arXiv subjects

Trisha Nath

Publications and source records attributed to Trisha Nath.

8 recordsLinked to original sources

arXiv2018

Rheology in dense assemblies of spherocylinders: frictional vs. frictionless

Using molecular dynamics simulations, we study the steady shear flow of dense assemblies of anisotropic spherocylindrical particles of varying aspect ratios. Comparing frictionless and frictional particles we discuss the specific role of frictional inter-particle forces for the rheological properties of the system. In the frictional system we evidence a shear-thickening regime, similar to that for spherical particles. Furthermore, friction suppresses alignment of the spherocylinders along the flow direction. Finally, the jamming density in frictional systems is rather insensitive to variations in aspect-ratio, quite contrary to what is known from frictionless systems.

cond-mat.soft↗

arXiv2017

Phase transitions in a system of hard $Y$-shaped particles on the triangular lattice

We study the different phases and the phase transitions in a system of $Y$-shaped particles, examples of which include Immunoglobulin-G and trinaphthylene molecules, on a triangular lattice interacting exclusively through excluded volume interactions. Each particle consists of a central site and three of its six nearest neighbours chosen alternately, such that there are two types of particles which are mirror images of each other. We study the equilibrium properties of the system using grand canonical Monte Carlo simulations that implements an algorithm with cluster moves that is able to equilibrate the system at densities close to full packing. We show that, with increasing density, the system undergoes two entropy-driven phase transitions with two broken-symmetry phases. At low densities, the system is in a disordered phase. As intermediate phases, there is a solid-like sublattice phase in which one type of particle is preferred over the other and the particles preferentially occupy one of four sublattices, thus breaking both particle-symmetry as well as translational invariance. At even higher densities, the phase is a columnar phase, where the particle-symmetry is restored, and the particles preferentially occupy even or odd rows along one of the three directions. This phase has translational order in only one direction, and breaks rotational invariance. From finite size scaling, we demonstrate that both the transitions are first order in nature. We also show that the simpler system with only one type of particles undergoes a single discontinuous phase transition from a disordered phase to a solid-like sublattice phase with increasing density of particles.

cond-mat.stat-mech↗

arXiv2017

Estimating the Critical Parameters of the Hard Square Lattice Gas Model

The hard square lattice gas model on a square lattice is known to undergo a continuous phase transition from a low density fluid-like phase to high density phase with columnar or smectic order. We estimate the critical activity $z_c$ by calculating, within an approximation scheme, the interfacial tension between two differently ordered columnar phases, and then setting it to zero. The approximation scheme allows for the ordered phases to have multiple defects and the interface between the ordered phases to have overhangs. We estimate $z_c=105.35$, which is in good agreement with existing Monte Carlo simulation results of $z_c \approx 97.5$, and is an improvement over earlier best estimates of $z_c=54.87$ and $z_c=135.63$.

cond-mat.stat-mech↗

arXiv2016

The High Density Phase of the $k$-NN Hard Core Lattice Gas Model

The $k$-NN hard core lattice gas model on a square lattice, in which the first $k$ next nearest neighbor sites of a particle are excluded from being occupied by another particle, is the lattice version of the hard disc model in two dimensional continuum. It has been conjectured that the lattice model, like its continuum counterpart, will show multiple entropy-driven transitions with increasing density if the high density phase has columnar or striped order. Here, we determine the nature of the phase at full packing for $k$ up to $820302$. We show that there are only eighteen values of $k$, all less than $k=4134$, that show columnar order, while the others show solid-like sublattice order.

cond-mat.stat-mech↗

arXiv2016

Stability of columnar order in assemblies of hard rectangles or squares

A system of $2\times d$ hard rectangles on square lattice is known to show four different phases for $d \geq 14$. As the covered area fraction $ρ$ is increased from $0$ to $1$, the system goes from low-density disordered phase, to orientationally-ordered nematic phase, to a columnar phase with orientational order and also broken translational invariance, to a high density phase in which orientational order is lost. For large d, the threshold density for the first transition $ρ_1^*$ tends to $0$, and the critical density for the third transition $ρ_3^*$ tends to $1$. Interestingly, simulations have shown that the critical density for the second transition $ρ_2^*$ tends to a non-trivial finite value $\approx 0.73$, as $d \rightarrow \infty$, and $ρ_2^* \approx 0.93$ for $d=2$. We provide a theoretical explanation of this interesting result. We develop an approximation scheme to calculate the surface tension between two differently ordered columnar phases. The density at which the surface tension vanishes gives an estimate $ρ_2^* = 0.746$, for $d\to \infty$, and $ρ_2^*=0.923$ for $d=2$. For all values of $d$, these estimates are in good agreement with Monte Carlo data.

cond-mat.stat-mech↗

arXiv2014

High-Activity Expansion for the Columnar Phase of the Hard Rectangle Gas

We study a system of monodispersed hard rectangles of size $m \times d$, where $d\geq m$ on a two dimensional square lattice. For large enough aspect ratio, the system is known to undergo three entropy driven phase transitions with increasing activity $z$: first from disordered to nematic, second from nematic to columnar and third from columnar to sublattice phases. We study the nematic-columnar transition by developing a high-activity expansion in integer powers of $z^{-1/d}$ for the columnar phase in a model where the rectangles are allowed to orient only in one direction. By deriving the exact expression for the first $d+2$ terms in the expansion, we obtain lower bounds for the critical density and activity. For $m$, $k\gg 1$, these bounds decrease with increasing $k$ and decreasing $m$.

cond-mat.stat-mech↗

arXiv2014

Multiple Phase Transitions in Extended Hard Core Lattice Gas Models in Two Dimensions

We study the $k$-NN hard core lattice gas model in which the first $k$ next nearest neighbor sites of a particle are excluded from occupation by other particles on a two dimensional square lattice. This model is the lattice version of the hard disc system with increasing $k$ corresponding to decreasing lattice spacing. While the hard disc system is known to undergo a two step freezing process with increasing density, the lattice model has been known to show only one transition. Here, based on Monte Carlo simulations and high density expansions of the free energy and density, we argue that for $k=4,10,11,14...$, the lattice model undergoes multiple transitions with increasing density. Using Monte Carlo simulations, we confirm the same for $k=4,\ldots, 11$. This, in turn, resolves an existing puzzle as to why the 4-NN model has a continuous transition against the expectation of a first order transition.

cond-mat.stat-mech↗

arXiv2012

Splitting of degenerate states in one-dimensional quantum mechanics

A classic no-go theorem in one-dimensional quantum mechanics can be evaded when the potentials are unbounded below, thus allowing for novel parity-paired degenerate energy bound states. We numerically determine the spectrum of one such potential and study the parametric variation of the transition wavelength between a bound state lying inside the valley of the potential and another, von Neumann-Wigner-like state, appearing above the potential maximum. We then construct a modified potential which is bounded below except when a parameter is tuned to vanish. We show how the spacing between certain energy levels gradually decreases as we tune the parameter to approach the value for which unboundedness arises, thus quantitatively linking the closeness of degeneracy to the steepness of the potential. Our results are generic to a large class of such potentials. Apart from their conceptual interest, such potentials might be realisable in mesoscopic systems thus allowing for the experimental study of the novel states. The numerical spectrum in this study is determined using the asymptotic iteration method which we briefly review.

quant-ph↗