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Kaushik Bhattacharya

Publications and source records attributed to Kaushik Bhattacharya.

At least 127 records · Page 7Linked to original sources
arXiv2015

Effective behavior of nematic elastomer membranes

We derive the effective energy density of thin membranes of liquid crystal elastomers as the Gamma-limit of a widely used bulk model. These membranes can display fine-scale features both due to wrinkling that one expects in thin elastic membranes and due to oscillations in the nematic director that one expects in liquid crystal elastomers. We provide an explicit characterization of the effective energy density of membranes and the effective state of stress as a function of the planar deformation gradient. We also provide a characterization of the fine-scale features. We show the existence of four regimes: one where wrinkling and microstructure reduces the effective membrane energy and stress to zero, a second where wrinkling leads to uniaxial tension, a third where nematic oscillations lead to equi-biaxial tension and a fourth with no fine scale features and biaxial tension. Importantly, we find a region where one has shear strain but no shear stress and all the fine-scale features are in-plane with no wrinkling.

math.AP↗
arXiv2014

Plates with incompatible prestrain

We study the effective elastic behavior of incompatibly prestrained plates, where the prestrain is independent of thickness as well as uniform through the thickness. We model such plates as three-dimensional elastic bodies with a prescribed pointwise stress-free state characterized by a Riemannian metric $G$ with the above properties, and seek the limiting behavior as the thickness goes to zero. Our results extand the prior analysis in M. Lewicka, M. R. Pakzad ESAIM Control Optim. Calc. Var. 17 (2011), no. 4. We first establish that the $Γ$-limit is a Kirchhoff type bending. Further, we show that the minimum energy configuration contains non-trivial Kirchhoff type bending -- i.e., the scaling of the three-dimensional energy is of the order of the cube of the plate thickness -- if and only if the Riemann curvatures $R^3_{112}, R^3_{221}$ and $ R_{1212}$ of $G$ do not identically vanish. We demonstrate through examples, the existence of a new regime where the three above curvatures of $G$ vanish (while the mid-plane of the plate may or may not be flat), but the limiting configuration still has energy that is of the order of Föppl - von Kármán plates. Finally, we apply these results to a model of nematic glass, including a characterization of the condition when the metric is immersible, for $G=\mbox{Id}_3 +γ\vec n\otimes \vec n$ given in terms of the inhomogeneous unit director field distribution $\vec n\in\mathbb{R}^3$.

math.AP↗
arXiv2014

Higgs vacuum stability and inflationary dynamics after BICEP2 and PLANCK dust polarisation data

If the recent detection of $B-$mode polarization of the Cosmic Microwave Background by BICEP2 observations, withstand the test of time after the release of recent PLANCK dust polarisation data, then it would surprisingly put the inflationary scale near Grand Unification scale if one considers single-field inflationary models. On the other hand, Large Hadron Collider has observed the elusive Higgs particle whose presently observed mass can lead to electroweak vacuum instability at high scale $(\sim{\mathcal O}(10^{10})$ GeV). In this article, we seek for a simple particle physics model which can simultaneously keep the vacuum of the theory stable and yield high-scale inflation successfully. To serve our purpose, we extend the Standard Model of particle physics with a $U(1)_{B-L}$ gauged symmetry which spontaneously breaks down just above the inflationary scale. Such a scenario provides a constrained parameter space where both the issues of vacuum stability and high-scale inflation can be successfully accommodated. The threshold effect on the Higgs quartic coupling due to the presence of the heavy inflaton field plays an important role in keeping the electroweak vacuum stable. Furthermore, this scenario is also capable of reheating the universe at the end of inflation. Though the issues of Dark Matter and Dark Energy, which dominate the late-time evolution of our universe, cannot be addressed within this framework, this model successfully describes the early universe dynamics according to the Big Bang model.

