arXiv subjects

J. Shamanna

Publications and source records attributed to J. Shamanna.

18 recordsLinked to original sources

arXiv2016

Surface properties and scaling behavior of a generalized ballistic deposition model in (1+1)-dimension

The surface exponents, the scaling behavior and the bulk porosity of a generalized ballistic deposition (GBD) model are studied. In nature, there exist particles with varying degrees of stickiness ranging from completely non-sticky to fully sticky. Such particles may adhere to any one of the successively encountered surfaces, depending on a sticking probability %should have the possibility of sticking to any of the %allowed points of contact on the surface with a sticking probability that is governed by the underlying stochastic mechanism. The microscopic configurations possible in this model are much larger than those allowed in existing models of ballistic deposition and competitive growth models that seek to mix ballistic and random deposition processes. In this article, we find the scaling exponents for surface width and porosity for the proposed GBD model. In terms of scaled width $\widetilde{W}$ and scaled time $\tilde{t}$, the numerical data collapse on to a single curve, demonstrating successful scaling with sticking probability p and system size L. Similar scaling behavior is also found for the porosity.

cond-mat.stat-mech↗

arXiv2015

Generalized ballistic deposition in 2 dimensions : scaling of surface width, porosity and conductivity

A deposition process with particles having realistic intermediate stickiness is studied in 2+1 dimensions. At each stage of the deposition process, for any given configuration, a newly depositing particle gives rise to allowed set of configurations that are vastly larger than those for deposition of a mixture of purely non-sticky (random like) and purely sticky (ballistic like) particles. We obtain scaling behavior and demonstrate collapse of scaled data for surface width and porosity. Scaling of conductivity, when a porous structure thus formed, is saturated with conductive fluid, e.g. brine, is studied. The results obtained are in good agreement with Archie's law for porous sedimentary rocks.

cond-mat.stat-mech↗

arXiv2013

Surface morphology of a modified ballistic deposition model

The surface and bulk properties of a modified ballistic deposition model are investigated. The deposition rule interpolates between nearest and next-nearest neighbor ballistic deposition and the random deposition models. The stickiness of the depositing particle is controlled by a parameter and the type of inter-particle force. Two such forces are considered - Coulomb and van der Waals type. The interface width shows three distinct growth regions before eventual saturation. The rate of growth depends more strongly on the stickiness parameter than on the type of inter-particle force. However, the porosity of the deposits is strongly influenced by the inter-particle force.

cond-mat.stat-mech↗

arXiv2011

Continuous Time Random Walk with time-dependent jump probability : A Direct Probabilistic Approach

We investigate the dynamics of a particle executing a general Continuous Time Random Walk (CTRW) in three dimensions under the influence of arbitrary time-varying external fields. Contrary to the general approach in recent works, our method invokes neither the Fractional Fokker-Planck equation (FFPE) nor the Stochastic Langevin Equation (SLE). Rather, we use rigorous probability arguments to derive the general expression for moments of all orders of the position probability density of the random walker for arbitrary waiting time density and jump probability density. Closed form expression for the position probability density is derived for the memoryless condition. For the special case of CTRW on a one-dimensional lattice with nearest neighbour jumps, our equations confirm the phenomena of "death of linear response" and "field-induced dispersion" for sub-diffusion pointed out in [I. M. Sokolov and J. Klafter, Phys. Rev. Lett. {\bf 97}, 140602 (2006)]. However, our analysis produces additional terms in the expressions for higher moments, which have non-trivial consequences. We show that the disappearance of these terms result from the approximation involved in taking the continuum limit to derive the generalized Fokker-Planck equation. This establishes the incompleteness of the FFPE formulation, especially in predicting the higher moments. We also discuss how different predictions of the model alter if we allow jumps beyond nearest neighbours and possible circumstances where this becomes relevant.

cond-mat.stat-mech↗

arXiv2011

Revisiting Surface Diffusion in Random Deposition

An investigation of the effect of surface diffusion in random deposition model is made by analytical methods and reasoning. For any given site, the extent to which a particle can diffuse is decided by the morphology in the immediate neighbourhood of the site. An analytical expression is derived to calculate the probability of a particle at any chosen site to diffuse to a given length, from first principles. Using the method, the probabilities for different diffusion lengths are calculated and their dependence on system size and the number of deposited layers is studied. Numerical simulation of surface diffusion in random deposition model with varying extents of diffusion are performed and their results are interpreted in the light of the analytical calculations. Thus, a clearer understanding of the diffusion process and the effect of diffusion length on surface roughness is obtained. Systems with surface diffusion show nearly random deposition-like behaviour upto monolayer deposition. Their interface widths, in a logarithmic plot, are initially linear, as in random deposition. With increase in the number of layers, correlation effects between neighbouring columns become dominant. The interface deviates from its initial linear growth and eventually becomes saturated. An explanation for this behaviour is discussed and the point of departure from the linear form is estimated analytically.

