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J Chowdhary

Publications and source records attributed to J Chowdhary.

7 recordsLinked to original sources
PubMed2004

Potential-energy-landscape-based extended van der Waals equation.

The inherent structures (IS) are the local minima of the 3N-dimensional potential energy surface, or landscape, of an N-atom system. Stillinger has given an exact IS formulation of thermodynamics. Here the implications for the equation of state are investigated. It is shown that the van der Waals (vdW) equation, with density-dependent a and b coefficients, holds if the averaged IS energy is close to its high-temperature plateau value. The density-dependence alone significantly enriches the equation of state. Furthermore, an additional "landscape" contribution to the pressure is found at lower T. The resulting extended vdW equation is capable of yielding a waterlike density anomaly, flat isotherms in the coexistence region vs vdW loops, and several other desirable features. The plateau IS energy, the width of the distribution of IS, and T(TOL), the "top of the landscape" temperature at which the plateau is reached, are simulated over a broad reduced density range, 2.0>or=rho>or=0.20, in the Lennard-Jones fluid. Fits to the data yield an explicit equation of state, which is argued to be plausible at high density. Nevertheless, a(rho(c)) and b(rho(c)), where rho(c) is the critical density, are in excellent agreement with the standard values obtained by fitting the vdW equation at the critical point.

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PubMed2002

Random energy model for dynamics in supercooled liquids: N dependence.

The random energy model (REM) for the critical points (saddles and minima) of the potential energy landscape of liquids is further developed. While thermodynamic properties may be calculated from the unconditional distribution of states G(E), dynamics requires the distribution G(c)(E';E) of energies E' of neighbors connected to a state with energy E. Previously it was shown [T. Keyes, Phys. Rev. E 62, 7905 (2000)] that an uncorrelated REM, G(c)(E';E)=G(E'), is badly behaved in the thermodynamic limit N--> infinity. In the following, a simple expression is obtained for G(c)(E';E), which leads to reasonable N dependences. Results are obtained for the fraction f(u) of imaginary-frequency instantaneous normal modes, the configuration entropy S(c), the distributions of the different-order critical points, and the rate R of escape from a state. Simulation data on f(u)(T) and the density of minima rho(0)(E) in Lennard-Jones and CS2 are fit with the theory, allowing a determination of some model parameters. A universal scaling form for f(u), and a consequent scheme for calculating the mode-coupling temperature T(c) consistently among different materials, is demonstrated. The dependence of the self-diffusion constant D upon R and f(u) is discussed, with the conclusion that D proportional, variant f(u) in deeply supercooled states. The phenomenology of fragile supercooled liquids is interpreted. It is shown that the REM need not have a Kauzmann transition in the relevant temperature range, i.e., above the glass transition.

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PubMed2002

Potential energy landscape and mechanisms of diffusion in liquids.

The mechanism of diffusion in supercooled liquids is investigated from the potential energy landscape point of view, with emphasis on the crossover from high- to low-T dynamics over the range T(A) > or =T > or =T(c). Molecular dynamics simulations with a time dependent mapping to the associated local minimum or inherent structure (IS) are performed on unit-density Lennard-Jones. Dynamical quantities introduced include r2(is)(t), the mean-square displacement (MSD) within a basin of attraction of an IS, R2(t), the MSD of the IS itself, and g(t), the distribution of IS waiting times. The configuration space is treated as a composite of the contributions of cooperative local regions, and a method is given to obtain the physically meaningful g(loc)(t) and mean waiting time tau(loc) from g(t). An understanding of the crossover is obtained in terms of r2(is)(t) and tau(loc). At intermediate T, r2(is)(t) possesses an interval of linear t dependence allowing calculation of an intrabasin diffusion constant D(is). Near T(c), where intrabasin diffusion is well established for t<tau(loc), diffusion is intrabasin dominated with D=D(is); D may be calculated within a basin. Below T(c), tau(loc) exceeds the time tau(pl) needed for the system to explore the basin, indicating the action of barriers at the border; tau(loc)=tau(pl) is a criterion for transition to activated hopping. Intrabasin diffusion provides a means of confinement not involving barriers and plays a key role in the dynamics above T(c). The distinction is discussed between motion among the IS (IS dynamics) below T(c) and saddle or border dynamics above T(c), where the system is always close to one of the saddle barriers connecting the basins and IS boundaries are closely spaced and easily crossed. A border index is introduced based upon the relation of R2(t) to the conventional MSD, and shown to vanish at T approximately T(c). It is proposed that intrabasin diffusion is a manifestation of saddle dynamics.

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PubMed2002

Conjugate gradient filtering of instantaneous normal modes, saddles on the energy landscape, and diffusion in liquids.

Instantaneous normal modes (INM's) are calculated during a conjugate-gradient (CG) descent of the potential energy landscape, starting from an equilibrium configuration of a liquid or crystal. A small number (approximately equal to 4) of CG steps removes all the Im-omega modes in the crystal and leaves the liquid with diffusive Im-omega which accurately represent the self-diffusion constant D. Conjugate gradient filtering appears to be a promising method, applicable to any system, of obtaining diffusive modes and facilitating INM theory of D. The relation of the CG-step dependent INM quantities to the landscape and its saddles is discussed.

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PubMed2001

Inherent-structure dynamics and diffusion in liquids.

The self-diffusion constant D is expressed in terms of transitions among the local minima (inherent structures, IS) of the N-body potential-energy surface or landscape, and their correlations. The formulas are evaluated and tested against simulation in the supercooled, unit-density Lennard-Jones liquid. The approximation of uncorrelated IS-transition (IST) vectors D0, greatly exceeds D for the highest T, but merges with simulation at reduced T approximately 0.50, close to the estimated mode-coupling temperature T(c). Since uncorrelated IST's are associated with a hopping mechanism, the condition D approximately D0 provides a new way to identify the crossover to hopping. The results suggest that theories of diffusion in deeply supercooled liquids may be based on weakly correlated IST's.

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