hep-ph↗
arXiv2014

Cosmological bounces in spatially flat FRW spacetimes in metric f(R) gravity

The present work analyzes the various conditions in which there can be a bouncing universe solution in f(R) gravity. In the article an interesting method, to analyze the bouncing FRW solutions in a spatially flat universe using f(R) gravity models using an effective Einstein frame description of the process, is presented. The analysis shows that a cosmological bounce in the f(R) theory need not be described by an equivalent bounce in the Einstein frame description of the process where actually there may be no bounce at all. Nevertheless the Einstein frame description of the bouncing phenomena turns out to be immensely important as the dynamics of the bounce becomes amenable to logic based on general relativistic intuition. The theory of scalar cosmological perturbations in the bouncing universe models in $f(R)$ theories has also been worked out in the Einstein frame.

gr-qc↗
arXiv2014

Collective behavior of viscoelastic asperities as a model for static and kinetic friction

We propose a statistical model for static and sliding friction between rough surfaces. Approximating the contact between rough surfaces by the contact of an ensemble of one-dimensional viscoelastic elements with a rough rigid surface, we study the collective behavior of the elements. We find that collective response of the contacts can lead to macroscopic behavior very different from the microscopic behavior. Specifically, various observed features of friction emerge as collective phenomena, without postulating them directly at the microscale. We discuss how parameters in our model can be related to material and surface properties of the contacting surfaces. We compare our results to commonly used rate and state phenomenological models, and propose a new interpretation of the state variable.

cond-mat.soft↗
arXiv2013

Astrophysics of Bertrand Space-times

We construct a model for galactic dark matter that arises as a solution of Einstein gravity, and is a Bertrand space-time matched with an external Schwarzschild metric. This model can explain galactic rotation curves. Further, we study gravitational lensing in these space-times, and in particular we consider Einstein rings, using the strong lensing formalism of Virbhadra and Ellis. Our results are in good agreement with observational data, and indicate that under certain conditions, gravitational lensing effects from galactic dark matter may be similar to that from Schwarzschild backgrounds.

astro-ph.GA↗
arXiv2013

Galactic Dark Matter and Bertrand Space-times

Bertrand space-times (BSTs) are static, spherically symmetric solutions of Einstein's equations, that admit stable, closed orbits. Starting from the fact that to a good approximation, stars in the disc or halo regions of typical galaxies move in such orbits, we propose that, under certain physical assumptions, the dark matter distribution of some low surface brightness (LSB) galaxies can seed a particular class of BSTs. In the Newtonian limit, it is shown that for flat rotation curves, our proposal leads to an analytic prediction of the NFW dark matter profile. We further show that the dark matter distribution that seeds the BST, is described by a two-fluid anisotropic model, and present its analytic solution. A new solution of the Einstein's equations, with an internal BST and an external Schwarzschild metric, is also constructed.

astro-ph.GA↗
arXiv2013

Lee-Wick radiation induced bouncing universe models

The present article discusses about the effect of a Lee-Wick partner infested radiation phase of the early universe. As Lee-Wick partners can contribute negative energy density so it is always possible that at some early phase of the universe when the Lee-Wick partners were thermalized the total energy density of the universe became very small making the effective Hubble radius very big. This possibility gives rise to the probability of a bouncing universe. As will be shown in the article that a simple Lee-Wick radiation is not enough to produce a bounce. There can be two possibilities which can produce a bounce in the Lee-Wick radiation phase. One requires a cold dark matter candidate to trigger the bounce and the other possibility requires the bouncing temperature to be fine tuned such as all the Lee-Wick partners of the standard fields are not thermalized at the bounce temperature. Both the possibilities give rise to blue-tilted power spectrum of metric perturbations. Moreover the bouncing universe model can predict the lower limit of the masses of the Lee-Wick partners of chiral fermions and massless gauge bosons. The mass limit intrinsically depends upon the bounce temperature.