cond-mat.soft↗

arXiv2008

Scaling of Rough Surfaces: Effects of Surface Diffusion on Growth and Roughness Exponents

Random deposition model with surface diffusion over several next nearest neighbours is studied. The results agree with the results obtained by Family for the case of nearest neighbour diffusion [F. Family, J. Phys. A 19(8), L441, 1986]. However for larger diffusion steps, the growth exponent and the roughness exponent show interesting dependence on diffusion length.

cond-mat.soft↗

arXiv2007

Gauge momentum operators for the Calogero-Sutherland model with anti-periodic boundary condition

The integrability of a classical Calogero systems with anti-periodic boundary condition is studied. This system is equivalent to the periodic model in the presence of a magnetic field. Gauge momentum operators for the anti-periodic Calogero system are constructed. These operators are hermitian and simultaneously diagonalizable with the Hamiltonian. A general scheme for constructing such momentum operators for trigonometric and hyperbolic Calogero-Sutherland model is proposed. The scheme is applicable for both periodic and anti-periodic boundary conditions. The existence of these momentum operators ensures the integrability of the system. The interaction parameter $λ$ is restricted to a certain subset of real numbers. This restriction is in fact essential for the construction of the hermitian gauge momentum operators.

hep-th↗

arXiv2007

Quasi-solvability of Calogero-Sutherland model with Anti-periodic Boundary Condition

The U(1) Calogero-Sutherland Model with anti-periodic boundary condition is studied. This model is obtained by applying a vertical magnetic field perpendicular to the plane of one dimensional ring of particles. The trigonometric form of the Hamiltonian is recast by using a suitable similarity transformation. The transformed Hamiltonian is shown to be integrable by constructing a set of momentum operators which commutes with the Hamiltonian and amongst themselves. The function space of monomials of several variables remains invariant under the action of these operators. The above properties imply the quasi-solvability of the Hamiltonian under consideration.

hep-th↗

arXiv2006

Understanding d'Alembert's principle: System of Pendulums

Lagrangian mechanics uses d'Alembert's principle of zero virtual work as an important starting point. The orthogonality of the force of constraint and virtual displacement is emphasized in literature, without a clear warning that this is true usually for a single particle system. For a system of particles connected by constraints, it is shown, that the virtual work of the entire system is zero, even though the virtual displacements of the particles are not perpendicular to the respective constraint forces. It is also demonstrated why d'Alembert's principle involves virtual work rather than the work done by constraint forces on allowed displacements.

physics.class-ph↗

arXiv2006

On Virtual Displacement and Virtual Work in Lagrangian Dynamics

The confusion and ambiguity encountered by students, in understanding virtual displacement and virtual work, is discussed in this article. A definition of virtual displacement is presented that allows one to express them explicitly for holonomic (velocity independent), non-holonomic (velocity dependent), scleronomous (time independent) and rheonomous (time dependent) constraints. It is observed that for holonomic, scleronomous constraints, the virtual displacements are the displacements allowed by the constraints. However, this is not so for a general class of constraints. For simple physical systems, it is shown that, the work done by the constraint forces on virtual displacements is zero. This motivates Lagrange's extension of d'Alembert's principle to system of particles in constrained motion. However a similar zero work principle does not hold for the allowed displacements. It is also demonstrated that d'Alembert's principle of zero virtual work is necessary for the solvability of a constrained mechanical problem. We identify this special class of constraints, physically realized and solvable, as {\it the ideal constraints}. The concept of virtual displacement and the principle of zero virtual work by constraint forces are central to both Lagrange's method of undetermined multipliers, and Lagrange's equations in generalized coordinates.

physics.ed-ph↗

arXiv2005

Calogero-Sutherland Model with Anti-periodic Boundary Conditions: Eigenvalues and Eigenstates

The U(1) Calogero Sutherland Model with anti-periodic boundary condition is studied. The Hamiltonian is reduced to a convenient form by similarity transformation. The matrix representation of the Hamiltonian acting on a partially ordered state space is obtained in an upper triangular form. Consequently the diagonal elements become the energy eigenvalues. The eigenstates are constructed using Young diagram and represented in terms of Jack symmetric polynomials. The eigenstates so obtained are orthonormalized.

math-ph↗

arXiv2005

Equation of state for asymmetric nuclear matter with infinite-order summation of ring diagrams

