arXiv subjects

Yashwant Singh

Publications and source records attributed to Yashwant Singh.

At least 19 recordsLinked to original sources

arXiv2026

Glassy dynamics, crossover temperature and density scaling in fragile glass-formers

We investigate the slowing down of dynamics in a glass-forming mixture interacting via an inverse-power-law (IPL) potential using a combination of theory and large-scale molecular dynamics simulations. We measure the static pair-correlation function, configurational entropy, inherent-structure energy, and structural relaxation time. We employ a theoretical framework to calculate the structural relaxation time $τ_α$, which is found to be in very good agreement with the simulation results. The theory identifies a local structural order which defines the cooperativity of the relaxation and brings forth a fluctuation induced parameter $ψ( T )$ and a crossover temperature $T_a$ that characterize the density and temperature dependence of the glassy dynamics. Furthermore, we determine a crossover temperature using independent dynamical and thermodynamic criteria and compare with the theoretically predicted crossover temperature $T_a$. Relaxation dynamics is shown to obey density-temperature scaling, similar to thermodynamic properties, in terms of a variable $Γ$ formed by an appropriate combination of density and temperature, characteristic of IPL interactions. Finally, we show that, when the excess thermodynamic and dynamic quantities obtained at different densities are plotted as functions of the reduced temperature $T/T_a$ (or $T_a/T$), the data collapse onto master curves with excellent agreement between theory and simulation. These scaling relations provide a unified description of the thermodynamics and dynamics in IPL systems, enabling the prediction of relaxation behavior over a wide range of densities from data at a single state point.

cond-mat.soft↗

arXiv2026

Ordering, correlation functions and phase transitions in molecular systems

Although the classical density functional theory (DFT) of inhomogeneous fluids was formulated more than four decades ago, its application to broken symmetry phases of molecular systems remained a challenge. Approximate free energy functionals proposed in the past failed to give accurate description of relative stability of phases, phase transitions, and of properties arising due to broken symmetry. In a DFT pair correlation functions (PCFs) play a fundamental role. While in the case of homogeneous fluids, PCFs are routinely determined using experimental, theoretical or simulation methods, determination of PCFs of broken symmetry phases remained a problem. Breaking of symmetry at the transition point gives rise a new contribution to correlation functions which may differ significantly from that of the coexisting higher symmetry phase. We review methods which have been developed in the last few years to calculate PCFs of broken symmetry phases and their inclusion in the expressions of the grand potential and the intrinsic free-energy. This leads to formulation of an exact DFT. We describe application of the theory to freezing of variety of fluids into ordered phases and transition from an ordered phase of higher symmetry to a phase of lower symmetry. Comparison of results found from different versions of DFT and simulations reveal their accuracy. A brief description of basics of statistical mechanics is included to make the article self-contained.

cond-mat.stat-mech↗

arXiv2026

Vortex ring formation from the interaction of a cavitation bubble with a confined air bubble: experiments and a timing criterion

We study vortex ring formation arising from the interaction between a cavitation bubble and a confined air bubble in a cylindrical blind hole, using high-speed shadowgraphy imaging. As the cavitation bubble grows above the hole, it drives a downward flow that compresses the air bubble at the base. The air bubble subsequently expands, expelling the overlying liquid column upward as a coherent slug; impact of this slug on the far boundary of the collapsing cavitation bubble produces a vortex ring. Parametric experiments across the dimensionless stand-off distance $\mathcal{H} = h/R_{\max}$ and the air bubble fill fraction $\mathcal{B} = (d_\text{hole} - d_\text{top})/d_\text{hole}$ identify three regimes: (i) liquid column impact during collapse, producing a vortex ring ($\mathcal{H} \lesssim 0.5$, $\mathcal{B} \lesssim 0.5$); (ii) late impact near the end of collapse (large $\mathcal{H}$); and (iii) direct air bubble impact after bypassing the liquid column (large $\mathcal{B}$), with neither (ii) nor (iii) producing a ring. Two one-dimensional models, based on the Rayleigh-Plesset equation and isentropic air bubble expansion, predict the liquid column impact location and its speed $U_\text{lc}$, respectively. A dimensionless timing parameter $Π= (h + R_{\max}) / (U_\text{lc} \cdot t_\text{cav}/2)$, comparing the liquid column travel time to the cavitation collapse half-period, distinguishes the three regimes: ring formation occurs for $1 \lesssim Π\lesssim 1.5$. The ring propagates from the hole at an initial speed of $5$ m/s, decelerating quadratically, and breaks apart via azimuthal instabilities at $Re \approx 4500$.

physics.flu-dyn↗

arXiv2021

How attractive and repulsive interactions affect structure ordering and dynamics of glass-forming liquids?

