Hard-core Repulsion Research Articles

Compatibility of Exotic States with Neutron Star Observation

We consider the effect of hard core repulsion in the baryon-baryon interaction at short distance to the properties of a neutron star. We obtain that, even with hyperons in the interior of a neutron star, the neutron star mass can be as large as $\sim 2 M_\odot$.

Collisions of ideal gas molecules with a rough/fractal surface. A computational study

The frequency of collisions of ideal gas molecules (argon) with a rough surface has been studied. The rough/fractal surface was created using random deposition technique. By applying various depositions, the roughness of the surface was controlled and, as a measure of the irregularity, the fractal dimensions of the surfaces were determined. The surfaces were next immersed in argon (under pressures 2 x 10(3) to 2 x 10(5) Pa) and the numbers of collisions with these surfaces were counted. The calculations were carried out using a simplified molecular dynamics simulation technique (only hard core repulsions were assumed). As a result, it was stated that the frequency of collisions is a linear function of pressure for all fractal dimensions studied (D = 2, ..., 2.5). The frequency per unit pressure is quite complex function of the fractal dimension; however, the changes of that frequency with the fractal dimension are not strong. It was found that the frequency of collisions is controlled by the number of weakly folded sites on the surfaces and there is some mapping between the shape of adsorption energy distribution functions and this number of weakly folded sites. The results for the rough/fractal surfaces were compared with the prediction given by the Langmuir-Hertz equation (valid for smooth surface), generally the departure from the Langmuir-Hertz equation is not higher than 48% for the studied systems (i.e. for the surfaces created using the random deposition technique).

Molecular dynamics study of the equilibrium flux of gas molecules to a fractal/rough surface: Effects of gas atom diameter

The frequency of collisions of ideal gas molecules (argon) with a rough surface has been studied. The rough/fractal surface was created using the random deposition technique. By applying various depositions the surface roughness was controlled and, as a measure of irregularity, the fractal dimensions of the surfaces were determined. The surfaces were next immersed in ideal gas and the numbers of collisions with these surfaces were counted. The calculations were carried out using the simplified molecular dynamics simulation technique (only hard core repulsions were assumed). The calculations were performed for various ratios of gas phase atoms diameter to the surface substrate atoms diameter. The results obtained showed that the size of a gas phase atom has crucial influence on the relation between the frequency of collision and the surface fractal dimension

Local Structure and Thermodynamics of a Core‐Softened Potential Fluid: Theory and Simulation

Phase behavior and structural properties of homogeneous and inhomogeneous core-softened (CS) fluid consisting of particles interacting via the potential, which combines the hard-core repulsion and double attractive well interaction, are investigated. The vapour-liquid coexistence curves and critical points for various interaction ranges of the potential are determined by discrete molecular dynamics simulations to provide guidance for the choice of the bulk density and potential parameters for the study of homogeneous and inhomogeneous structures. Spatial correlations in the homogeneous CS system are studied by the Ornstein-Zernike integral equation in combination with the modified hypernetted chain (MHNC) approximation. The local structure of CS fluid subjected to diverse external fields maintaining the equilibrium with the bulk CS fluid are studied on the basis of a recently proposed third order+second order perturbation density functional approximation (DFA). The accuracy of DFA predictions is tested against the results of a grand canonical ensemble Monte Carlo simulation. Reasonable agreement between the results of both methods proves that the DFA theory applied in this work is a convenient theoretical tool for the investigation of the CS fluid, which is practically applicable for modeling numerous real systems.

Density anomaly and liquid-liquid transition from perturbation theories

We report on theoretical results concerning the relation between the liquid-liquid transition and the density anomaly for a family of ramp potentials (hard-core plus linear short range repulsion and linear long range attraction). Using first order perturbation, we have studied the influence of the range of the attractive interactions, taking the repulsive part of the interaction as the reference system. Two different mechanisms of liquid-liquid coexistence have been predicted: attraction and compression. The attractive case is attributed to long ranged potentials, while the second one is obtained when the interaction is shortened. The density anomaly appears linked to regions where the temperature derivative of the density derivative of the energy is bigger (in absolute value) than a limit. This condition is fulfilled when the range of the attractive part of the potential is short enough.

