in this case. For a bulk transition that is more strongly first-order, the violation of self-averaging is milder, and a phase transition is observed.

cond-mat.stat-mech↗

arXiv2010

Finite size scaling in Ising-like systems with quenched random fields: Evidence of hyperscaling violation

In systems belonging to the universality class of the random field Ising model, the standard hyperscaling relation between critical exponents does not hold, but is replaced by a modified hyperscaling relation. As a result, standard formulations of finite size scaling near critical points break down. In this work, the consequences of modified hyperscaling are analyzed in detail. The most striking outcome is that the free energy cost ΔF of interface formation at the critical point is no longer a universal constant, but instead increases as a power law with system size, ΔF proportional to $L^θ$, with $θ$ the violation of hyperscaling critical exponent, and L the linear extension of the system. This modified behavior facilitates a number of new numerical approaches that can be used to locate critical points in random field systems from finite size simulation data. We test and confirm the new approaches on two random field systems in three dimensions, namely the random field Ising model, and the demixing transition in the Widom-Rowlinson fluid with quenched obstacles.

cond-mat.stat-mech↗

arXiv2010

The isotropic-to-nematic transition in confined liquid crystals : an essentially non-universal phenomenon

Computer simulations are presented of the isotropic-to-nematic transition in a liquid crystal confined between two parallel plates a distance H apart. The plates are neutral and do not impose any anchoring on the particles. Depending on the shape of the pair potential acting between the particles, we find that the transition either changes from first-order to continuous at a critical film thickness H=Hx, or that the transition remains first-order irrespective of H. This demonstrates that the isotropic-to-nematic transition in confined geometry is not characterized by any universality class, but rather that its fate is determined by microscopic details. The resulting capillary phase diagrams can thus assume two topologies: one where the isotropic and nematic branches of the binodal meet at H=Hx, and one where they remain separated. For values of H where the transition is strongly first-order the shift DT of the transition temperature is in excellent agreement with the Kelvin equation. Not only is the relation DT~1/H recovered but also the prefactor of the shift is in quantitative agreement with the independently measured bulk latent heat and interfacial tension.

cond-mat.stat-mech↗

arXiv2009

The Widom-Rowlinson mixture on a sphere: Elimination of exponential slowing down at first-order phase transitions

Computer simulations of first-order phase transitions using standard toroidal boundary conditions are generally hampered by exponential slowing down. This is partly due to interface formation, and partly due to shape transitions. The latter occur when droplets become large such that they self-interact through the periodic boundaries. On a spherical simulation topology, however, shape transitions are absent. By using an appropriate bias function, we expect that exponential slowing down can be largely eliminated. In this work, these ideas are applied to the two-dimensional Widom-Rowlinson mixture confined to the surface of a sphere. Indeed, on the sphere, we find that the number of Monte Carlo steps needed to sample a first-order phase transition does not increase exponentially with system size, but rather as a power law $τ\propto V^α$, with $α\approx 2.5$, and $V$ the system area. This is remarkably close to a random walk for which $α$ equals 2. The benefit of this improved scaling behavior for biased sampling methods, such as the Wang-Landau algorithm, is investigated in detail.

cond-mat.soft↗

arXiv2009

The isotropic-to-nematic transition in a two-dimensional fluid of hard needles : a finite-size scaling study

The isotropic-to-nematic transition in a two-dimensional fluid of hard needles is studied using grand canonical Monte Carlo simulations, multiple histogram reweighting, and finite size scaling. The transition is shown to be of the Kosterlitz-Thouless type, via a direct measurement of the critical exponents eta and beta, of the susceptibility and order parameter, respectively. At the transition, eta=1/4 and beta=1/8 are observed, in excellent agreement with Kosterlitz-Thouless theory. Also the shift in the chemical potential of the nematic susceptibility maximum with system size is in good agreement with theoretical expectations. Some evidence of singular behavior in the density fluctuations is observed, but no divergence, consistent with a negative specific heat critical exponent. At the transition, a scaling analysis assuming a conventional critical point also gives reasonable results. However, the apparent critical exponent beta_eff obtained in this case is not consistent with theoretical predictions.

cond-mat.stat-mech↗

arXiv2009

Finite-size effects at first-order isotropic-to-nematic transitions

We present simulation data of first-order isotropic-to-nematic transitions in lattice models of liquid crystals and locate the thermodynamic limit inverse transition temperature $ε_\infty$ via finite-size scaling. We observe that the inverse temperature of the specific heat maximum can be consistently extrapolated to $ε_\infty$ assuming the usual $α/ L^d$ dependence, with $L$ the system size, $d$ the lattice dimension and proportionality constant $α$. We also investigate the quantity $ε_{L,k}$, the finite-size inverse temperature where $k$ is the ratio of weights of the isotropic to nematic phase. For an optimal value $k = k_{\rm opt}$, $ε_{L,k}$ versus $L$ converges to $ε_\infty$ much faster than $α/L^d$, providing an economic alternative to locate the transition. Moreover, we find that $α\sim \ln k_{\rm opt} / {\cal L}_\infty$, with ${\cal L}_\infty$ the latent heat density. This suggests that liquid crystals at first-order IN transitions scale approximately as $q$-state Potts models with $q \sim k_{\rm opt}$.

cond-mat.stat-mech↗

arXiv2009

Restricted orientation "liquid crystal" in two dimensions: Isotropic-nematic transition or liquid-gas (?)

