Isotropic Potential Research Articles

Spectral lineshapes of collision-induced absorption (CIA) using isotropic intermolecular potential for N2-CH4

Quantum mechanical lineshapes of collision-induced absorption (CIA) at different temperatures are computed for gaseous mixtures of molecular nitrogen and methane using theoretical values for the induced dipole moments and intermolecular potential as input. Comparison with theoretical absorption spectra shows satisfactory agreement. An empirical model of the dipole moment which reproduces the experimental spectra and the first three spectral moments more closely than the fundamental theory, is also presented. Good agreement between computed and experimental absorption lineshapes is obtained when a potential model which is constructed from the thermophysical and transport properties is used.

Fermi-Pasta-Ulam phenomena and persistent breathers in the harmonic trap.

We consider the long-term weakly nonlinear evolution governed by the two-dimensional nonlinear Schrödinger (NLS) equation with an isotropic harmonic oscillator potential. The dynamics in this regime is dominated by resonant interactions between quartets of linear normal modes, accurately captured by the corresponding resonant approximation. Within this approximation, we identify Fermi-Pasta-Ulam-like recurrence phenomena, whereby the normal-mode spectrum passes in close proximity of the initial configuration, and two-mode states with time-independent mode amplitude spectra that translate into long-lived breathers of the original NLS equation. We comment on possible implications of these findings for nonlinear optics and matter-wave dynamics in Bose-Einstein condensates.

The Energy of the Ground State of the Two-Dimensional Hamiltonian of a Parabolic Quantum Well in the Presence of an Attractive Gaussian Impurity

In this article, we provide an expansion (up to the fourth order of the coupling constant) of the energy of the ground state of the Hamiltonian of a quantum mechanical particle moving inside a parabolic well in the x-direction and constrained by the presence of a two-dimensional impurity, modelled by an attractive two-dimensional isotropic Gaussian potential. By investigating the associated Birman–Schwinger operator and exploiting the fact that such an integral operator is Hilbert–Schmidt, we use the modified Fredholm determinant in order to compute the energy of the ground state created by the impurity.

Analytical eigenstate solutions of Schrödinger equation with noncentral generalized oscillator potential by extended Nikiforov-Uvarov method

Exact eigenstate solutions of Schrödinger equation for a generalized oscillator system that includes, as special cases; ring shaped oscillator potential and isotropic harmonic oscillator potential are examined in an analytical treatment by using extended Nikiforov Uvarov method. Radial and angular parts of the Schrödinger equation for the relevant potential can be systematically solved in the same manner. Moreover the relation between the eigenfunction solutions for this potential and Heun polynomials are presented.

Fourth- and fifth-order virial expansion of harmonically trapped fermions at unitarity

By generalizing our automated algebra approach from homogeneous space to harmonically trapped systems, we have calculated the fourth- and fifth-order virial coefficients of universal spin-1/2 fermions in the unitary limit, confined in an isotropic harmonic potential. We present results for said coefficients as a function of trapping frequency (or, equivalently, temperature), which compare favorably with previous Monte Carlo calculations (available only at fourth order) as well as with our previous estimates in the untrapped limit (high temperature, low frequency). We use our estimates of the virial expansion, together with resummation techniques, to calculate the compressibility and spin susceptibility.

Две модели резинокордного слоя

Breker layers in a pneumatic tire are an important part in the tire construction. These layers have a metal cord resulting in substantial bending stiffness. When homogenizing such layers, a “shave” method is applied to the breaker layer. This results in a thinner layer having adequate stiffness in both tension and bending. In this work, a phenomenological approach is used to obtain the effective properties of a homogeneous anisotropic hyper elastic material of an equivalent layer. Two models utilize transverse isotropic or orthotropic potential used to describe the homogenized properties. Comparison is made between these models for the “shaved” rubber-cord layer based on numerical experiments. In both cases, the potentials are built on the basis of the Treloar or Mooney potentials. Note that in the case of an inhomogeneous thin layer, the traditional definition of homogenization needs to be modified. In previous works of the authors, it was proposed to determine 3D averaged elastic properties of a layer by surrounding it with a homogeneous material. This makes it possible to correctly take into account the fact that the boundary effect from the upper to lower surfaces that penetrates through the whole periodicity cell. A set of local problems formulated for the periodicity cell is proposed. This set is sufficient for determining elastic potential material parameters. Nonlinear local problems on a periodic cell are solved and the material constants of the elastic potential are determined. The applicability of the orthotropic potential (second model) is determined for the “shaved” layer. It was found that orthotropic properties are manifested relative to longitudinal shears. The results show the suitability of the proposed potential and the scheme for determining the material parameters.