hep-th↗
arXiv2012

Effect of Lee-Wick thermodynamics in the cosmology of the early universe

The Lee-Wick theories require unusual Lee-Wick (LW) partners to the standard model (SM) particles. The excitations of the unusual fields may have indefinite norms in the Hilbert space. In the present talk the thermodynamic results of a toy LW (where each normal particle has only one LW partner and the standard massless gauge fields do not appear in the normal particle spectrum as their LW partners has the potential to produce negative energy density) as well as a realistic LW universe (where the above restrictions are not present) will be discussed.

hep-ph↗
arXiv2012

Coarse-graining Kohn-Sham Density Functional Theory

We present a real-space formulation for coarse-graining Kohn-Sham Density Functional Theory that significantly speeds up the analysis of material defects without appreciable loss of accuracy. The approximation scheme consists of two steps. First, we develop a linear-scaling method that enables the direct evaluation of the electron density without the need to evaluate individual orbitals. We achieve this by performing Gauss quadrature over the spectrum of the linearized Hamiltonian operator appearing in each iteration of the self-consistent field method. Building on the linear-scaling method, we introduce a spatial approximation scheme resulting in a coarse-grained Density Functional Theory. The spatial approximation is adapted so as to furnish fine resolution where necessary and to coarsen elsewhere. This coarse-graining step enables the analysis of defects at a fraction of the original computational cost, without any significant loss of accuracy. Furthermore, we show that the coarse-grained solutions are convergent with respect to the spatial approximation. We illustrate the scope, versatility, efficiency and accuracy of the scheme by means of selected examples.

physics.comp-ph↗
arXiv2012

Geodesic Congruences and Their Deformations in Bertrand Space-times

We study the energy conditions and geodesic deformations in Bertrand space-times. We show that these can be thought of as interesting physical space-times in certain regions of the underlying parameter space, where the weak and strong energy conditions hold. We further compute the ESR parameters and analyze them numerically. The focusing of radial time-like and radial null geodesics is shown explicitly, which verifies the Raychaudhuri equation.

gr-qc↗
arXiv2012

A toy model based analysis on the effect of the Lee-Wick partners in the evolution of the early universe

In the present article the thermodynamic results of the Lee-Wick partner infested universe have been applied in a toy model where there is one Lee-Wick partner to each of the standard model particle and more over the longitudinal degrees of freedom of the massive partners of the standard massless gauge bosons are neglected at high temperatures. For practical purposes, the chiral fermionic sector of Lee-wick theories requires two Lee-Wick partners per fermion which opens up the possibility for a negative energy density of the early universe. A toy Lee-Wick model with one fermionic partner relaxes such oddities and hence easy to deal with. In a similar way, the longitudinal degrees of freedom of the massive gauge boson partners also have the potential to yield negative energy densities and thus those will be neglected in a toy model study. In such a toy model one can analytically calculate the time-temperature relation in the very early radiation dominated universe which shows interesting new physics. The article also tries to point out how a Lee-Wick particle dominated early cosmology transforms into the standard cosmological model. Based on the results of this toy model analysis a brief discussion on the more realistic model, which can accommodate two Lee-Wick partners for each standard fermionic field and the longitudinal degree of freedom of partners of the gauge fields, is presented. It has been shown that such an universe is mostly very difficult to attain but there are certain conditions where one can indeed think of such an universe which can evolve into the standard cosmological universe in a short time duration.

hep-ph↗
arXiv2012

Effective behavior of an interface propagating through a periodic elastic medium

We consider a moving interface that is coupled to an elliptic equation in a heterogeneous medium. The problem is motivated by the study of displacive solid-solid phase transformations. We show that a nearly flat interface is given by the graph of the function $g$ which evolves according to the equation $g_t (x) = -(-Δ)^{1/2}g (x) + φ(x, g(x)) + F$. This equation also arises in the study of dislocations and fracture. We show in the periodic setting that such interfaces exhibit a stick-slip behavior associated with pinning and depinning. Further, we present some numerical evidence that the effective velocity of the phase boundary scales as the square-root of the excess macroscopic force above the depinning transition.