We present Monte Carlo simulation results of the two-dimensional Zwanzig fluid, which consists of hard line segments which may orient either horizontally or vertically. At a certain critical fugacity, we observe a phase transition with a two-dimensional Ising critical point. Above the transition point, the system is in an ordered state, with the majority of particles being either horizontally or vertically aligned. In contrast to previous work, we identify the transition as being of the liquid-gas type, as opposed to isotropic-to-nematic. This interpretation naturally accounts for the observed Ising critical behavior. Furthermore, when the Zwanzig fluid is extended to more allowed particle orientations, we argue that in some cases the symmetry of a q-state Potts model with q>2 arises. This observation is used to interpret a number of previous results.

cond-mat.stat-mech↗

arXiv2008

Structure and phase equilibria of the Widom-Rowlinson model

The Widom-Rowlinson model plays an important role in the statistical mechanics of second order phase transitions and yet there currently exists no theoretical approach capable of accurately predicting both the microscopic structure and phase equilibria. We address this issue using computer simulation, density functional theory and integral equation theory. A detailed study of the pair correlation functions obtained from computer simulation motivates a closure of the Ornstein-Zernike equations which gives a good description of the pair structure and locates the critical point to an accuracy of 2 percent.

cond-mat.soft↗

arXiv2008

Colloid-polymer mixtures in random porous media: Finite size scaling and connected versus disconnected susceptibilities

As a generic model for liquid-vapour type transitions in random porous media, the Asakura-Oosawa model for colloid-polymer mixtures is studied in a matrix of quenched spheres using extensive Monte Carlo (MC) simulations. Since such systems at criticality, as well as in the two-phase region, exhibit lack of self-averaging, the analysis of MC data via finite size scaling requires special care. After presenting the necessary theoretical background and the resulting subtleties of finite size scaling in random-field Ising-type systems, we present data on the order parameter distribution (and its moments) as a function of colloid and polymer fugacities for a broad range of system sizes, and for many (thousands) realizations of the porous medium. Special attention is paid to the connected and disconnected susceptibilities, and their respective critical behavior. We show that both susceptibilities diverge at the critical point, and we demonstrate that this is compatible with the predicted scenario of random-field Ising universality.

cond-mat.soft↗

arXiv2007

First-order phase transitions in two-dimensional off-lattice liquid crystals

We consider an off-lattice liquid crystal pair potential in strictly two dimensions. The potential is purely repulsive and short-ranged. Nevertheless, by means of a single parameter in the potential, the system is shown to undergo a first-order phase transition. The transition is studied using mean-field density functional theory, and shown to be of the isotropic-to-nematic kind. In addition, the theory predicts a large density gap between the two coexisting phases. The first-order nature of the transition is confirmed using computer simulation and finite-size scaling. Also presented is an analysis of the interface between the coexisting domains, including estimates of the line tension, as well as an investigation of anchoring effects.

cond-mat.soft↗

arXiv2007

Anchoring effects at the isotropic-nematic interface in liquid crystals

The isotropic-to-nematic transition in liquid crystals is studied in d=3 spatial dimensions. A simulation method is proposed to measure the angle dependent interfacial tension g(theta), with theta the anchoring angle of the nematic phase at the interface. In addition, an alternative liquid crystal model is introduced, defined on a lattice. The advantage of the lattice model is that accurate simulations of anchoring effects become possible. For the lattice model, g(theta) depends sensitively on the nearest-neighbor pair interaction, and both stable and metastable anchoring angles can be detected. We also measure g(theta) for an off-lattice fluid of soft rods. For soft rods, only one stable anchoring angle is found, corresponding to homogeneous alignment of the nematic director in the plane of the interface. This finding is in agreement with most theoretical predictions obtained for hard rods.

cond-mat.soft↗

arXiv2007

Liquid crystals in two dimensions: First-order phase transitions and nonuniversal critical behavior

Liquid crystals in two dimensions undergo a first-order isotropic-to-quasi-nematic transition, provided the particle interactions are sufficiently ``sharp and narrow''. This implies phase coexistence between isotropic and quasi-nematic domains, separated by interfaces. The corresponding line tension is determined, and shown to be very small, giving rise to strong interface fluctuations. When the interactions are no longer ``sharp and narrow'', the transition becomes continuous, with non-universal critical behavior obeying hyperscaling, and approximately resembling the two-dimensional Potts model.

cond-mat.stat-mech↗

arXiv2006

Critical behavior of colloid-polymer mixtures in random porous media

We show that the critical behavior of a colloid-polymer mixture inside a random porous matrix of quenched hard spheres belongs to the universality class of the random-field Ising model. We also demonstrate that random-field effects in colloid-polymer mixtures are surprisingly strong. This makes these systems attractive candidates to study random-field behavior experimentally.

cond-mat.soft↗