Moving beyond the constraints of chemistry via crystal structure discovery with isotropic multiwell pair potentials

The rigid constraints of chemistry-dictated by quantum mechanics and the discrete nature of the atom-limit the set of observable atomic crystal structures. What structures are possible in the absence of these constraints? Here, we systematically crystallize one-component systems of particles interacting with isotropic multiwell pair potentials. We investigate two tunable families of pairwise interaction potentials. Our simulations self-assemble a multitude of crystal structures ranging from basic lattices to complex networks. Sixteen of the structures have natural analogs spanning all coordination numbers found in inorganic chemistry. Fifteen more are hitherto unknown and occupy the space between covalent and metallic coordination environments. The discovered crystal structures constitute targets for self-assembly and expand our understanding of what a crystal structure can look like.

Polymer-Like Self-Assembled Structures from Particles with Isotropic Interactions: Dependence upon the Range of the Attraction.

We conduct Metropolis Monte Carlo simulations on models of dilute colloidal dispersions, where the particles interact via isotropic potentials of mean force (PMFs) that display a long-ranged repulsion, combined with a short-ranged and narrow attraction. Such systems are known to form anisotropic clusters. There are two main conclusions from this work. First, we demonstrate that the width of the attractive region has a significant impact on the type of structures that are formed. A narrow attractive well tends to produce clusters in which particles possess fewer neighbors than in systems where the attraction is wider. Second, metastable clusters appear to persist in the absence of specific simulation moves designed to overcome large energy barriers to particle accumulation. The so-called “Aggregation-Volume Bias Monte Carlo” moves were previously developed by Chen and Siepmann, and they facilitate particle exchanges between clusters via unphysical moves that bypass high energy intermediate states. These facilitate the progression of metastable clusters to equilibrium clusters. Metastable clusters are generally large with significant branching of thin filaments of aggregated particles, while stable clusters have thicker backbones and tend to be more compact with significantly fewer particles. This general behavior is observed in both two- and three-dimensional systems. In two dimensions, less anisotropic clusters with backbones possessing lattice structures will occur, particularly for systems where the particles interact with a PMF that has a relatively wide attractive region. We compare our results with PMF calculations established from a more specific model, namely weakly charged polystyrene particles, which carry a thin surface layer of grafted polyethylene oxide polymers in aqueous solution. We hope that our investigations can serve as crude guidelines for experimental research, aiming to construct linear or branched polymers in aqueous solution built up by colloidal monomers that are large enough to be studied by confocal microscopy. We suggest that metastable clusters are more relevant to experimental scenarios where the energetic barriers are too large to be surmounted over typical timescales.

BoltzmaNN: Predicting effective pair potentials and equations of state using neural networks.

Neural networks (NNs) are employed to predict equations of state from a given isotropic pair potential using the virial expansion of the pressure. The NNs are trained with data from molecular dynamics simulations of monoatomic gases and liquids, sampled in the NVT ensemble at various densities. We find that the NNs provide much more accurate results compared to the analytic low-density limit estimate of the second virial coefficient and the Carnahan-Starling equation of state for hard sphere liquids. Furthermore, we design and train NNs for computing (effective) pair potentials from radial pair distribution functions, g(r), a task that is often performed for inverse design and coarse-graining. Providing the NNs with additional information on the forces greatly improves the accuracy of the predictions since more correlations are taken into account; the predicted potentials become smoother, are significantly closer to the target potentials, and are more transferable as a result.

Autonomous Brownian gyrators: A study on gyrating characteristics.

We study the nonequilibrium steady-state (NESS) dynamics of two-dimensional Brownian gyrators under harmonic and nonharmonic potentials via computer simulations and analyses based on the Fokker-Planck equation, while our nonharmonic cases feature a double-well potential and an isotropic quartic potential. In particular, we report two simple methods that can help understand gyrating patterns. For harmonic potentials, we use the Fokker-Planck equation to survey the NESS dynamical characteristics; i.e., the NESS currents gyrate along the equiprobability contours and the stationary point of flow coincides with the potential minimum. As a contrast, the NESS results in our nonharmonic potentials show that these properties are largely absent, as the gyrating patterns are very distinct from those of corresponding probability distributions. Furthermore, we observe a critical case of the double-well potential, where the harmonic contribution to the gyrating pattern becomes absent, and the NESS currents do not circulate about the equiprobability contours near the potential minima even at low temperatures.