Surface properties of fluids of charged platelike colloids

Surface properties of mixtures of charged platelike colloids and salt in contact with a charged planar wall are studied within density functional theory. The particles are modeled by hard cuboids with their edges constrained to be parallel to the Cartesian axes corresponding to the Zwanzig model [J. Chem. Phys. 39, 1714 (1963)] and the charges of the particles are concentrated at their centers. The density functional applied is an extension of a recently introduced functional for charged platelike colloids. It provides a qualitative approach because it does not determine the relation between the actual and the effective charges entering into the model. Technically motivated approximations, such as using the Zwanzig model, are expected not to influence the results qualitatively. Analytically and numerically calculated bulk and surface phase diagrams exhibit first-order wetting for sufficiently small macroion charges and isotropic bulk order as well as first-order drying for sufficiently large macroion charges and nematic bulk order. The asymptotic wetting and drying behaviors are investigated by means of effective interface potentials which turn out to be asymptotically the same as for a suitable neutral system governed by isotropic nonretarded dispersion forces. Wetting and drying points as well as predrying lines and the corresponding critical points have been located numerically. A crossover from monotonic to nonmonotonic electrostatic potential profiles upon varying the surface charge density has been observed. Nonmonotonic electrostatic potential profiles are equivalent to the occurrence of charge inversion. Due to the presence of both the Coulomb interactions and the hard-core repulsions, the surface potential and the surface charge do not vanish simultaneously, i.e., the point of zero charge and the isoelectric point of the surface do not coincide.

Self-consistent Ornstein-Zernike approximation for molecules with soft cores

The self-consistent Ornstein-Zernike approximation (SCOZA) is an accurate liquid state theory. So far it has been tied to interactions composed of hard core repulsion and long-range attraction, whereas real molecules have soft core repulsion at short distances. In the present work, this is taken into account through the introduction of an effective hard core with a diameter that depends upon temperature only. It is found that the contribution to the configurational internal energy due to the repulsive reference fluid is of prime importance and must be included in the thermodynamic self-consistency requirement on which SCOZA is based. An approximate but accurate evaluation of this contribution relies on the virial theorem to gauge the amplitude of the pair distribution function close to the molecular surface. Finally, the SCOZA equation is transformed by which the problem is reformulated in terms of the usual SCOZA with fixed hard core reference system and temperature-dependent interaction.

A molecular-thermodynamic model for the interactions between globular proteins in aqueous solutions: Applications to bovine serum albumin (BSA), lysozyme, α-chymotrypsin, and immuno-gamma-globulins (IgG) solutions

To investigate globular protein–protein and protein–salt interactions in electrolyte solutions, a potential of mean force including hard-core repulsion, van der Waals attraction and electric double layer repulsion is proposed in this work. Both van der Waals attraction and double-layer repulsion are represented using hard spheres with two-Yukawa tails. The explicit analytical solution of osmotic pressure is derived from the first-order mean spherical approximation. From the comparison between the calculated and experimental values of osmotic pressures for aqueous bovine serum albumin (BSA), lysozyme, α-chymotrypsin, and immuno-gamma-globulins (IgG) solutions, we found that the proposed model is adequate for the description of the interactions between proteins at low ionic strength and small self-association of protein molecules. At high ionic strength, the charge inversions of protein molecules should be taken into account.

Commensurate and incommensurate ground states ofCs2CuCl4in a magnetic field

We present calculations of the magnetic ground state of ${\mathrm{Cs}}_{2}\mathrm{Cu}{\mathrm{Cl}}_{4}$ in an applied magnetic field, with the aim of understanding the commensurately ordered state that has been discovered in recent experiments. This layered material is a realization of a Heisenberg antiferromagnet on an anisotropic triangular lattice. Its behavior in a magnetic field depends on field orientation, because of weak Dzyaloshinskii-Moriya interactions. We study the system by mapping the spin-$1∕2$ Heisenberg Hamiltonian onto a Bose gas with hardcore repulsion. This Bose gas is dilute, and calculations are controlled, close to the saturation field. We find a zero-temperature transition between incommensurate and commensurate phases as longitudinal field strength is varied, but only incommensurate order in a transverse field. Results for both field orientations are consistent with experiment.