The theory developed in our previous papers is applied in this paper to investigate the dependence of slowing down of dynamics of glass-forming liquids on the attractive and repulsive parts of intermolecular interactions. Through an extensive comparison of the behavior of a Lennard-Jones glass-forming liquid and that of its WCA reduction to a model with truncated pair potential without attractive tail, we demonstrate why the two systems exhibit very different dynamics despite having nearly identical pair correlation functions. In particular, we show that local structures characterized by number of mobile and immobile particles around a central particle markedly differ in the two systems at densities and temperatures where their dynamics show large difference and nearly identical where dynamics nearly overlap. We also show how the parameter ψ(T ) that measures the role of fluctuations embedded in the system on size of the cooperatively reorganizing cluster (CRC) and the crossover temperature T a depend on the intermolecular interactions. These parameters stemming from the intermolecular interactions characterize the temperature and density dependence of structural relaxation time τ α. The quantitative and qualitative agreements found with simulation results for the two systems suggest that our theory brings out the underlying features that determine dynamics of glass-forming liquids.

cond-mat.soft↗

arXiv2020

Emergence of cooperatively reorganizing cluster and super-Arrhenius dynamics of fragile supercooled liquids

In this paper we develop a theory to calculate the structural relaxation time τ α of fragile su percooled liquids. Using the information of the configurational entropy and structure we calculate the number of dynamically free, metastable, and stable neighbors around a central particle. In supercooled liquids the cooperatively reorganizing clusters (CRCs) in which the stable neighbors form stable nonchemical bonds with the central particle emerge. For an event of relaxation to take place these bonds have to reorganize irreversibly; the energy involved in the processes is the effective activation energy of relaxation. The theory brings forth a temperature T a and a temper ature dependent parameter ψ(T ) which characterize slowing down of dynamics on cooling. It is shown that the value of ψ(T ) is equal to 1 for T > T a indicating that the underlying microscopic mechanism of relaxation is dominated by the entropy driven processes while for T < T a , ψ(T ) decreases on cooling indicating the emergence of the energy driven processes. This crossover of ψ(T ) from high to low temperatures explains the crossover seen in τ α . The dynamics of systems that may have similar static structure but very different dynamics can be understood in terms of ψ(T ). We present results for the Kob-Anderson model for three densities and show that the calculated values of τ α are in excellent agreement with simulation values for all densities. We also show that when ψ(T ), τ α and other quantities are plotted as a function of T /T a (or T a /T ) the data collapse on master curves.

cond-mat.soft↗

arXiv2020

The solvent mediated interaction potential between solute particles: Theory and applications

In this paper we develop a theory to calculate the solvent mediated interaction potential between solute particles dispersed in a solvent. The potential is a functional of the instantaneous distribution of solute particles and is expressed in terms of the solute-solvent direct pair correlation function and the density-density correlation function of the bulk solvent. The dependence of the direct pair correlation function on multi-point correlations of the solute distribution is simplified with a mean field approximation. A self consistent approach is developed to calculate the effective potential between solute particles, the solute-solvent and the solute-solute correlation functions. The significance of the solvent fluctuations on the range of the effective potential is elucidated. The theory is applied to calculate equilibrium properties of the Asakura-Oosawa (AO) model for several values of solute and solvent densities and for several values of the particles size ratio. The results give a quantitative description of many-body effect on the effective potential and on the pair correlation functions.

cond-mat.soft↗

arXiv2019

Understanding the phenomenon of viscous slowing down of glass-forming liquids from the static pair correlation function

