arXiv subjects

R. Rajesh

Publications and source records attributed to R. Rajesh.

At least 73 records · Page 4Linked to original sources

arXiv2015

Aggregation Dynamics of Rigid Polyelectrolytes

Similarly-charged polyelectrolytes are known to attract each other and aggregate into bundles when the charge density of the polymers exceeds a critical value that depends on the valency of the counterions. The dynamics of aggregation of such rigid polyelectrolytes are studied using large scale molecular dynamics simulations. We find that the morphology of the aggregates depends on the value of the charge density of the polymers. For values close to the critical value, the shape of the aggregates is cylindrical with height equal to the length of a single polyelectrolyte chain. However, for larger values of charge, the linear extent of the aggregates increases as more and more polymers aggregate.In both the cases, we show that the number of aggregates decrease with time as power laws with exponents that are not numerically distinguishable from each other, and are independent of charge density of the polymers, valency of the counterions, density, and length of the polyelectrolyte chain. We model the aggregation dynamics using the Smoluchowski coagulation equation with kernels determined from the molecular dynamics simulations, and justify the numerically obtained value of the exponent. Our results suggest that, once counterions condense, effective interactions between polyelectrolyte chains short-ranged and the aggregation of polyelectrolytes is diffusion-limited.

cond-mat.soft↗

arXiv2015

Phase transitions in systems of hard rectangles with non-integer aspect ratio

We investigate, using Monte Carlo simulations, the phase diagram of a system of hard rectangles of size $m\times mk$ on a square lattice when the aspect ratio $k$ is a non-integer. The existence of a disordered isotropic phase, a nematic with only orientational order, a columnar phase with orientational and partial translational order, and a high density phase with no orientational order is shown. The high density phase is a solid-like sublattice phase only if the length and width of the rectangles are not mutually prime, else, it is an isotropic phase. The minimum value of $k$ beyond which the nematic and columnar phases exist are determined for $m=2$ and $3$. The nature of the transitions between different phases is determined, and the critical exponents are numerically obtained for the continuous transitions.

cond-mat.stat-mech↗

arXiv2014

Polydispersed rods on the square lattice

We study the grand-canonical solution of a system of hard polydispersed rods placed on the square lattice using transfer matrix and finite size scaling calculations. We determine the critical line separating an isotropic from a nematic phase. No second transition to a disordered phase is found at high density, contrary to what is observed in the monodispersed case. The estimates of critical exponents and the central charge on the critical line are consistent with the Ising universality class.

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

Asymptotic Behavior of the Isotropic-Nematic and Nematic-Columnar Phase Boundaries for the System of Hard Rectangles on a Square lattice

A system of hard rectangles of size $m\times mk$ on a square lattice undergoes three entropy driven phase transitions with increasing density for large enough aspect ratio $k$: first from a low density isotropic to an intermediate density nematic phase, second from the nematic to a columnar phase, and third from the columnar to a high density sublattice phase. In this paper we show, from extensive Monte Carlo simulations of systems with $m=1,2$ and $3$, that the transition density for the isotropic-nematic transition is $\approx A_1/k$ when $k \gg 1$, where $A_1$ is independent of $m$. We estimate $A_1=4.80\pm 0.05$. Within a Bethe approximation, we obtain $A_1=2$ and the virial expansion truncated at second virial coefficient gives $A_1=1$. The critical density for the nematic-columnar transition when $m=2$ is numerically shown to tend to a value less than the full packing density as $k^{-1}$ when $k\to \infty$. We find that the critical Binder cumulant for this transition is non-universal and decreases as $k^{-1}$ for $k \gg 1$. However, the transition is shown to be in the Ising universality class.

cond-mat.stat-mech↗

arXiv2014

Inhomogeneous Cooling of the Rough Granular Gas in Two Dimensions

We study the inhomogeneous clustered regime of a freely cooling granular gas of rough particles in two dimensions using large-scale event driven simulations and scaling arguments. During collisions, rough particles dissipate energy in both the normal and tangential directions of collision. In the inhomogeneous regime, translational kinetic energy and the rotational energy decay with time $t$ as power-laws $t^{-θ_T}$ and $t^{-θ_R}$. We numerically determine $θ_T \approx 1$ and $θ_R \approx 1.6$, independent of the coefficients of restitution. The inhomogeneous regime of the granular gas has been argued to be describable by the ballistic aggregation problem, where particles coalesce on contact. Using scaling arguments, we predict $θ_T=1$ and $θ_R=1$ for ballistic aggregation, $θ_R$ being different from that obtained for the rough granular gas. Simulations of ballistic aggregation with rotational degrees of freedom are consistent with these exponents.

