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RETKUTE, RENATA, i JAMES P. GLEESON. "ROLE OF INTERACTION ON NOISE-INDUCED TRANSPORT OF TWO COUPLED PARTICLES IN BROWNIAN RATCHET DEVICES". Fluctuation and Noise Letters 06, nr 03 (wrzesień 2006): L263—L277. http://dx.doi.org/10.1142/s0219477506003409.
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The motion of elastically coupled Brownian particles in ratchet-like potentials has attracted much recent interest due to its application to transport processes in many fields, including models of DNA polymers. We consider the influence of the type of interacting force on the transport of two particles in a one-dimensional flashing ratchet. Our aim is to examine whether the common assumption of elastic coupling captures the important features of ratchet transport when the inter-particle forces are more complex. We compare Lennard-Jones type interaction to the classical case of elastically coupled particles. Numerical simulations agree with analytical formulas for the limiting cases where the coupling is very weak or very strong. Parameter values where the Lennard-Jones force is not well approximated by a linearization of the force about the equilibrium distance are identified.
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GRIDNEV, K. A., S. YU TORILOV, D. K. GRIDNEV, V. G. KARTAVENKO i W. GREINER. "MODEL OF BINDING ALPHA-PARTICLES AND APPLICATIONS TO SUPERHEAVY ELEMENTS". International Journal of Modern Physics E 14, nr 04 (czerwiec 2005): 635–43. http://dx.doi.org/10.1142/s0218301305003387.
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A model of nuclear matter built from alpha-particles is proposed. In this model, nuclei possess the molecular-like structure. Analyzing the numbers of bonds, one gets the formula for the binding energy of a nucleus. The structure is determined by the minimum of the total potential energy, where interaction between alpha-particles is pairwise and the pair-potential is of Lennard–Jones type. The calculated binding energies show a good agreement with experiment. Calculations predict the stability island for superheavy nuclei around Z=120.
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TEWARI, S. P., GRIMA DHINGRA i POONAM SILOTIA. "COLLECTIVE DYNAMICS OF A NANO-FLUID: FULLERENE, C60". International Journal of Modern Physics B 24, nr 22 (10.09.2010): 4281–92. http://dx.doi.org/10.1142/s0217979210055974.
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Collective dynamics of a strongly correlated nano-fluid of fullerenes, C 60 having number density 0.945 particles/nm3 at 1850 K has been predicted using the sphericalized inter-fullerene interaction and the self-consistent microscopic theory of fluids. The dynamical structure factors have been computed to yield much different dispersion relation of the collective excitations from that of the Lennard–Jones type fluid. The wave-vector dependent longitudinal viscosity of the nano-fluid has also been reported.
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Camrud, Evan, David P. Herzog, Gabriel Stoltz i Maria Gordina. "Weighted L 2-contractivity of Langevin dynamics with singular potentials". Nonlinearity 35, nr 2 (29.12.2021): 998–1035. http://dx.doi.org/10.1088/1361-6544/ac4152.
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Abstract Convergence to equilibrium of underdamped Langevin dynamics is studied under general assumptions on the potential U allowing for singularities. By modifying the direct approach to convergence in L 2 pioneered by Hérau and developed by Dolbeault et al, we show that the dynamics converges exponentially fast to equilibrium in the topologies L 2(dμ) and L 2(W* dμ), where μ denotes the invariant probability measure and W* is a suitable Lyapunov weight. In both norms, we make precise how the exponential convergence rate depends on the friction parameter γ in Langevin dynamics, by providing a lower bound scaling as min(γ, γ −1). The results hold for usual polynomial-type potentials as well as potentials with singularities such as those arising from pairwise Lennard-Jones interactions between particles.
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Steinhauser, Martin O., i Erkai Watson. "Discrete Particle Methods for Simulating Quasi-Static Load and Hypervelocity Impact Phenomena". International Journal of Computational Methods 16, nr 05 (28.05.2019): 1740009. http://dx.doi.org/10.1142/s0219876217400096.