The binary absorption coefficients for H2 + CO2 mixtures in the 2.12–2.35 µm spectral region determined by CRDS and by semi-empirical calculations

Spectra of CO2 + H2 mixtures have been recorded at room temperature by using the cavity ring down technique, for four spectral intervals in the 2.12–2.35 µm CO2 transparency window which is within the (1-0) band of H2. The binary coefficients BCO2−H2+BH2−CO2 have been retrieved from the spectra recorded at different pressures after subtraction of the CO2 monomer contribution and of the H2-H2 and CO2-CO2 collision induced absorptions (CIAs). In order to reduce the uncertainties, new measurement of the pure H2 CIA, the main subtracted contribution, at the percent level are also reported. The new set of experimental binary coefficients is compared to values provided by semi-empirical calculations made with the assumption of an isotropic CO2-H2 interaction potential and neglecting the short-range interaction-induced electric dipole. This comparison shows the limits of using such a model, which is the only one available, in that spectral region.

Interaction Patterns for Staggered Assembly of Fibrils from Semiflexible Chains

The design of colloidal interactions to achieve target self-assembled structures has especially been done for compact objects such as spheres with isotropic interaction potentials, patchy spheres and other compact objects with patchy interactions. Inspired by the self-assembly of collagen-I fibrils and intermediate filaments, we here consider the design of interaction patterns on semiflexible chains that could drive their staggered assembly into regular (para)crystalline fibrils. We consider semiflexible chains composed of a finite number of types of interaction beads (uncharged hydrophilic, hydrophobic, positively charged and negatively charged) and optimize the sequence of these interaction beads with respect to the interaction energy of the semiflexible chains in a number of target-staggered crystalline packings. We find that structures with the lowest interaction energies, that form simple lattices, also have low values of L/D (where L is chain length and D is stagger). In the low interaction energy sequences, similar types of interaction beads cluster together to form stretches. Langevin Dynamics simulations confirm that semiflexible chains with optimal sequences self-assemble into the designed staggered (para)crystalline fibrils. We conclude that very simple interaction patterns should suffice to drive the assembly of long semiflexible chains into staggered (para)crystalline fibrils.

Anisotropic Stark shift, field-induced dissociation, and electroabsorption of excitons in phosphorene

We compute binding energies, Stark shifts, electric-field-induced dissociation rates, and the Franz-Keldysh effect for excitons in phosphorene in various dielectric surroundings. All three effects show a pronounced dependence on the direction of the in-plane electric field, with the dissociation rates in particular decreasing by several orders of magnitude upon rotating the electric field from the armchair to the zigzag axis. To better understand the numerical dissociation rates, we derive an analytical approximation to the anisotropic rates induced by weak electric fields, thereby generalizing the previously obtained result for isotropic two-dimensional semiconductors. This approximation is shown to be valid in the weak-field limit by comparing it to the exact rates. The anisotropy is also apparent in the large difference between armchair and zigzag components of the exciton polarizability tensor, which we compute for the five lowest lying states. As expected, we also find much more pronounced Stark shifts in either the armchair or zigzag direction, depending on the symmetry of the state in question. Finally, an isotropic interaction potential is shown to be an excellent approximation to a more accurate anisotropic interaction derived from the Poisson equation, confirming that the anisotropy of phosphorene is largely due to the direction dependence of the effective masses.

A mean-field approach to simulating anisotropic particles.

We introduce a mean-field theoretical framework for generalizing isotropic pair potentials to anisotropic shapes. This method is suitable for generating pair potentials that can be used in both Monte Carlo and molecular dynamics simulations. We demonstrate the application of this theory by deriving a Lennard-Jones (LJ)-like potential for arbitrary geometries along with a Weeks-Chandler-Anderson-like repulsive variant, showing that the resulting potentials behave very similarly to standard LJ potentials while also providing a nearly conformal mapping of the underlying shape. We then describe an implementation of this potential in the simulation engine HOOMD-blue and discuss the challenges that must be overcome to achieve a sufficiently robust and performant implementation. The resulting potential can be applied to smooth geometries like ellipsoids and to convex polytopes. We contextualize these applications with reference to the existing methods for simulating such particles. The pair potential is validated using standard criteria, and its performance is compared to existing methods for comparable simulations. Finally, we show the results of self-assembly simulations, demonstrating that this method can be used to study the assembly of anisotropic particles into crystal structures.

Fast evaluation of interaction integrals for confined systems with machine learning

The calculation of interaction integrals is a bottleneck for the treatment of many-body quantum systems due to its high numerical cost. We conduct configuration interaction calculations of the few-electron states confined in III-V semiconductor 2D structures using a shallow neural network to calculate the two-electron integrals, that can be used for general isotropic interaction potentials. This approach allows for a speed up of the evaluation of the energy levels and a controllable accuracy.

