arXiv subjects

R. Rajesh

Publications and source records attributed to R. Rajesh.

At least 91 records · Page 5Linked to original sources

arXiv2012

Shock Propagation in Granular Flow Subjected to an External Impact

We analyze a recent experiment [Phys. Rev. Lett., {\bf103}, 224501 (2009)] in which the shock, created by the impact of a steel ball on a flowing monolayer of glass beads, is quantitatively studied. We argue that radial momentum is conserved in the process, and hence show that in two dimensions the shock radius increases in time $t$ as a power law $t^{1/3}$. This is confirmed in event driven simulations of an inelastic hard sphere system. The experimental data are compared with the theoretical prediction, and is shown to compare well at intermediate times. At late times, the experimental data exhibit a crossover to a different scaling behavior. We attribute this to the problem becoming effectively three dimensional due to accumulation of particles at the shock front, and propose a simple hard sphere model which incorporates this effect. Simulations of this model capture the crossover seen in the experimental data.

cond-mat.soft↗

arXiv2011

Capacity of Fading Gaussian Channel with an Energy Harvesting Sensor Node

Network life time maximization is becoming an important design goal in wireless sensor networks. Energy harvesting has recently become a preferred choice for achieving this goal as it provides near perpetual operation. We study such a sensor node with an energy harvesting source and compare various architectures by which the harvested energy is used. We find its Shannon capacity when it is transmitting its observations over a fading AWGN channel with perfect/no channel state information provided at the transmitter. We obtain an achievable rate when there are inefficiencies in energy storage and the capacity when energy is spent in activities other than transmission.

cs.IT↗

arXiv2011

Ensemble Equivalence for Counterion Condensation on a Two Dimensional Charged Disc

We study the counterion condensation on a two dimensional charged disc in the limit of infinite dilution, and compare the energy-temperature relation obtained from the canonical free energy and microcanonical entropy. The microcanonical entropy is piecewise linear in energy, and is shown to be concave for all energies. As a result, even though the interactions are long-ranged, the energy-temperature relation and hence the counterion condensation transition points are identical in both the ensembles.

cond-mat.stat-mech↗

arXiv2011

Phase transitions of a single polyelectrolyte in a poor solvent with explicit counterions

Conformational properties of a single flexible polyelectrolyte chain in a poor solvent are studied using constant temperature molecular dynamics simulation. The effects of counterions are explicitly taken in to account. Structural properties of various phases and the transition between these phases are studied by tracking the values of asphericity, radius of gyration, fraction of condensed counterions, number of non-bonded neighbours and Coulomb interaction energies. From our simulations, we find strong evidence for a first-order phase transition from extended to collapsed phase consistent with earlier theoretical predictions. We also identify a continuous phase transition associated with the condensation of counterions and estimate the critical exponents associated with the transition. Finally, we argue that previous suggestions of existence of an independent intermediate phase between extended and collapsed phases is only a finite size effect.

cond-mat.stat-mech↗

arXiv2011

Thermodynamic behaviour of two-dimensional vesicles revisited

We study pressurised self-avoiding ring polymers in two dimensions using Monte Carlo simulations, scaling arguments and Flory-type theories, through models which generalise the model of Leibler, Singh and Fisher [Phys. Rev. Lett. Vol. 59, 1989 (1987)]. We demonstrate the existence of a thermodynamic phase transition at a non-zero scaled pressure $\tilde{p}$, where $\tilde{p} = Np/4π$, with the number of monomers $N \rightarrow \infty$ and the pressure $p \rightarrow 0$, keeping $\tilde{p}$ constant, in a class of such models. This transition is driven by bond energetics and can be either continuous or discontinuous. It can be interpreted as a shape transition in which the ring polymer takes the shape, above the critical pressure, of a regular N-gon whose sides scale smoothly with pressure, while staying unfaceted below this critical pressure. In the general case, we argue that the transition is replaced by a sharp crossover. The area, however, scales with $N^2$ for all positive $p$ in all such models, consistent with earlier scaling theories.

cond-mat.stat-mech↗

arXiv2011

Coarse grained dynamics of the freely cooling granular gas in one dimension

We study the dynamics and structure of clusters in the inhomogeneous clustered regime of a freely cooling granular gas of point particles in one dimension. The coefficient of restitution is modeled as $r_0<1$ or 1 depending on whether the relative speed is greater or smaller than a velocity scale $δ$. The effective fragmentation rate of a cluster is shown to rise sharply beyond a $δ$ dependent time scale. This crossover is coincident with the velocity fluctuations within a cluster becoming order $δ$. Beyond this crossover time, the cluster size distribution develops a nontrivial power law distribution, whose scaling properties are related to those of the velocity fluctuations. We argue that these underlying features are responsible behind the recently observed nontrivial coarsening behaviour in the one dimensional freely cooling granular gas.