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In this paper, we introduce a mesh-free computational model for the simulation of high-speed impact phenomena. Within the framework of particle dynamics simulations we model a macroscopic solid ceramic tile as a network of overlapping discrete particles of microscopic size. Using potentials of the Lennard–Jones type, we integrate the classical Newtonian equations of motion and perform uni-axial, quasi-static load simulations to customize our three model parameters to the typical tensile strength, Young’s modulus and the compressive strength of a ceramic. Subsequently we perform shock load simulations in a standard experimental setup, the edge-on impact (EOI) configuration. Our obtained results concerning crack initiation and propagation through the material agree well with corresponding high-speed EOI experiments with Aluminum Oxinitride (AlON), Aluminum Oxide [Formula: see text] and Silicon Carbide (SiC), performed at the Fraunhofer Ernst-Mach-Institute (EMI). Additionally, we present initial simulation results where we use our particle–based model to simulate a second type of high-speed impact experiments where an accelerated sphere strikes a thin aluminum plate. Such experiments are done at our institute to investigate the debris clouds arising from such impacts, which constitute a miniature model version of a generic satellite structure that is hit by debris in the earth’s orbit. Our findings are that a discrete particle based method leads to very stable, energy-conserving simulations of high–speed impact scenarios. Our chosen interaction model works particularly well in the velocity range where the local stresses caused by impact shock waves markedly exceed the ultimate material strength.
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Golabczak, Marcin, Andrzej Konstantynowicz i Andrzej Golabczak. "Use of Cellular Automata for Modelling of the Carbon Nanolayer Growth on a Light Alloy Substrate". Journal of Nano Research 26 (grudzień 2013): 159–67. http://dx.doi.org/10.4028/www.scientific.net/jnanor.26.159.
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Carbon deposition forming a nanolayer on a light alloy substrate is a physico-chemical process of the discrete type in all of its aspects. Thus, use of cellular automata, intrinsic discrete, as a mathematical tool for modelling, is fully justified. We adopted two-dimensional (i.e. surface), two-layer automation with Moore vicinity of a cell, for modelling of the carbon deposition process, starting from bonding to the light alloy substrate, leading through layer growth and finishing at the phase transition process, converting graphite into diamond form. To achieve this, we related the transition probabilities of the automaton with the Lennard-Jones potentials for carbon and metal atoms, as well as the physico-chemical conditions in the reaction environment gaseous hydrocarbons density and their particles energy distribution (Maxwell). Taking it into account allowed us to establish an automation time scale of about 1s per calculations run, which has resulted in a simulated layer thickness growth rate well matched with observed results. Using of the two-layer automation allowed us to make some survey into the mechanism of the graphite/diamond transition in the real environmental conditions we met. This demanded further thorough investigations to properly model the spatial structure of mutually interleaved areas of the graphite and diamond type carbon, giving not only a flat-surface but also a vertical structure. The overall surface morphology of the simulated nanolayer we have compared with those of AFM survey performed on real samples, observing relatively good matching in terms of statistical parameters of the surface.
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Prozorova, Evelina. "Some Consequences of Mathematical Inaccuracies in Mechanics". WSEAS TRANSACTIONS ON APPLIED AND THEORETICAL MECHANICS 17 (16.09.2022): 124–31. http://dx.doi.org/10.37394/232011.2022.17.17.
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The article is devoted to the study of some violations of the known laws of mathematics and classical mechanics in continuum mechanics and kinetics. The most common is open non-stationary systems. From the equations formulated earlier and some experiments, a connection traced between the gradients of physical quantities and the angular momentum (force). The use of Hamilton's formalism and the dependence of force only on the distance between particles limits the study. In the collision integral, for example, for a rarefied gas, the Lennard-Jones potential, which not related to the type under consideration, is often used. Hamilton's formalism traces the behavior of closed systems. The general form of boundary conditions and forces changes the theory proposed in the works of N.N. Bogolyubov. The results of the reformulation discussed. Even in the classical theory, after taking into account the moments, we come to the absence of symmetric stress tensor in Boltzmann theory. The symmetric tensor obtains after assumption of small influence from absence of symmetry at the condition of the forces balance. No symmetric tensor leads to the existence of two solutions. New examples of solving problems on hydromechanics, elasticity theory and kinetic theory are given. A correspondence between the terms of the Liouville equation with more general and traditional forces established for continues mechanics. Previously considered boundary layer problems, jet problems and the simplest problems of elasticity theory. The paper proposes a method for finding the second solution for no symmetric problems, if the solution of the symmetric problem we know. The mathematical inaccuracies of the theory of continuum mechanics and kinetics discussed.
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Thiel, Robert, i Jens Jäkel. "Simulation of a passive position control for ferromagnetic particles with multiple Halbach rings". Current Directions in Biomedical Engineering 8, nr 2 (1.08.2022): 773–76. http://dx.doi.org/10.1515/cdbme-2022-1197.
