[Show abstract][Hide abstract] ABSTRACT: Auto-correlation functions in an equilibrium stochastic process are well-characterized by Bochnerʼs theorem as Fourier transforms of a finite symmetric Borel measure. The existence of a long-time limit of these correlation functions depends on the spectral properties of the measure. Here we provide conditions applicable to a wide class of dynamical theories guaranteeing the existence of the long-time limit. We discuss the implications in the context of the mode-coupling theory of the glass transition where a non-trivial long-time limit signals an idealized glass state.
Journal of Physics A Mathematical and Theoretical 07/2014; 47(32):325004. DOI:10.1088/1751-8113/47/32/325004 · 1.58 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Glass forming liquids exhibit a rich phenomenology upon confinement. This is often related to the effects arising from wall-fluid interactions. Here we focus on the interesting limit where the separation of the confining walls becomes of the order of a few particle diameters. For a moderately polydisperse, densely packed hard-sphere fluid confined between two smooth hard walls, we show via event-driven molecular dynamics simulations the emergence of a multiple reentrant glass transition scenario upon a variation of the wall separation. Using thermodynamic relations, this reentrant phenomenon is shown to persist also under constant chemical potential. This allows straightforward experimental investigation and opens the way to a variety of applications in micro- and nanotechnology, where channel dimensions are comparable to the size of the contained particles. The results are in-line with theoretical predictions obtained by a combination of density functional theory and the mode-coupling theory of the glass transition.
[Show abstract][Hide abstract] ABSTRACT: We investigate the properties of a class of mode-coupling equations for the
glass transition where the density mode decays into multiple relaxation
channels. We prove the existence and uniqueness of the solutions for Newtonian
as well as Brownian dynamics and demonstrate that they fulfill the requirements
of correlation functions, in the latter case the solutions are purely
relaxational. Furthermore, we construct an effective mode-coupling functional
which allows to map the theory to the case of a single decay channel, such that
the covariance principle found for the mode-coupling theory for simple liquids
is properly generalized. This in turn allows establishing the maximum theorem
stating that long-time limits of mode-coupling solutions can be calculated as
maximal solutions of a fixed-point equation without relying on the dynamic
solutions.
Journal of Statistical Mechanics Theory and Experiment 01/2014; 2013(12). DOI:10.1088/1742-5468/2013/12/P12007 · 2.40 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We determine the nonlinear time-dependent response of a tracer on a lattice with randomly distributed hard obstacles as a force is switched on. The calculation is exact to first order in the obstacle density and holds for arbitrarily large forces. Whereas, on the impurity-free lattice, the nonlinear drift velocity in the stationary state is analytic in the driving force, interactions with impurities introduce logarithmic contributions beyond the linear regime. The long-time decay of the velocity toward the steady state is exponentially fast for any finite value of the force, in striking contrast to the power-law relaxation predicted within linear response. We discuss the range of validity of our analytic results by comparison to stochastic simulations.
[Show abstract][Hide abstract] ABSTRACT: Molecular building blocks interacting at the nanoscale organize spontaneously into stable monolayers that display intriguing long-range ordering motifs on the surface of atomic substrates. The patterning process, if appropriately controlled, represents a viable route to manufacture practical nanodevices. With this goal in mind, we seek to capture the salient features of the self-assembly process by means of an interaction-site model. The geometry of the building blocks, the symmetry of the underlying substrate, and the strength and range of interactions encode the self-assembly process. By means of Monte Carlo simulations, we have predicted an ample variety of ordering motifs which nicely reproduce the experimental results. Here, we explore in detail the phase behavior of the system in terms of the temperature and the lattice constant of the underlying substrate.
The European Physical Journal E 03/2012; 35(3):1-8. DOI:10.1140/epje/i2012-12025-x · 1.76 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We discuss the dynamic behavior of a tagged particle close to a classical localization transition in the framework of the mode-coupling theory of the glass transition. Asymptotic results are derived for the order parameter as well as the dynamic correlation functions and the mean-squared displacement close to the transition. The influence of an infrared cutoff is discussed.
[Show abstract][Hide abstract] ABSTRACT: Molecular building blocks interacting at the nanoscale organize spontaneously
into stable mono- layers that display intriguing long-range ordering motifs on
the surface of atomic substrates. The patterning process, if appropriately
controlled, represents a viable route to manufacture practical nanodevices.
