arXiv subjects

A. K. Bhattacharjee

Publications and source records attributed to A. K. Bhattacharjee.

12 recordsLinked to original sources

arXiv2015

Fluctuating hydrodynamics of multispecies reactive mixtures

We formulate and study computationally the fluctuating compressible Navier-Stokes equations for reactive multi-species fluid mixtures. We contrast two different expressions for the covariance of the stochastic chemical production rate in the Langevin formulation of stochastic chemistry, and compare both of them to predictions of the chemical Master Equation for homogeneous well-mixed systems close to and far from thermodynamic equilibrium. We develop a numerical scheme for inhomogeneous reactive flows, based on our previous methods for non-reactive mixtures [K. Balakrishnan, A. L. Garcia, A. Donev and J. B. Bell, Phys. Rev. E 89:013017, 2014]. We study the suppression of non-equilibrium long-ranged correlations of concentration fluctuations by chemical reactions, as well as the enhancement of pattern formation by spontaneous fluctuations. Good agreement with available theory demonstrates that the formulation is robust and a useful tool in the study of fluctuations in reactive multi-species fluids. At the same time, several problems with Langevin formulations of stochastic chemistry are identified, suggesting that future work should examine combining Langevin and Master Equation descriptions of hydrodynamic and chemical fluctuations.

physics.flu-dyn↗

arXiv2015

Low Mach Number Fluctuating Hydrodynamics of Multispecies Liquid Mixtures

We develop a low Mach number formulation of the hydrodynamic equations describing transport of mass and momentum in a multispecies mixture of incompressible miscible liquids at specified temperature and pressure that generalizes our prior work on ideal mixtures of ideal gases and binary liquid mixtures. In this formulation we combine and extend a number of existing descriptions of multispecies transport available in the literature. The formulation applies to non-ideal mixtures of arbitrary number of species, without the need to single out a 'solvent' species, and includes contributions to the diffusive mass flux due to gradients of composition, temperature and pressure. Momentum transport and advective mass transport are handled using a low Mach number approach that eliminates fast sound waves (pressure fluctuations) from the full compressible system of equations and leads to a quasi-incompressible formulation. Thermal fluctuations are included in our fluctuating hydrodynamics description following the principles of nonequilibrium thermodynamics. We extend the semi-implicit staggered-grid finite-volume numerical method developed in our prior work on binary liquid mixtures, and use it to study the development of giant nonequilibrium concentration fluctuations in a ternary mixture subjected to a steady concentration gradient. We also numerically study the development of diffusion-driven gravitational instabilities in a ternary mixture, and compare our numerical results to recent experimental measurements in a Hele-Shaw cell. We find that giant nonequilibrium fluctuations can trigger the instability but are eventually dominated by the deterministic growth of the unstable mode, in both quasi two-dimensional (Hele-Shaw), and fully three-dimensional geometries used in typical shadowgraph experiments.

physics.flu-dyn↗

arXiv2010

Acceptor and donor impurities in GaN nanocrystals

We investigate acceptor and donor states in GaN nanocrystals doped with a single substitutional impurity. Quantum dots (QD's) of zinc-blende structure and spherical shape are considered with the radius ranging from 4.5 to 67.7 A. The size-dependent energy spectra are calculated within the sp3d5s* tight-binding model, which yields a good agreement with the confinement-induced blue shifts observed in undoped QD's. The computed binding energy is strongly enhanced with respect to the experimental bulk value when the dopant is placed at the center of the smallest QD's. It decreases with increasing QD size following a scaling law that extrapolates to the bulk limit. In order to estimate the degree of localization of the bound carriers we analyze their wave functions and average radii. The resulting physical picture points to a highly localized acceptor hole, mostly distributed over the nearest-neighbor anion shell, and a much more extended donor electron. We also study off-center impurities in intermediate-size QD's. The acceptor binding energy is approximately independent of the dopant position unless it is placed within a surface shell of thickness of the order of the bulk Bohr radius, where the ionization energy abruptly drops. On the contrary, the donor binding energy gradually decreases as the impurity is moved away from the center toward the QD surface.