Thermodynamics of rotating quantum matter in the virial expansion

We characterize the high-temperature thermodynamics of rotating bosons and fermions in two- (2D) and three-dimensional (3D) isotropic harmonic trapping potentials. We begin by calculating analytically the conventional virial coefficients $b_n$ for all $n$ in the noninteracting case, as functions of the trapping and rotational frequencies. We also report on the virial coefficients for the angular momentum and associated moment of inertia. Using the bn coefficients, we analyze the deconfined limit (in which the angular frequency matches the trapping frequency) and derive explicitly the limiting form of the partition function, showing from the thermodynamic standpoint how both the 2D and 3D cases become effectively homogeneous 2D systems. To tackle the virial coefficients in the presence of weak interactions, we implement a coarse temporal lattice approximation and obtain virial coefficients up to third order.

Integral-equation theories of fluid phase equilibria in simple fluids

We briefly review the application of integral equation theories (IETs) of the fluid state in order to predict fluid phase equilibria of simple fluids. In spite of the relatively simple picture emerging from an isotropic pair potential, IETs have been instrumental in the last few decades to show a quite complex phase behaviour, where multiple critical points are observed in the phase diagram. The application of thermodynamic self-consistency within the theory is shown to dramatically improve the reliability of IETs, allowing them to become a valid and computationally cheap tool, in comparison to computer simulation, to investigate the limits of stability of the fluid phase.

Phase diagram of two-patch colloids with competing anisotropic and isotropic interactions

Patchy particles are considered to be a good model for protein aggregation. We propose a novel method to generate different structures of glucose isomerase protein such as chains, crystals and bundles by utilising aggregation of two-patch colloidal particles in presence of competing isotropic and anisotropic potential. We calculate the equilibrium phase diagram of two-patch colloidal particles and demonstrates the coexistence of different phases like disordered clusters, chains, crystals and bundles depending on the relative strength of isotropic and anisotropic potential. We also show that the formation of network of bundles is metastable against the formation of thermodynamically favored finite sized bundles along with thermodynamically stable crystals. These bundles appear to be helical in structure similar to that observed in sickle cell hemoglobin. The simulation results show that the method can characterize phase behaviour of glucose isomerase protein, which provides a novel tool to unveil self-assembly mechanism of protein under different conditions.

A uniformly charged circular disk with an anisotropic Coulomb interaction potential

We consider a uniformly charged circular disk containing elementary charges that interact with an anisotropic Coulomb interaction potential. Such an anisotropic Coulomb interaction potential has been recently considered within the framework of a two-dimensional system of electrons in the quantum Hall regime. The anisotropy of the potential is introduced by a phenomenological parameter that can be tuned continuously as to incorporate the standard isotropic Coulomb interaction potential as a special case. The energy of the uniformly charged circular disk is calculated exactly for the given anisotropic interaction potential as a function of the anisotropy parameter. The results obtained are related to electrostatic problems that involve uniformly charged flat elliptical plates and may be useful to understand finite two-dimensional systems of electrons in the quantum Hall regime in which all point charges interact with the anisotropic Coulomb interaction potential presently considered.

Measurements and calculations of Kr-broadening and shift parameters of water vapour transitions in a wide spectral region

The water vapour line broadening (γ) and shifting (δ) coefficients for 497 lines of 16 vibrational bands ν1, ν3, 2ν2, ν1 + ν2, ν2 + ν3, 3ν2, 2ν2 + ν3, ν1 + 2ν2, ν1 + ν3, 2ν1, 2ν3, 6ν2, 2ν1 + ν2,ν2 + 2ν3, ν1 + 3ν2, and 3ν2 + ν3 induced by krypton pressure were measured with Bruker IFS 125 HR Fourier transform spectrometer. The measurements were performed at room temperature, at the spectral resolution of 0.01 cm−1 and in a wide pressure range of Kr (0.303–0.980 atm). The calculations of the broadening and shift coefficients γ and δ were performed in the framework of the semi-classical method. The intermolecular potential was taken as the sum of the anisotropic atom–atom potential and the vibrationally and rotationally dependent isotropic Lennard-Jones potential. The measured coefficients γ and δ were combined with literature data for the ν2 and rotational bands, and optimal sets of potential parameters that gave the best agreements with the measured broadening coefficients for each vibrational band separately were found. Experimental data for ten vibrational bands of H2O perturbed by Kr were used to determine the analytical dependence of some of the potential parameters on the vibrational quantum numbers. Combined experimental data for the coefficients γ of 19 vibrational bands of H2O perturbed by Kr were fitted to the empirical function. The computed coefficients γ and δ derived from the semi-classical method and the fitted parameters were compared statistically to the measurements. The vibrational dependence of the potential as well as of the coefficients γ and δ is discussed.