cond-mat.soft↗

arXiv2014

Phase transitions in a system of hard rectangles on the square lattice

The phase diagram of a system of monodispersed hard rectangles of size $m\times m k$ on a square lattice is numerically determined for $m=2,3$ and aspect ratio $k= 1,2,\ldots, 7$. We show the existence of a disordered phase, a nematic phase with orientational order, a columnar phase with orientational and partial translational order, and a solid-like phase with sublattice order, but no orientational order. The asymptotic behavior of the phase boundaries for large $k$ are determined using a combination of entropic arguments and a Bethe approximation. This allows us to generalize the phase diagram to larger $m$ and $k$, showing that for $k \geq 7 $, the system undergoes three entropy driven phase transitions with increasing density. The nature of the different phase transitions are established and the critical exponents for the continuous transitions are determined using finite size scaling.

cond-mat.stat-mech↗

arXiv2014

Force fluctuations in stretching a tethered polymer

The recently proposed fluctuation relation in unfolding forces [Phys. Rev. E ${\bf 84}$, $060101$(R) $(2011)$] is re-examined taking into account the explicit time dependence of the force distribution. The stretching of a tethered Rouse polymer is exactly solved and the ratio of the probabilities of positive to negative forces is shown to be an exponential in force. Extensive steered molecular dynamics simulations of unfolding of deca alanine peptide confirm the form of fluctuation relation proposed earlier, but with explicit correct time dependence of unfolding forces taken into account. From exact calculations and simulations, a linear dependence of the constant in the exponential of the fluctuation relation on average unfolding forces and inverse temperature is proposed.

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↗

arXiv2014

On Secrecy above Secrecy Capacity

We consider secrecy obtained when one transmits on a Gaussian Wiretap channel above the secrecy capacity. Instead of equivocation, we consider probability of error as the criterion of secrecy. The usual channel codes are considered for transmission. The rates obtained can reach the channel capacity. We show that the "confusion" caused to the Eve when the rate of transmission is above capacity of the Eve's channel is similar to the confusion caused by using the wiretap channel codes used below the secrecy capacity.

cs.IT↗

arXiv2013

Energy decay in three-dimensional freely cooling granular gas

The kinetic energy of a freely cooling granular gas decreases as a power law $t^{-θ}$ at large times $t$. Two theoretical conjectures exist for the exponent $θ$. One based on ballistic aggregation of compact spherical aggregates predicts $θ= 2d/(d+2)$ in $d$ dimensions. The other based on Burgers equation describing anisotropic, extended clusters predicts $θ=d/2$ when $2\le d \le 4$. We do extensive simulations in three dimensions to find that while $θ$ is as predicted by ballistic aggregation, the cluster statistics and velocity distribution differ from it. Thus, the freely cooling granular gas fits to neither the ballistic aggregation or a Burgers equation description.

cond-mat.soft↗

arXiv2013

Re-entrant Disordered Phase in a System of Repulsive Rods on a Bethe-like Lattice

We solve exactly a model of monodispersed rigid rods of length $k$ with repulsive interactions on the random locally tree like layered lattice. For $k\geq 4$ we show that with increasing density, the system undergoes two phase transitions: first from a low density disordered phase to an intermediate density nematic phase and second from the nematic phase to a high density re-entrant disordered phase. When the coordination number is $4$, both the phase transitions are continuous and in the mean field Ising universality class. For even coordination number larger than $4$, the first transition is discontinuous while the nature of the second transition depends on the rod length $k$ and the interaction parameters.

cond-mat.stat-mech↗

arXiv2013

The nematic-disordered phase transition in systems of long rigid rods on two dimensional lattices