The particle-particle hole-hole ring-diagram summation method is employed to obtain the equation of state of asymmetric nuclear matter over a wide range of asymmetry fraction. Compared with Brueckner Hartree-Fock and model-space Brueckner Hartree-Fock calculations, this approach gives a softer equation of state, increased symmetry energy and a lower value for the incompressibility modulus which agrees quite well with the values used in the hydrodynamical model for the supernovae explosion.

nucl-th↗

arXiv2005

Self-organized critical dynamics of a directed bond percolation model

We study roughening interfaces with a constant slope that become self organized critical by a rule that is similar to that of invasion percolation. The transient and critical dynamical exponents show Galilean invariance. The activity along the interface exhibits non-trivial power law correlations in both space and time. The probability distribution of the activity pattern follows an algebraic relation.

cond-mat.soft↗

arXiv2005

A Bethe Ansatz Study of Free Energy and Excitation Spectrum for Even Spin Fateev Zamolodchikov Model

A Bethe Ansatz study of a self dual Z_N spin model is undertaken for even spin system. One has to solve a coupled system of Bethe Ansatz Equations (BAE) involving zeroes of two families of transfer matrices. A numerical study on finite size lattices is done for identification of elementary excitations over the Ferromagnetic and Antiferromagnetic ground states. The free energies for both Ferromagnetic and Antiferromagnetic ground states and dispersion relation for elementary excitations are found.

hep-th↗

arXiv2004

Orbits in a central force field: Bounded orbits

The nature of boundedness of orbits of a particle moving in a central force field is investigated. General conditions for circular orbits and their stability are discussed. In a bounded central field orbit, a particle moves clockwise or anticlockwise, depending on its angular momentum, and at the same time oscillates between a minimum and a maximum radial distance, defining an inner and an outer annulus. There are generic orbits suggested in popular texts displaying the general features of a central orbit. In this work it is demonstrated that some of these orbits, seemingly possible at the first glance, are not compatible with a central force field. For power law forces, the general nature of boundedness and geometric shape of orbits are investigated.

physics.ed-ph↗

arXiv2004

Virtual Displacement in Lagrangian Dynamics

The confusion and ambiguity encountered by students, in understanding virtual displacement and virtual work, is addressed in this article. A definition of virtual displacement is presented that allows one to express them explicitly for both time independent and time dependent constraints. It is observed that for time independent constraints the virtual displacements are the displacements allowed by the constraints. However this is not so for a general time dependent case. For simple physical systems, it is shown that, the work done on virtual displacements by the constraint forces is zero in both the situations. For allowed displacements however, this is not always true. It is also demonstrated that when constraint forces do zero work on virtual displacement, as defined here, we have a solvable mechanical problem. We identify this special class of constraints, physically realized and solvable, as the ideal constraints. The concept of virtual displacement and the principle of zero virtual work by constraint forces are central to both Lagrange's method of undetermined multipliers, and Lagrange's equations in generalized coordinates.

physics.ed-ph↗

arXiv1996

Isospin Lattice-Gas Model and Liquid-Gas Phase Transition in Asymmetric Nuclear Matter

An isospin lattice-gas model, which is a spin-1 Ising model, is employed to investigate the liquid-gas phase transition in asymmetric nuclear matter. We consider nuclear matter as a lattice where each lattice site can be either empty or occupied by a proton or a neutron, with a nearest-neighbor interaction among the nucleons. With the Bragg-Williams mean field approximation, we calculate various thermodynamic properties of nuclear matter for different densities and different proton-neutron asymmetry parameter $s$. Our model exhibits liquid-gas phase transition below a critical temperature $T_c$, and predicts a monotonic decreasing of $T_c$ as the magnitude of $s$ is increased. The dependence of the nuclear matter isotherms on the asymmetry parameter $s$ is discussed.

nucl-th↗

arXiv1995

Isospin Lattice Gas Model and Nuclear-Matter Phase Diagram and Pressure-Volume Isotherms

We study a cubic lattice gas model for nuclear matter where each lattice site can be either occupied, by one proton or one neutron, or unoccupied. A nearest-neighbor interaction of the form $ - \sum_{ } J_{ij}τ_{zi} τ_{zj}$ is assumed. Our model is an isospin-1 Ising model, with ${τ_z}$ = (1,0,-1) representing respectively (proton, vacancy, neutron). A kinetic-energy term has been included in our model. Under the Bragg-Williams mean field approximation our model exhibits the existence of a dense phase (liquid-like) and a rare phase (gas-like). The nuclear-matter p-v isotherms given by our model are discussed.

nucl-th↗