A theory which uses data of the static pair-correlation function is developed to calculate quantities associated with the viscous slowing down of supercooled liquids. We calculate value of the energy fluctuations that determine the number of stable bonds a particle forms with neighbors from data of the structural relaxation time. The number of bonds and the activation energy for relaxation are shown to increase sharply in a narrow temperature range close to the glass temperature. The configurational entropy calculated from values of the configurational fluctuations is found in good agreement with the value determined from simulations.

cond-mat.stat-mech↗

arXiv2019

Super-Arrhenius behaviour of molecular glass formers

A theory is developed to calculate values of the potential energy barriers to structural relaxation in molecular glass formers from the data of static pair correlation function. The barrier height is shown to increase due to increase in number of the stable bonds a particle forms with its neighbours and energy of each bond as liquids move deeper into the supercooled (super-compressed) region. We present results for a system of hard-spheres and compare calculated values of the structural relaxation time with experimental and simulation results.

cond-mat.soft↗

arXiv2014

Fluid - solid transition in simple systems using density functional theory

A free energy functional for a crystal proposed by Singh and Singh (Europhysics Letters \textbf{88}, 16005 (2009)) which contains both the symmetry-conserved and symmetry-broken parts of the direct pair correlation function has been used to investigate the fluid-solid transition in systems interacting via purely repulsive WCA Lennard - Jones (RLJ) potential and the full Lennard - Jones (LJ) potential. The results found for freezing parameters for the fluid - face centred cubic (fcc) crystal transition are in very good agreement with simulation results. It is shown that although the contribution made by the symmetry broken part to the grand thermodynamic potential at the freezing point is small compared to that of the symmetry conserving part, its role is crucial in stabilizing the crystalline structure and on values of freezing parameters. The effect of attractive part of the LJ potential on the freezing parameters is found to be small, confirming the view that the fluid - solid transition is primarily determined by the repulsive part of the potential.

cond-mat.soft↗

arXiv2014

Integral Equation Theory for Pair Correlation Functions in a Crystal

A method for calculating pair correlation functions in a crystal is developed. The method is based on separating the one- and two- particle correlation functions into the symmetry conserving and the symmetry broken parts. The conserving parts are calculated using the integral equation theory of homogeneous fluids. The symmetry broken part of the direct pair correlation function is calculated from a series written in powers of order parameters and that of the total pair correlation function from the Ornstein- Zernike equation. The results found for a two-dimensional hexagonal lattice show that the method provides accurate and detailed informations about the pair correlation functions in a crystal.

cond-mat.soft↗

arXiv2013

Correlation functions in liquids and crystals : Free energy functional and liquid - crystal transition

A free energy functional for a crystal that contains both the symmetry conserved and symmetry broken parts of the direct pair correlation function has been used to investigate the crystallization of fluids in three-dimensions. The symmetry broken part of the direct pair correlation function has been calculated using a series in ascending powers of the order parameters and which contains three- and higher-bodies direct correlation functions of the isotropic phase. It is shown that a very accurate description of freezing transitions for a wide class of potentials is found by considering the first two terms of this series. The results found for freezing parameters including structure of the frozen phase for fluids interacting via the inverse power potential u(r) = ε(σ/r)^{n} for n ranging from 4 to \infty are in very good agreement with simulation results. It is found that for n > 6.5 the fluid freezes into a face centred cubic (fcc) structure while for n \leq 6 the body centred cubic (bcc) structure is preferred. The fluid-bcc-fcc triple point is found to be at 1/n = 0.158 which is in good agreement with simulation result.

cond-mat.soft↗

arXiv2012

Freezing of a two dimensional fluid in to a crystalline phase : Density functional approach

A free-energy functional for a crystal proposed by Singh and Singh (Europhys. Lett. {\bf {88}}, 16005 (2009)) and which contains both the symmetry conserved and symmetry broken parts of the direct pair correlation function has been used to investigate the crystallization of a two-dimensional fluid. The results found for fluids interacting via the inverse power potential $ u(r)= ε(σ/{r})^{n} $ for n= 3, 6 and 12 are in good agreement with experimental and simulation results. The contribution made by the symmetry broken part to the grand thermodynamic potential at the freezing point is found to increase with the softness of the potential. Our results explain why the Ramakrishnan-Yussouff (Phys. Rev. B {\bf 19}, 2775 (1979)) free-energy functional gave good account of freezing transitions of hard-core potentials but failed for potentials that have soft core and/or attractive tail.