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Abstract Various types of magnetic nanoparticles have been developed for a range of medical applications and some have the potential to treat diseases. In this paper, a new method for controlling the position of these magnetic particles by changing the magnetic field surrounding them using three Halbach ringsis investigated with the aid of a simulation. The inner ring controls the direction, and the position of the two outer rings can keep the group of particles together. In the simulation, the magnetic field is calculated analytically for each time step and the movement of the particles is simulated by applying the corresponding forces. These result from the manipulable external magnetic field, the magnetic field between the particles, the Lennard-Jones potential to model attractive interactions between the particles and the drag. In the simulation, we show how the particles are manipulated using a Levenberg-Marquard algorithm and develop a closedloop control for the position of the grouped particles by manipulating the magnetic field inside the Halbach rings by changing the angular position of these rings.
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OKABE, TSUNEYASU, i HIROAKI YAMADA. "DYNAMICAL INSTABILITY OF ONE-DIMENSIONAL MORSE SYSTEM". Modern Physics Letters B 13, nr 09n10 (30.04.1999): 303–15. http://dx.doi.org/10.1142/s0217984999000403.
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Dynamical instability in an one-dimensional many-body system with Morse-type interaction potential is studied by computer simulation. The dynamical instability of the Morse system is caused by two kinds of instability. One is the parametric instability caused by the stochastic fluctuation of positive curvature of a Riemannian manifold and the other is the local instability approximated by the local negative eigenvalues of the Hessian matrix for the potential function. We investigate the energy dependence of the maximal Lyapunov exponent in order to emphasize the characteristic dynamical instability of the Morse system and compare the characteristics with results have been reported in Fermi–Pasta–Ulam system and Lennard–Jones system. We also investigate the energy dependence of the particle diffusion in the Morse system.
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Mizerski, Krzysztof A. "The detrimental effect of hydrodynamic interactions on the process of Brownian flocculation in shear flow". Journal of Fluid Mechanics 748 (29.04.2014): 328–49. http://dx.doi.org/10.1017/jfm.2014.190.
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AbstractThe problem of Brownian flocculation of spherical particles in strong shearing flow without hydrodynamic interactions is studied in detail using the singular perturbation method. All other types of interparticle interactions, such as van der Waals or Lennard-Jones forces, are also ignored. In the limit of strong external flow, the strength of which is measured by the Péclet number ($Pe\gg 1$), a complicated boundary layer structure for the pair probability density function ($P_{2}$) is identified and the complete stationary spatial distribution of $P_{2}(\boldsymbol {x})$ in the domain is found. The results, in particular the total mass flux in the accumulation process, are compared qualitatively and quantitatively with the case where the spheres interact hydrodynamically and it is demonstrated that the hydrodynamic interactions tend to decrease the rate of flocculation. An explicit simple formula for the flocculation rate for a general form of hydrodynamic interactions is provided. The limit of small Péclet number is also discussed to confirm the conclusion on the detrimental influence of hydrodynamic interactions on the rate of Brownian flocculation in shearing flow.
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EISENBERG, BOB. "IONS IN FLUCTUATING CHANNELS: TRANSISTORS ALIVE". Fluctuation and Noise Letters 11, nr 01 (marzec 2012): 1240001. http://dx.doi.org/10.1142/s0219477512400019.
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Ion channels are proteins with a hole down the middle embedded in cell membranes. Membranes form insulating structures and the channels through them allow and control the movement of charged particles, spherical ions, mostly Na+ , K+ , Ca++ , and Cl- . Membranes contain hundreds or thousands of types of channels, fluctuating between open conducting and closed insulating states. Channels control an enormous range of biological function by opening and closing in response to specific stimuli using mechanisms that are not yet understood in physical language. Open channels conduct current of charged particles following laws of Brownian movement of charged spheres rather like the laws of electrodiffusion of quasi-particles in semiconductors. Open channels select between similar ions using a combination of electrostatic and "crowded charge" (Lennard-Jones) forces. The specific location of atoms and the exact atomic structure of the channel protein seem much less important than certain properties of the structure, namely the volume accessible to ions and the effective density of fixed and polarization charge. There is no sign of other chemical effects like delocalization of electron orbitals between ions and the channel protein. Channels play a role in biology as important as transistors in computers, and they use rather similar physics to perform part of that role. Understanding their fluctuations awaits physical insight into the source of the variance and mathematical analysis of the coupling of the fluctuations to the other components and forces of the system.