math.AP↗
arXiv2012

Toughening and asymmetry in peeling of heterogeneous adhesives

The effective adhesive properties of heterogeneous thin films are characterized through a combined experimental and theoretical investigation. By bridging scales, we show how variations of elastic or adhesive properties at the microscale can significantly affect the effective peeling behavior of the adhesive at the macroscale. Our study reveals three elementary mechanisms in heterogeneous systems involving front propagation: (i) patterning the elastic bending stiffness of the film produces fluctuations of the driving force resulting in dramatically enhanced resistance to peeling; (ii) optimized arrangements of pinning sites with large adhesion energy are shown to control the effective system resistance, allowing the design of highly anisotropic and asymmetric adhesives; (iii) heterogeneities of both types result in front motion instabilities producing sudden energy releases that increase the overall adhesion energy. These findings open potentially new avenues for the design of thin films with improved adhesion properties, and motivate new investigation of other phenomena involving front propagation.

cond-mat.soft↗
arXiv2011

Localization of Dirac-like excitations in graphene in the presence of smooth inhomogeneous magnetic fields

The present article discusses magnetic confinement of the Dirac excitations in graphene in presence of inhomogeneous magnetic fields. In the first case a magnetic field directed along the z axis whose magnitude is proportional to $1/r$ is chosen. In the next case we choose a more realistic magnetic field which does not blow up at the origin and gradually fades away from the origin. The magnetic fields chosen do not have any finite/infinite discontinuity for finite values of the radial coordinate. The novelty of the two magnetic fields is related to the equations which are used to find the excited spectra of the excitations. It turns out that the bound state solutions of the two-dimensional hydrogen atom problem are related to the spectra of graphene excitations in presence of the $1/r$ (inverse-radial) magnetic field. For the other magnetic field profile one can use the knowledge of the bound state spectrum of a two-dimensional cut-off Coulomb potential to dictate the excitation spectra of the states of graphene. The spectrum of the graphene excitations in presence of the inverse-radial magnetic field can be exactly solved while the other case cannot be. In the later case we give the localized solutions of the zero-energy states in graphene.

cond-mat.mes-hall↗
arXiv2011

Thermodynamics of the Pauli oscillators and Lee-Wick partners of the Standard Model particles

The present article is about the statistical mechanics of non-trivial field configurations. The non-trivial fields arise from the negative sign of the commutators and the anticommutators of the bosonic and fermionic field excitations. These kinds of fields were previously studied by Pauli and Lee and Wick. The thermal distribution function of the above mentioned fields are calculated in the article and using the thermal distribution functions the energy density, pressure and entropy density of the non-trivial field configurations are found out. The results match exactly with a previous calculation done by Fornal et. al. for higher derivative Lee-Wick theories showing a deeper similarity with the earlier work. It is assumed that such kinds of non-trivial fields may have existed in the early universe and may have some cosmological relevance.

hep-ph↗
arXiv2011

Thermodynamics of the Lee-Wick partners: An alternative approach

It was pointed out some time ago that there can be two variations in which the divergences of a quantum field theory can be tamed using the ideas presented by Lee and Wick. In one variation the Lee-Wick partners of the normal fields live in an indefinite metric Hilbert space but have positive energy and in the other variation the Lee-Wick partners can live in a normal Hilbert space but carry negative energy. Quantum mechanically the two variations mainly differ in the way the fields are quantized. In this article the second variation of Lee and Wick's idea is discussed. Using statistical mechanical methods the energy density, pressure and entropy density of the negative energy Lee-Wick fields have been calculated. The results exactly match with the thermodynamic results of the conventional, positive energy Lee-Wick fields. The result sheds some light on the second variation of Lee-Wick's idea. The result seems to say that the thermodynamics of the theories do not care about the way they are quantized.

hep-ph↗