Computer simulation study of a simple cubatic mesogenic lattice model

Over the last , the possible existence of a cubatic mesophase, possessing cubic orientational order (i.e., along three mutually orthogonal axes) but no translational one, has been addressed theoretically, and predicted in some cases, where the investigated interaction models involved hard-core repulsion only; on the other hand, no experimental realizations of such a phase are known at the time being. The present paper addresses a very simple cubatic mesogenic lattice model, involving continuous interactions; we consider particles possessing Oh symmetry, whose centers of mass are associated with a three-dimensional simple-cubic lattice; the pair potential is taken to be isotropic in orientation space, and restricted to nearest neighboring sites; let the two orthonormal triads {uj, j=1, 2, 3} and {vk, k=1, 2, 3} define orientations of a pair of interacting particles, and let fjk=vj.uk. The interaction model studied here is defined by the simplest nontrivial (quartic) polynomial in the scalar products f jk, consistent with the assumed symmetry and favoring orientational order; it is, so to speak, the cubatic counterpart of the Lebwohl-Lasher model for uniaxial nematics. The model was investigated by mean field theory and Monte Carlo simulation, and found to produce a low-temperature cubatically ordered phase, undergoing a first order transition to the isotropic phase at higher temperature; the mean field treatment yielded results in reasonable qualitative agreement with simulation.

Berezinskii-Kosterlitz-Thouless transition in two-dimensional lattice gas models

We have considered two classical lattice-gas models, consisting of particles that carry multicomponent magnetic momenta, and associated with a two-dimensional square lattices; each site can host one particle at most, thus implicitly allowing for hard-core repulsion; the pair interaction, restricted to nearest neighbors, is ferromagnetic and involves only two components. The case of zero chemical potential has been investigated by Grand--Canonical Monte Carlo simulations; the fluctuating occupation numbers now give rise to additional fluid-like observables in comparison with the usual saturated--lattice situation; these were investigated and their possible influence on the critical behaviour was discussed. Our results show that the present model supports a Berezinskii-Kosterlitz-Thouless phase transition with a transition temperature lower than that of the saturated lattice counterpart due to the presence of ``vacancies''; comparisons were also made with similar models studied in the literature.

Entanglement generation via scattering of two particles with hard-core repulsion

We analyse the entanglement generation in a one dimensional scattering process. The two colliding particles have a Gaussian wave function and interact by hard--core repulsion.In our analysis results on the entanglement of two mode Gaussian states are used. The produced entanglement depends in a non-obvious way on the parameters ratio of masses and initial widths. The asymptotic wavefunction of the two particles and its associated ellipse yield additional geometric insight into these conditions. The difference to the quantitative analysis of the amount of entanglement generated by beam splitters with squeezed light is discussed.

The structural properties of a two-Yukawa fluid: Simulation and analytical results

Standard Monte Carlo simulations are carried out to assess the accuracy of theoretical predictions for the structural properties of a model fluid interacting through a hard-core two-Yukawa potential composed of a short-range attractive well next to a hard repulsive core, followed by a smooth, long-range repulsive tail. Theoretical calculations are performed in the framework provided by the Ornstein-Zernike equation, solved either analytically with the mean spherical approximation (MSA) or iteratively with the hypernetted-chain (HNC) closure. Our analysis shows that both theories are generally accurate in a thermodynamic region corresponding to a dense vapor phase around the critical point. For a suitable choice of potential parameters, namely, when the attractive well is deep and/or large enough, the static structure factor displays a secondary low-Q peak. In this case HNC predictions closely follow the simulation results, whereas MSA results progressively worsen the more pronounced this low-Q peak is. We discuss the appearance of such a peak, also experimentally observed in colloidal suspensions and protein solutions, in terms of the formation of equilibrium clusters in the homogeneous fluid.