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Aminfar, Habib, Mohammad Ali Jafarizadeh i Nayyer Razmara. "Nanoparticles aggregation in nanofluid flow through nanochannels: Insights from molecular dynamic study". International Journal of Modern Physics C 25, nr 11 (15.10.2014): 1450066. http://dx.doi.org/10.1142/s0129183114500661.
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This paper deals with the molecular dynamics simulation (MDS) of nanofluid under Poiseuille flow in a model nanochannel. The nanofluid is created by exerting four solid nanoparticles dispersed in Argon ( Ar ), as base fluid, between two parallel solid walls. The flow is simulated by molecules with the Lennard-Jones (LJ) intermolecular potential function. Different simulations are done with two different types of solid particles and two cut-off radii. In each case, Copper ( Cu ) and Platinum ( Pt ) LJ parameters are applied for the nanoparticles and solid walls particles with cut-off ratios of 2.2σ and 2.5σ. The microstructure of the system at different time steps is investigated to describe the aggregation kinetics of nanofluid on Poiseuille flow. When a few nanoparticles or a cluster of them reach each other, they stick together and the interaction surface of the solid–fluid interface reduces, so the potential energy of the system decreases at these time steps. Therefore, the system enthalpy reduces at the aggregation time steps. Results show that the simulations with cut-off radius 2.5σ indicate minimum clustering effect at the same time. Based on the obtained results, the system with Cu nanoparticles makes it to aggregate later than that of Pt nanoparticles which is due to differences in potential interaction of two materials. The new simulation results enhance our understanding of cluster morphology and aggregation mechanisms.
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Ge, Yunhui, i Vincent A. Voelz. "Estimation of binding rates and affinities from multiensemble Markov models and ligand decoupling". Journal of Chemical Physics 156, nr 13 (7.04.2022): 134115. http://dx.doi.org/10.1063/5.0088024.
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Accurate and efficient simulation of the thermodynamics and kinetics of protein–ligand interactions is crucial for computational drug discovery. Multiensemble Markov Model (MEMM) estimators can provide estimates of both binding rates and affinities from collections of short trajectories but have not been systematically explored for situations when a ligand is decoupled through scaling of non-bonded interactions. In this work, we compare the performance of two MEMM approaches for estimating ligand binding affinities and rates: (1) the transition-based reweighting analysis method (TRAM) and (2) a Maximum Caliber (MaxCal) based method. As a test system, we construct a small host–guest system where the ligand is a single uncharged Lennard-Jones (LJ) particle, and the receptor is an 11-particle icosahedral pocket made from the same atom type. To realistically mimic a protein–ligand binding system, the LJ ϵ parameter was tuned, and the system was placed in a periodic box with 860 TIP3P water molecules. A benchmark was performed using over 80 µs of unbiased simulation, and an 18-state Markov state model was used to estimate reference binding affinities and rates. We then tested the performance of TRAM and MaxCal when challenged with limited data. Both TRAM and MaxCal approaches perform better than conventional Markov state models, with TRAM showing better convergence and accuracy. We find that subsampling of trajectories to remove time correlation improves the accuracy of both TRAM and MaxCal and that in most cases, only a single biased ensemble to enhance sampled transitions is required to make accurate estimates.
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Gusev, V. Yu. "Monte Carlo Simulations of Fluid Phase Transitions in Micropores: Hysteresis and Van Der Waals-Type Loops". MRS Proceedings 492 (1997). http://dx.doi.org/10.1557/proc-492-35.
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ABSTRACTWe report the results of the Monte Carlo simulation study of the fluid phase transitions in micropores. The Gibbs, Canonical, and Grand Canonical ensembles were employed to obtain the adsorption isotherms of the Lennard-Jones nitrogen in carbon slit micropores at 77.4 K. It is shown for the first time that depending on the choice of the parameters of the Monte Carlo simulations, such as the number of particles in the simulation cells, the sampling from the Gibbs ensemble may supply either van der Waals-type or hysteresis loops in the phase transition zones. The existence of these loops is confirmed by independent sampling from the Canonical ensemble using Widom method of test particles. The Grand Canonical ensemble simulations always produce hysteresis loops within the phase transition zone. Outside the phase transition zones, sampling from all three ensembles yield essentially identical isotherms.
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Sasajima, Y., i Shigeo Okuda. "Computer Simulation of the Structure of Nanocrystals". MRS Proceedings 457 (1996). http://dx.doi.org/10.1557/proc-457-547.