We study the phase transition from a nematic phase to a high-density disordered phase in systems of long rigid rods of length $k$ on the square and triangular lattices. We use an efficient Monte Carlo scheme that partly overcomes the problem of very large relaxation times of nearly jammed configurations. The existence of a continuous transition is observed on both lattices for $k=7$. We study correlations in the high-density disordered phase, and we find evidence of a crossover length scale $ξ^* \gtrsim 1400$, on the square lattice. For distances smaller than $ξ^*$, correlations appear to decay algebraically. Our best estimates of the critical exponents differ from those of the Ising model, but we cannot rule out a crossover to Ising universality class at length scales $\gg ξ^*$. On the triangular lattice, the critical exponents are consistent with those of the two dimensional three-state Potts universality class.

cond-mat.stat-mech↗

arXiv2012

Comment on "Growth Inside a Corner: The Limiting Interface Shape"

We examine the conjectured asymptotic shape of the three dimensional corner growth model [Olejarz et. al.,PRL, 108, 016102 (2012)] by mapping the model onto a restricted solid on solid model on a triangular lattice. By choosing appropriate boundary conditions, we are able to obtain high precision numerical results for the growth velocity using Monte Carlo simulations. We find that the numerical results are not consistent with the conjecture.

cond-mat.stat-mech↗

arXiv2012

Aggregation of rod-like polyelectrolyte chains in the presence of monovalent counterions

Using molecular dynamics simulations, it is demonstrated that monovalent counterions can induce aggregation of similarly charged rod-like polyelectrolyte chains. The critical value of the linear charge density for aggregation is shown to be close to the critical value for the extended-collapsed transition of a single flexible polyelectrolyte chain, and decreases with increasing valency of the counterions. The effective interaction potential between two rod-like polyelectrolyte chains is measured, and is related to the angular distribution of the condensed counterions.

cond-mat.soft↗

arXiv2012

Quasi-Orthogonal Space-Time-Frequency Trellis Codes for MIMO-OFDM Systems

The main objective of this project is to design the full-rate Space-Time-Frequency Trellis code (STFTC), which is based on Quasi-Orthogonal designs for Multiple-Input Multiple-Output (MIMO) Orthogonal Frequency Division Multiplexing (OFDM) systems. The proposed Quasi-Orthogonal Space-Time-Frequency Trellis code combines set partitioning and the structure of quasi-orthogonal space-frequency designs in a systematic way. In addition to multipath diversity and transmit diversity, the proposed code provides receive diversity, array gain, and achieve high-coding gain over a frequency selective fading channel. As simulation results demonstrate, the code outperforms the existing Quasi-Orthogonal Space-Time-Frequency Trellis codes in terms of frame error rate performance.

cs.IT↗

arXiv2012

Collective oscillations in driven coagulation

We present a novel form of collective oscillatory behavior in the kinetics of irreversible coagulation with a constant input of monomers and removal of large clusters. For a broad class of collision rates, this system reaches a non-equilibrium stationary state at large times and the cluster size distribution tends to a universal form characterised by a constant flux of mass through the space of cluster sizes. Universality, in this context, means that the stationary state becomes independent of the cut-off as the cut-off grows. This universality is lost, however, if the aggregation rate between large and small clusters increases sufficiently steeply as a function of cluster sizes. We identify a transition to a regime in which the stationary state vanishes as the cut-off grows. This non-universal stationary state becomes unstable, however, as the cut-off is increased and undergoes a Hopf bifurcation. After this bifurcation, the stationary kinetics are replaced by persistent and periodic collective oscillations. These oscillations carry pulses of mass through the space of cluster sizes. As a result, the average mass flux remains constant. Furthermore, universality is partially restored in the sense that the scaling of the period and amplitude of oscillation is inherited from the dynamical scaling exponents of the universal regime. The implications of this new type of long-time asymptotic behaviour for other driven non-equilibrium systems are discussed.

cond-mat.stat-mech↗

arXiv2012

Spatial Structures and Giant Number Fluctuations in Models of Active Matter

The large scale fluctuations of the ordered state in active matter systems are usually characterised by studying the "giant number fluctuations" of particles in any finite volume, as compared to the expectations from the central limit theorem. However, in ordering systems, the fluctuations in density ordering are often captured through their structure functions deviating from Porod law. In this paper we study the relationship between giant number fluctuations and structure functions, for different models of active matter as well as other non-equilibrium systems. A unified picture emerges, with different models falling in four distinct classes depending on the nature of their structure functions. For one class, we show that experimentalists may find Porod law violation, by measuring subleading corrections to the number fluctuations.

cond-mat.soft↗