Exact Solution of the One-Dimensional N-Component BarievModel with a Hard-Core Repulsion under Open Boundary Conditions

We analyse the integrable boundary conditions for the one-dimensionalN-component generalized Bariev model with a hard-core repulsion. TheBethe ansatz equations and the energy spectrum are obtained in theframework of the nested Bethe ansatz method.

Entropic Sampling of Free and Ring Polymer Chains

AbstractSummary: We extend Monte Carlo (MC) methods developed in our previous paper (J. Phys. A, Math. Gen. 2004, 37, 1573) and based on entropic sampling within Wang‐Landau (WL) algorithm to the simulation of lattice and continuous models of ring polymers. For a continuous freely joined ring chain (an equilateral polygon) with hard sphere monomer units, the excess entropy of rings relative to the corresponding reference system, a phantom ring chain, is obtained. The excess specific entropy is calculated for a set of various diameters of monomer units d and chain lengths N. Its limiting values for $N\to \infty$ ($N^{-1}\to 0$) are estimated for each d and coincidence with those for corresponding free chains is demonstrated. We also develop a WL approach to calculate thermal properties of free and ring continuous chains with an Lennard‐Jones attraction between nonbonded beads being added to hard core repulsion at fixed d. The obtained energy distributions provide calculation of canonical properties such as conformational energy, heat capacity, entropy, and mean square radius of inertia. Thermal results for free and ring chains are being finally compared. Analogous calculations are performed for lattice‐free chains and rings. magnified image

The Maximin Principle of π-Radical Packings

A two-term model is proposed for hydrocarbon and N-containing pi-radicals which are in close contact with one another. The first term is attractive (due to partially occupied frontier pi-orbitals), and the second, repulsive (due to hard-core repulsion between close-lying atoms). This model is applied to dimers where intermolecular contacts are closer than <0.95 x the sum of the atomic van der Waals radii. The maximin principle is proposed. The maximin principle states that the lowest energy conformation maximizes overlap of the frontier orbitals while simultaneously minimizing intermolecular contacts. A Hückel Hamiltonian, the mu(2)-Hamiltonian, which contains the above attractive and repulsive terms, is applied. The interaction surfaces of two pi-hydrocarbon radical cations were calculated for the three systems known crystallographically to contain cations in close contact: naphthalene, fluoranthene, and pyrene. The global minima of these surfaces correspond to the experimentally determined structures. The mu(2)-Hamiltonian energy surfaces of the naphthalene cation dimer are qualitatively similar to those calculated at the RHF/6-311G(d,p) and MP2/6-311G(d,p) levels. The maximin principle is applied to N-containing pi-radicals. Except in the case of tetracyanoethene, the maximin principle correctly predicts the most common dimer crystal packing. (MgPc)(NO(3)).0.5THF and (MgPc)(ReO(4)).1.5THF (Pc = phthalocyanine) were prepared: both new crystal structures follow the maximin principle. The maximin principle is used to suggest the dimer cation ground state of oligoacenes, cations important as organic hole-based semiconductors.

Two-dimensional lattice gas models with extremely anisotropic spin interactions

The effect of anisotropic magnetic interactions on the physical properties of lattice gases is considered in the framework of two simple models, consisting of particles that carry an $n$-component classical spin (unit vector, $n=2$ or 3), and associated with a two-dimensional square lattice; each site can host one particle at most, thus implicitly allowing for hard-core repulsion; the pair potential, restricted to nearest neighbors, is ferromagnetic and extremely anisotropic in spin space, in the sense that only one component is involved in the interaction; the models are rigorously known to support an orientational ordering transition in appropriate ranges of temperature and chemical potential. Thermodynamic properties and phase diagrams of both models have been studied by means of mean-field and two-site cluster treatments, and their tricritical points have been identified. The case of zero chemical potential has been investigated by Monte Carlo simulations, so as to obtain a quantitative test of the named approximations, as well as a more detailed physical characterization.