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ABSTRACTStructural characteristics of nanocrystals were investigated by molecular dynamics simulation. The structural models were constructed in two dimension, assuming the Lennard-Jones type potential as interaction between atoms. The nanocrystal model consisted of ultra-fine particles as a unit structure, like atoms in normal crystals. In the present study, the diameter of the ultra-fine particles is assumed to be constant and the unit particles are assembled in densely packed structure to form a nanocrystal. The orientations of the unit particles were varied randomly to form various kinds of interfaces between their nearest-neighbor particles. This initial structure was relaxed by the molecular dynamics method with controlling the system temperature by rescaling the velocities of the atoms. The system temperature was set to be so high as to accelerate the relaxation process in the nanocrystal structure. If the diameter of the fine particle is less than 6 (the unit length is nearest-neighbor distance between atoms), the assembled particles were relaxed to form single crystal structure. When the diameter increased larger than 10, the nanocrystal structure was stable and the grain boundaries, vacancies and edge dislocations were remained in the system.
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Nelson, K. M., S. T. Smith i L. T. Wille. "Cluster Molecular Dynamics on Massively Parallel Computers". MRS Proceedings 278 (1992). http://dx.doi.org/10.1557/proc-278-231.
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AbstractWe report the results of computer simulations of phase transitions in noble-gas clusters. The calculations were performed on a MasPar MP-l massively parallel computer with 8,192 processing elements (PE's). We discuss the efficient implementation of molecular dynamics algorithms for small clusters on this type of architecture. The simulations are based on a classical Lennard-Jones pair potential and follow the temporal evolution of the system by numerically integrating Newton's equations of motion using the Gear algorithm. Because the number of particles is much smaller than the number of PE's, optimal partitioning of the processing element array is an essential and non-trivial task.
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Benettin, Giancarlo, Giuseppe Orsatti i Antonio Ponno. "On the Role of the Integrable Toda Model in One-Dimensional Molecular Dynamics". Journal of Statistical Physics 190, nr 8 (29.07.2023). http://dx.doi.org/10.1007/s10955-023-03147-x.
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AbstractWe prove that the common Mie–Lennard-Jones (MLJ) molecular potentials, appropriately normalized via an affine transformation, converge, in the limit of hard-core repulsion, to the Toda exponential potential. Correspondingly, any Fermi–Pasta–Ulam (FPU)-like Hamiltonian, with MLJ-type interparticle potential, turns out to be 1/n-close to the Toda integrable Hamiltonian, n being the exponent ruling repulsion in the MLJ potential. This means that the dynamics of chains of particles interacting through typical molecular potentials, is close to integrable in an unexpected sense. Theoretical results are accompanied by a numerical illustration; numerics shows, in particular, that even the very standard 12–6 MLJ potential is closer to integrability than the FPU potentials which are more commonly used in the literature.
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Jansen, Sabine, Wolfgang König, Bernd Schmidt i Florian Theil. "Distribution of Cracks in a Chain of Atoms at Low Temperature". Annales Henri Poincaré, 23.06.2021. http://dx.doi.org/10.1007/s00023-021-01076-7.
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AbstractWe consider a one-dimensional classical many-body system with interaction potential of Lennard–Jones type in the thermodynamic limit at low temperature $$1/\beta \in (0,\infty )$$ 1 / β ∈ ( 0 , ∞ ) . The ground state is a periodic lattice. We show that when the density is strictly smaller than the density of the ground state lattice, the system with N particles fills space by alternating approximately crystalline domains (clusters) with empty domains (voids) due to cracked bonds. The number of domains is of the order of $$N\exp (- \beta e_\mathrm {surf}/2)$$ N exp ( - β e surf / 2 ) with $$e_\mathrm {surf}>0$$ e surf > 0 a surface energy. For the proof, the system is mapped to an effective model, which is a low-density lattice gas of defects. The results require conditions on the interactions between defects. We succeed in verifying these conditions for next-nearest neighbor interactions, applying recently derived uniform estimates of correlations.
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Frommer, Fabio, i Martin Hanke. "A variational framework for the inverse Henderson problem of statistical mechanics". Letters in Mathematical Physics 112, nr 4 (17.07.2022). http://dx.doi.org/10.1007/s11005-022-01563-w.