With this goal in mind, we seek to capture the salient features of the
self-assembly process by means of an interaction-site model. The geometry of
the building blocks, the symmetry of the underlying substrate, and the strength
and range of interactions encode the self-assembly pro- cess. By means of Monte
Carlo simulations, we have predicted an ample variety of ordering motifs which
nicely reproduce the experimental results. Here, we explore in detail the phase
behavior of the system in terms of the temperature and the lattice constant of
the underlying substrate. Our method is suitable to investigate the stability
of the emergent patterns as well as to identify the nature of the melting
transition monitoring appropriate order parameters.
[Show abstract][Hide abstract] ABSTRACT: Self-organized monolayers of highly flexible \Frechet dendrons were deposited
on graphite surfaces by solution casting. Scanning tunneling microscopy (STM)
reveals an unprecedented variety of patterns with up to seven stable
hierarchical ordering motifs serving as a versatile model system. The essential
molecular properties determined by molecular mechanics simulations are
condensed to a coarse grained interaction site model of various chain
configurations. In a Monte Carlo approach with random starting configurations
the experimental pattern diversity can be reproduced in all facets of the local
and global ordering. Based on an energy analysis of the Monte Carlo and
molecular mechanics modeling the thermodynamically most stable pattern is
predicted coinciding with the pattern, which dominates in the STM images after
several hours or upon moderate heating.
[Show abstract][Hide abstract] ABSTRACT: An interaction-site model can a priori predict molecular self-organisation on a new substrate in Monte Carlo simulations. This is experimentally confirmed with scanning tunnelling microscopy on Fréchet dendrons of a pentacontane template. Local and global ordering motifs, inclusion molecules and a rotated unit cell are correctly predicted.
Chemical Communications 02/2011; 47(6):1800-2. DOI:10.1039/c0cc03603j · 6.83 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Scanning tunneling microscopy (STM) images of self-organized monolayers of Frechet dendrons display a variety of two-dimensional ordering motifs, which are influenced by engineering the molecular interactions. An interaction-site model condenses the essential molecular properties determined by molecular mechanics modeling, which in a Monte Carlo approach successfully predicts the various ordering motifs. This confirms that geometry as well as a few salient weak interaction sites encode these structural motifs.
[Show abstract][Hide abstract] ABSTRACT: We investigate the delocalization transition appearing in an exclusion process with two internal states, respectively on two parallel lanes. At the transition, delocalized domain walls form in the density profiles of both internal states, in agreement with a mean-field approach. Remarkably, the topology of the system's phase diagram allows for the delocalization of a (localized) domain wall when approaching the transition. We quantify the domain wall's delocalization close to the transition by analytic results obtained within the framework of the domain wall picture. Power law dependences of the domain wall width on the distance to the delocalization transition as well as on the system size are uncovered, they agree with numerical results.
The European Physical Journal E 10/2008; 27(1):47-56. DOI:10.1140/epje/i2008-10350-3 · 1.76 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The constitutive equations including the energy conservation aspect, for the long-wavelength dynamics of a liquid comprised of identical, axially symmetric, rigid molecules are microscopically derived. These equations are extended to the case where the dynamics is generated by the interactions of two coherent lasers (the pumps) with the liquid. This interaction corresponds to a weak energy absorption and also to the coupling of the pumps with fluctuations in the mass density, the molecular orientation density and the temperature of the liquid. The microscopic equations generalise those phenomenologically derived in Pick et al. [1] where the role of the temperature fluctuations was ignored. Constraints on the relaxation functions related to the temperature fluctuations and to their coupling with density are derived.
[Show abstract][Hide abstract] ABSTRACT: The phase behavior of a two-dimensional colloidal system subject to a commensurate triangular potential is investigated. We consider the integer number of colloids in each potential minimum as rigid composite objects with effective discrete degrees of freedom. It is shown that there is a rich variety of phases including "herringbone" and "Japanese 6 in 1" phases. The ensuing phase diagram and phase transitions are analyzed analytically within variational mean-field theory and supplemented by Monte Carlo simulations. Consequences for experiments are discussed.
[Show abstract][Hide abstract] ABSTRACT: Constitutive equations for the long-wavelength behaviour of the orientational dynamics of a super-cooled liquid are derived using a projection-operator technique and resulting expressions for light-scattering spectra are formulated. We thus extend recent studies for axially symmetric molecules to the general case of arbitrarily shaped rigid molecules. The second part of the discussion considers hydrodynamic energy-fluctuations and thus arrives at expressions for light-scattering spectra which also include a Rayleigh-line. The role of the memory-kernels in the theory is treated in detail. In particular, the derivation of a theory that formally resembles earlier approaches to the problem is presented using a mathematically rigorous description of the Laplace-transforms of correlation-functions.