cond-mat.soft↗

arXiv2011

Lattice models for ballistic aggregation in one-dimension

We propose two lattice models in one dimension, with stochastically hopping particles which aggregate on contact. The hops are guided by "velocity rates" which themselves evolve according to the rules of ballistic aggregation as in a sticky gas in continuum. Our lattice models have both velocity and density fields and an appropriate real time evolution, such that they can be compared directly with event driven molecular dynamics (MD) results for the sticky gas. We demonstrate numerically that the long time and large distance behavior of the lattice models are identical to that of the MD, and some exact results known for the sticky gas. In particular, the exactly predicted form of the non-Gaussian tail of the velocity distribution function is clearly exhibited. This correspondence of the lattice models and the sticky gas in continuum is nontrivial, as the latter has a deterministic dynamics with local kinematic constraint, in contrast with the former; yet the spatial velocity profiles (with shocks) of the lattice models and the MD have striking match.

cond-mat.stat-mech↗

arXiv2011

Bethe approximation for a system of hard rigid rods: the random locally tree-like layered lattice

We study the Bethe approximation for a system of long rigid rods of fixed length k, with only excluded volume interaction. For large enough k, this system undergoes an isotropic-nematic phase transition as a function of density of the rods. The Bethe lattice, which is conventionally used to derive the self-consistent equations in the Bethe approximation, is not suitable for studying the hard-rods system, as it does not allow a dense packing of rods. We define a new lattice, called the random locally tree-like layered lattice, which allows a dense packing of rods, and for which the approximation is exact. We find that for a 4-coordinated lattice, k-mers with k>=4 undergo a continuous phase transition. For even coordination number q>=6, the transition exists only for k >= k_{min}(q), and is first order.

cond-mat.stat-mech↗

arXiv2010

On the Non-equilibrium Phase Transition in Evaporation-Deposition Models

We study a system of diffusing-aggregating particles with deposition and evaporation of monomers. By combining theoretical and numerical methods, we establish a clearer understanding of the non-equilibrium phase transition known to occur in such systems. The transition is between a growing phase in which the total mass increases for all time and a non-growing phase in which the total mass is bounded. In addition to deriving rigorous bounds on the position of the transition point, we show that the growing phase is in the same universality class as diffusion-aggregation models with deposition but no evaporation. In this regime, the flux of mass in mass space becomes asymptotically constant (as a function of mass) at large times. The magnitude of this flux depends on the evaporation rate but the fact that it is asymptotically constant does not. The associated constant flux relation exactly determines the scaling of the two-point mass correlation function with mass in all dimensions while higher-order mass correlation functions exhibit nonlinear multi-scaling in dimension less than 2. If the deposition rate is below some critical value, a different stationary state is reached at large times characterised by a global balance between evaporation and deposition with a scale-by-scale balance between the mass fluxes due to aggregation and evaporation. Both the mass distribution and the flux decay exponentially in this regime. Finally, we develop a scaling theory of the model near the critical point, which yields non-trivial scaling laws for the critical two-point mass correlation function with mass. These results are well supported by numerical measurements.

cond-mat.stat-mech↗

arXiv2009

Universal scaling dynamics in a perturbed granular gas

We study the response of a granular system at rest to an instantaneous input of energy in a localised region. We present scaling arguments that show that, in $d$ dimensions, the radius of the resulting disturbance increases with time $t$ as $t^α$, and the energy decreases as $t^{-αd}$, where the exponent $α=1/(d+1)$ is independent of the coefficient of restitution. We support our arguments with an exact calculation in one dimension and event driven molecular dynamic simulations of hard sphere particles in two and three dimensions.

cond-mat.soft↗

arXiv2009

Joint Source-Channel Coding on a Multiple Access Channel with Side Information

We consider the problem of transmission of several distributed correlated sources over a multiple access channel (MAC) with side information at the sources and the decoder. Source-channel separation does not hold for this channel. Sufficient conditions are provided for transmission of sources with a given distortion. The source and/or the channel could have continuous alphabets (thus Gaussian sources and Gaussian MACs are special cases). Various previous results are obtained as special cases. We also provide several good joint source-channel coding schemes for discrete sources and discrete/continuous alphabet channel.

cs.IT↗

arXiv2009

On the equivalence of the freely cooling granular gas to the sticky gas

A freely cooling granular gas with velocity dependent restitution coefficient is studied in one dimension. The restitution coefficient becomes near elastic when the relative velocity of the colliding particles is less than a velocity scale $δ$. Different statistical quantities namely density distribution, occupied and empty cluster length distributions, and spatial density and velocity correlation functions, are obtained using event driven molecular dynamic simulations. We compare these with the corresponding quantities of the sticky gas (inelastic gas with zero coefficient of restitution). We find that in the inhomogeneous cooling regime, for times smaller than a crossover time $t_1$ where $t_1 \sim δ^{-1}$, the behaviour of the granular gas is equivalent to that of the sticky gas. When $δ\rt 0$, then $t_1 \rt \infty$ and hence, the results support an earlier claim that the freely cooling inelastic gas is described by the inviscid Burgers equation. For a real granular gas with finite $δ$, the existence of the time scale $t_1$ shows that, for large times, the granular gas is not described by the inviscid Burgers equation.