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AbstractThe inverse Henderson problem refers to the determination of the pair potential which specifies the interactions in an ensemble of classical particles in continuous space, given the density and the equilibrium pair correlation function of these particles as data. For a canonical ensemble in a bounded domain, it has been observed that this pair potential minimizes a corresponding convex relative entropy functional, and that the Newton iteration for minimizing this functional coincides with the so-called inverse Monte Carlo (IMC) iterative scheme. In this paper, we show that in the thermodynamic limit analogous connections exist between the specific relative entropy introduced by Georgii and Zessin and a proper formulation of the IMC iteration in the full space. This provides a rigorous variational framework for the inverse Henderson problem, valid within a large class of pair potentials, including, for example, Lennard-Jones-type potentials. It is further shown that the pressure is strictly convex as a function of the pair potential and the chemical potential, and that the specific relative entropy at fixed density is a strictly convex function of the pair potential. At a given reference potential and a corresponding density in the gas phase, we determine the gradient and the Hessian of the specific relative entropy, and we prove that the Hessian extends to a symmetric positive semidefinite quadratic functional in the space of square integrable perturbations of this potential.
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Paul, Sanjib, i Harish Vashisth. "Self-Assembly of Porous Structures From a Binary Mixture of Lobed Patchy Particles". Frontiers in Physics 9 (19.10.2021). http://dx.doi.org/10.3389/fphy.2021.767623.
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We report simulation studies on the self-assembly of a binary mixture of snowman and dumbbell shaped lobed particles. Depending on the lobe size and temperature, different types of self-assembled structures (random aggregates, spherical aggregates, liquid droplets, amorphous wire-like structures, amorphous ring structures, crystalline structures) are observed. At lower temperatures, heterogeneous structures are formed for lobed particles of both shapes. At higher temperatures, homogeneous self-assembled structures are formed mainly by the dumbbell shaped particles, while the snowman shaped particles remain in a dissociated state. We also investigated the porosities of self-assembled structures. The pore diameters in self-assemblies increased with an increase in temperature for a given lobe size. The particles having smaller lobes produced structures with larger pores than the particles having larger lobes. We further investigated the effect of σ, a parameter in the surface-shifted Lennard-Jones potential, on the self-assembled morphologies and their porosities. The self-assembled structures formed at a higher σ value are found to produce larger pores than those at a lower σ.
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Eckert, Tobias, Nico C. X. Stuhlmüller, Florian Sammüller i Matthias Schmidt. "Local measures of fluctuations in inhomogeneous liquids: Statistical mechanics and illustrative applications". Journal of Physics: Condensed Matter, 6.07.2023. http://dx.doi.org/10.1088/1361-648x/ace50c.
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Abstract We show in detail how three one-body fluctuation profiles, namely the local compressibility, the local thermal susceptibility, and the reduced density, can be obtained from a statistical mechanical many-body description of classical particle-based systems.
 We present several different and equivalent routes to the definition of each fluctuation profile, facilitating their explicit numerical calculation in inhomogeneous equilibrium systems.
 This underlying framework is used for the derivation of further properties such as hard wall contact theorems and novel types of inhomogeneous one-body Ornstein-Zernike equations.
 The practical accessibility of all three fluctuation profiles is exemplified by grand canonical Monte Carlo simulations that we present for hard sphere, Gaussian core and Lennard-Jones fluids in confinement.
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Chen, Bin. "Direct evidence on the crossover from BCC to FCC stability: A lattice-based aggregation-volume-bias Monte Carlo approach to polymorphism". Journal of Chemical Physics 159, nr 7 (16.08.2023). http://dx.doi.org/10.1063/5.0165492.
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A lattice-based version of the aggregation-volume-bias Monte Carlo method that was introduced recently has allowed for the extension of the calculation of the nucleation free energies from liquid clusters to solid clusters. Here, it was used to calculate the nucleation free energies of both bcc and fcc clusters formed by Lennard–Jones particles. Under the simulation conditions considered in this study, a cross-over of the thermodynamic stability from the bcc to the fcc structure was observed directly from the free energy results. In addition, the free energies obtained for both types of clusters were used to extrapolate bulk phase information, including chemical potential and surface tension, which revealed that bcc clusters are favored due to the lower surface tension. These results corroborate a recent classical density functional theory study. This work also demonstrates that this approach can be used to predict the entire thermodynamic landscape (i.e., free energies for clusters of different structures and sizes, including an infinitely large cluster, which is the bulk phase), which is important to answer fundamental questions related to crystallization such as the origin of polymorphism.