Soft chaos in a Hamiltonian system with step potential. II. Topological properties

Abstract In this series of papers the stochastic and topological properties of the relative motion of three particles on the line which interact through piecewise constant pair potentials (hard-core repulsion, short-range attraction, and long-range confinement) are examined. In part I we first present the results of molecular dynamics simulations which were performed for a large number of initial data, most of them belonging to low energies E. Poincare sections strongly suggest the following configurational ergodicity: If P is one of the observed momenta, then the set of all configurations X such that the potential energy V(X) = E−P2/2 is filled uniformly, as time proceeds, by those sections of X(t) for which X ˙ ( t ) = P . Based on this assumption we decompose the energy surface into ergodic components and infer the related invariant density. The velocity distribution functions calculated as ensemble averages over these components are found to be in excellent agreement with the corresponding time averages from the simulation data. Then it is shown that each trajectory travels in only finitely many directions in the lowest energy range E ∈ (−2, −1/2), whereas for all E ⩾ −1/2 the number of different momenta in the ergodic components is infinite.

Membrane Lateral Mobility Obstructed by Polymer-Tethered Lipids Studied at the Single Molecule Level

Obstructed long-range lateral diffusion of phospholipids (TRITC-DHPE) and membrane proteins (bacteriorhodopsin) in a planar polymer-tethered 1-stearoyl-2-oleoyl-sn-glycero-3-phosphocholine bilayer is studied using wide-field single molecule fluorescence microscopy. The obstacles are well-controlled concentrations of hydrophobic lipid-mimicking dioctadecylamine moieties in the polymer-exposed monolayer of the model membrane. Diffusion of both types of tracer molecules is well described by a percolating system with different percolation thresholds for lipids and proteins. Data analysis using a free area model of obstructed lipid diffusion indicates that phospholipids and tethered lipids interact via hard-core repulsion. A comparison to Monte Carlo lattice calculations reveals that tethered lipids act as immobile obstacles, are randomly distributed, and do not self-assemble into large-scale aggregates for low to moderate tethering concentrations. A procedure is presented to identify anomalous subdiffusion from tracking data at a single time lag. From the analysis of the cumulative distribution function of the square displacements, it was found that TRITC-DHPE and W80i show normal diffusion at lower concentrations of tethered lipids and anomalous diffusion at higher ones. This study may help improve our understanding of how lipids and proteins in biomembranes may be obstructed by very small obstacles comprising only one or very few molecules.

Renormalization of the singular attractive1∕r4potential

We study the radial Schr\"odinger equation for a particle of mass $m$ in the field of a singular attractive ${g}^{2}∕{r}^{4}$ potential with particular emphasis on the bound-states problem. Using the regularization method of Beane et al. [Phys. Rev. A 64, 042103 (2001)], we solve analytically the corresponding ``renormalization-group flow'' equation. We find in agreement with previous studies that its solution exhibits a limit cycle behavior and has infinitely many branches. We show that a continuous choice for the solution corresponds to a given fixed number of bound states and to low-energy phase shifts that vary continuously with energy. We study in detail the connection between this regularization method and a conventional method modifying the short-range part of the potential with an infinitely repulsive hard core. We show that both methods yield bound-states results in close agreement even though the regularization method of Beane et al. does not include explicitly any new scale in the problem. We further illustrate the use of the regularization method in the computation of electron bound states in the field of neutral polarizable molecules without dipole moment. We find the binding energy of $s$-wave polarization bound electrons in the field of ${\mathrm{C}}_{60}$ molecules to be 17 meV for a scattering length corresponding to a hard-core radius of the size of the molecule radius $(\ensuremath{\sim}3.37\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}})$. This result can be further compared with recent two-parameter fits using the Lennard-Jones potential yielding binding energies ranging from 3 to 25 meV.