cond-mat.soft↗

arXiv2008

Multi-Avalanche Correlations in Directed Sandpile Models

Multiple avalanches, initiated by simultaneously toppling neighbouring sites, are studied in three different directed sandpile models. It is argued that, while the single avalanche exponents are different for the three models, a suitably defined two-avalanche distribution has identical exponents. The origin of this universality is traced to particle conservation.

cond-mat.stat-mech↗

arXiv2008

Role of pulling direction in understanding the energy landscape of proteins

Single molecule force spectroscopy provide details of the underlying energy surfaces of proteins which are essential to the understanding of their unfolding process. Recently, it has been observed experimentally that by pulling proteins in different directions relative to their secondary structure, one can gain a better understanding of the shape of the energy landscape. We consider simple lattice models which are anisotropic in nature to study the response of a force in unfolding of a polymer. Our analytical solution of the model, supported by extensive numerical calculations, reveal that the force temperature diagrams are very different depending on the direction of the applied force. We find that either unzipping or shearing kind transitions dominate the dynamics of the unfolding process depending solely on the direction of the applied force.

cond-mat.stat-mech↗

arXiv2008

Constant Flux Relation for diffusion limited cluster-cluster aggregation

In a non-equilibrium system, a Constant Flux Relation (CFR) expresses the fact that a constant flux of a conserved quantity exactly determines the scaling of the particular correlation function linked to the flux of that conserved quantity. This is true regardless of whether mean--field theory is applicable or not. We focus on cluster--cluster aggregation and discuss the consequences of mass conservation for the steady state of aggregation models with a monomer source in the diffusion-limited regime. We derive the CFR for the flux-carrying correlation function for binary aggregation with a general scale-invariant kernel and show that this exponent is unique. It is independent of both the dimension and of the details of the spatial transport mechanism, a property which is very atypical in the diffusion-limited regime. We then discuss in detail the ``locality criterion'' which must be satisfied in order for the CFR scaling to be realisable. Locality may be checked explicitly for the mean-field Smoluchowski equation. We show that if it is satisfied at the mean-field level, it remains true over some finite range as one perturbatively decreases the dimension of the system below the critical dimension, $d_c=2$, entering the fluctuation-dominated regime. We turn to numerical simulations to verify locality for a range of systems in one dimension which are, presumably, beyond the perturbative regime. Finally, we illustrate how the CFR scaling may break down as a result of a violation of locality or as a result of finite size effects and discuss the extent to which the results apply to higher order aggregation processes.

cond-mat.stat-mech↗

arXiv2008

Distributed Joint Source-Channel Coding on a Multiple Access Channel with Side Information

We consider the problem of transmission of several distributed sources over a multiple access channel (MAC) with side information at the sources and the decoder. Source-channel separation does not hold for this channel. Sufficient conditions are provided for transmission of sources with a given distortion. The source and/or the channel could have continuous alphabets (thus Gaussian sources and Gaussian MACs are special cases). Various previous results are obtained as special cases. We also provide several good joint source-channel coding schemes for a discrete/continuous source and discrete/continuous alphabet channel. Channels with feedback and fading are also considered. Keywords: Multiple access channel, side information, lossy joint source-channel coding, channels with feedback, fading channels.

cs.IT↗

arXiv2007

Asymptotic Behavior of Inflated Lattice Polygons

We study the inflated phase of two dimensional lattice polygons with fixed perimeter $N$ and variable area, associating a weight $\exp[pA - Jb ]$ to a polygon with area $A$ and $b$ bends. For convex and column-convex polygons, we show that $ /A_{max} = 1 - K(J)/\tilde{p}^2 + \mathcal{O}(ρ^{-\tilde{p}})$, where $\tilde{p}=pN \gg 1$, and $ρ<1$. The constant $K(J)$ is found to be the same for both types of polygons. We argue that self-avoiding polygons should exhibit the same asymptotic behavior. For self-avoiding polygons, our predictions are in good agreement with exact enumeration data for J=0 and Monte Carlo simulations for $J \neq 0$. We also study polygons where self-intersections are allowed, verifying numerically that the asymptotic behavior described above continues to hold.

cond-mat.stat-mech↗

arXiv2007

Phase Transitions in Pressurised Semiflexible Polymer Rings

We propose and study a model for the equilibrium statistical mechanics of a pressurised semiflexible polymer ring. The Hamiltonian has a term which couples to the algebraic area of the ring and a term which accounts for bending (semiflexibility). The model allows for self-intersections. Using a combination of Monte Carlo simulations, Flory-type scaling theory, mean-field approximations and lattice enumeration techniques, we obtain a phase diagram in which collapsed and inflated phases are separated by a continuous transition. The scaling properties of the averaged area as a function of the number of units of the ring are derived. For large pressures, the asymptotic behaviour of the area is calculated for both discrete and lattice versions of the model. For small pressures, the area is obtained through a mapping onto the quantum mechanical problem of an electron moving in a magnetic field. The simulation data agree well with the analytic and mean-field results.

cond-mat.stat-mech↗