[Show abstract][Hide abstract] ABSTRACT: Abstract. We present an analysis, based on a phenomenological set of Generalised Navier Stokes equations, of Heterodyne Detected Transient Gratings on supercooled molecular liquids of anisotropic molecules. This set of equations generalises equations proven in Franosch, Latz and Pick [24] for the same type of liquids. It also takes into account the three different sources generated by the laser pumping process pertinent for these experiments. We give analytical expressions for the response functions that can be measured using the different polarisation of the experimental set up. Specialising to the case of parallel polarisation where longitudinal phonons are launched , we show that each response function is a sum of the same seven elementary response functions ERFs whose time and temperature evolutions are individually analysed. We also show that the response functions corresponding to two of the sources can be directly connected to the Laplace Transform of a light scattering signal. The ERFs generated by the heat absorption process, which is the third source, are of a different nature. They do not have the same time and temperature behaviours and they can provide, inter alia, unique information on the rotation translation coupling function characteristic of these liquids.
[Show abstract][Hide abstract] ABSTRACT: We discuss a class of driven lattice gas obtained by coupling the one-dimensional totally asymmetric simple exclusion process to Langmuir kinetics. In the limit where these dynamics are competing, the resulting nonconserved flow of particles on the lattice leads to stationary regimes for large but finite systems. We observe unexpected properties such as localized boundaries (domain walls) that separate coexisting regions of low and high density of particles (phase coexistence). A rich phase diagram, with high and low density phases, two and three phase coexistence regions, and a boundary independent "Meissner" phase is found. We rationalize the average density and current profiles obtained from simulations within a mean-field approach in the continuum limit. The ensuing analytic solution is expressed in terms of Lambert W functions. It allows one to fully describe the phase diagram and extract unusual mean-field exponents that characterize critical properties of the domain wall. Based on the same approach, we provide an explanation of the localization phenomenon. Finally, we elucidate phenomena that go beyond mean-field such as the scaling properties of the domain wall.
[Show abstract][Hide abstract] ABSTRACT: The coupling of the rotational dynamics of anisotropic molecules to longitudinal phonons gives rise to different effects in the interaction of light with supercooled liquids formed of such molecules. One is the opening of new light scattering channels in Brillouin scattering; this can alter the corresponding phonon lineshape. Another one is the possible appearance of a depolarized signal in transient grating experiments (TG), also called impulsive stimulated scattering. We give a brief theoretical description of these two effects for supercooled liquids formed of linear rigid molecules. We also present preliminary results on the analysis of such a TG experiment performed on m-toluidine.
[Show abstract][Hide abstract] ABSTRACT: We study a one-dimensional totally asymmetric exclusion process with random particle attachments and detachments in the bulk. The resulting dynamics leads to unexpected stationary regimes for large but finite systems. Such regimes are characterized by a phase coexistence of low and high density regions separated by domain walls. We use a mean-field approach to interpret the numerical results obtained by Monte Carlo simulations, and we predict the phase diagram of this nonconserved dynamics in the thermodynamic limit.
[Show abstract][Hide abstract] ABSTRACT: We derive expressions for the intensity of the Brillouin polarized spectrum
of a molecular liquid formed of axially symmetric molecules. These expressions
take into account both the molecular dielectric anisotropy and the modulation
of the local polarisability by density fluctuations. They also incorporate all
the retardation effects which occur in such liquids. We show that the spectrum
splits into a q-independent rotational contribution and q-dependent term, which
reflects the propagation of longitudinal phonons. In the latter, the two light
scattering mechanisms enter on an equal footing and generate three scattering
channels. We study the influence of the two new channels and show that they may
substantially modify the Brillouin line-shape when the relaxation time of the
supercooled liquid and the phonon period are of the same order of magnitude.
[Show abstract][Hide abstract] ABSTRACT: The constitutive equations for the orientational dynamics of a liquid formed
of linear molecules are derived microscopically. The resulting generalised
Langevin equations coincide with the phenomenological approach of Dreyfus et
al. Formally exact expressions are given for the phenomenological coefficients
and various constraints are shown to be consequences of this microscopic
approach.