cond-mat.soft↗

arXiv2011

Shear unzipping of double stranded DNA

We propose a simple nonlinear scaler displacement model to calculate the distribution of effect created by a shear stress on a double stranded DNA (dsDNA) molecule and the value of shear force $F_c$ which is required to separate the two strands of a molecule. It is shown that as long as the force pulls entire strand in the direction of its application the value of $F_c$ depends linearly on the length; the deviation from linear behaviour takes place when part of a strand moves in opposite direction under the influence of force acting on the other strand. The calculated values of $F_c$ as a function of length of dsDNA molecules are in very good agreement with the experimental values of Hatch et al (Phys. Rev. E $\bf 78$, 011920 (2008)).

cond-mat.soft↗

arXiv2011

Free-energy functional for freezing transitions: Hard sphere systems freezing into crystalline and amorphous structures

A free-energy functional that contains both the symmetry conserved and symmetry broken parts of the direct pair correlation function has been used to investigate the freezing of a system of hard spheres into crystalline and amorphous structures. The freezing parameters for fluid-crystal transition have been found to be in very good agreement with the results found from simulations. We considered amorphous structures found from the molecular dynamics simulations at packing fractions $η$ lower than the glass close packing fraction $η_{J}$ and investigated their stability compared to that of a homogeneous fluid. The existence of free-energy minimum corresponding to a density distribution of overlapping Gaussians centered around an amorphous lattice depicts the deeply supercooled state with a heterogeneous density profile.

cond-mat.soft↗

arXiv2009

Partition function of a bubble formed in double stranded DNA

We calculate the entropic part of partition function of a bubble embedded in a double stranded DNA (dsDNA) by considering the total weights of possible configurations of a system of two single stranded DNA (ssDNA) of given length which start from a point along the contour of dsDNA and reunite at a position vector {\bf r} measured from the first point and the distribution function of the position vector {\bf r} which separates the two zipper forks of the bubble in dsDNA. For the distribution function of position vector {\bf r} we use the distribution of the end-to-end vector {\bf r} of strands of given length of dsDNA found from the wormlike chain model. We show that when the chains forming the bubble are assumed to be Gaussian the so called loop closure exponent $c$ is 3 and when we made correction by including self avoidence in each chain the value of $c$ becames 3.2.

cond-mat.soft↗

arXiv2009

Crystallization of Simple Fluids: Relative Stability of f.c.c. and b.c.c Structures

A free-energy functional for a crystal that contains both the symmetry conserved and symmetry broken parts of the direct pair correlation function is developed. The free-energy functional is used to investigate the crystallization of fluids interacting via the inverse power potential ; $u(r)=ε{(σ/r)}^n$. In agreement with simulation results we find that for $n=12$ the freezing is into close packed f.c.c structure while for soft repulsions $(n\leq 6)$ b.c.c phase is more stable.

cond-mat.soft↗

arXiv2008

Dynamics of a bubble formed in double stranded DNA

We study the fluctuational dynamics of a tagged base-pair in double stranded DNA. We calculate the drift force which acts on the tagged base-pair using a potential model that describes interactions at base pairs level and use it to construct a Fokker-Planck equation.The calculated displacement autocorrelation function is found to be in very good agreement with the experimental result of Altan-Bonnet {\it et. al.} Phys. Rev. Lett. {\bf 90}, 138101 (2003) over the entire time range of measurement. We calculate the most probable displacements which predominately contribute to the autocorrelation function and the half-time history of these displacements.

cond-mat.soft↗

arXiv2008

On the generalization of Gurland distribution

In the present paper a generalization of Gurland distribution [3] is obtained as a beta mixture of the generalized Poisson distribution (GPD) of Consul and Jain [2]. The first two moments of the distribution and a recurrence relation among probabilities are obtained. The present distribution is supposed to be more general in nature and wider in scope.

math.ST↗