cond-mat.mes-hall↗

arXiv2010

Fluctuating Nematodynamics using the Stochastic Method of Lines

We construct Langevin equations describing the fluctuations of the tensor order parameter $Q_{αβ}$ in nematic liquid crystals by adding noise terms to time-dependent variational equations that follow from the Ginzburg-Landau-de Gennes free energy. The noise is required to preserve the symmetry and tracelessness of the tensor order parameter and must satisfy a fluctuation-dissipation relation at thermal equilibrium. We construct a noise with these properties in a basis of symmetric traceless matrices and show that the Langevin equations can be solved numerically in this basis using a stochastic version of the method of lines. The numerical method is validated by comparing equilibrium probability distributions, structure factors and dynamic correlations obtained from these numerical solutions with analytic predictions. We demonstrate excellent agreement between numerics and theory. This methodology can be applied to the study of phenomena where fluctuations in both the magnitude and direction of nematic order are important, as for instance in the nematic swarms which produce enhanced opalescence near the isotropic-nematic transition or the problem of nucleation of the nematic from the isotropic phase.

cond-mat.soft↗

arXiv2009

The Isotropic-Nematic Interface with an Oblique Anchoring Condition

We present numerical and analytic results for uniaxial and biaxial order at the isotropic-nematic interface within Ginzburg-Landau-de Gennes theory. We study the case where an oblique anchoring condition is imposed asymptotically on the nematic side of the interface, reproducing results of previous work when this condition reduces to planar or homoeotropic anchoring. We construct physically motivated and computationally flexible variational profiles for uniaxial and biaxial order, comparing our variational results to numerical results obtained from a minimization of the Ginzburg-Landau-de Gennes free energy. While spatial variations of the scalar uniaxial and biaxial order parameters are confined to the neighbourhood of the interface, nematic elasticity requires that the director orientation interpolate linearly between either planar or homoeotropic anchoring at the location of the interface and the imposed boundary condition at infinity. The selection of planar or homoeotropic anchoring at the interface is governed by the sign of the Ginzburg-Landau-de Gennes elastic coefficient L_2. Our variational calculations are in close agreement with our numerics and agree qualitatively with results from density functional theory and molecular simulations.

cond-mat.soft↗

arXiv2009

Biaxiality at the Isotropic-Nematic Interface with Planar Anchoring

We revisit the classic problem of the structure of the isotropic-nematic interface within Ginzburg-Landau-de Gennes theory, refining previous analytic treatments of biaxiality at the interface. We compare our analysis with numerical results obtained through a highly accurate spectral collocation scheme for the solution of the Landau-Ginzburg-de Gennes equations. In comparison to earlier work, we obtain improved agreement with numerics for both the uniaxial and biaxial profiles, accurate asymptotic results for the decay of biaxial order on both nematic and isotropic sides of the interface and accurate fits to data from density functional approaches to this problem.

cond-mat.soft↗

arXiv2008

Numerical Method of Lines for the Relaxational Dynamics of Nematic Liquid Crystals

We propose an efficient numerical scheme, based on the method of lines, for solving the Landau-de Gennes equations describing the relaxational dynamics of nematic liquid crystals. Our method is computationally easy to implement, balancing requirements of efficiency and accuracy. We benchmark our method through the study of the following problems: the isotropic-nematic interface, growth of nematic droplets in the isotropic phase and the kinetics of coarsening following a quench into the nematic phase. Our results, obtained through solutions of the full coarse-grained equations of motion with no approximations, provide a stringent test of the de Gennes ansatz for the isotropic - nematic interface, illustrate the anisotropic character of droplets in the nucleation regime and validate dynamical scaling in the coarsening regime.

cond-mat.soft↗

arXiv2003

Electronic structure and optical properties of ZnS/CdS nanoheterostructures

The electronic and optical properties of spherical nanoheterostructures are studied within the semi-empirical $sp^{3}s^{*}$ tight-binding model including the spin-orbit interaction. We use a symmetry-based approach previously applied to CdSe and CdTe quantum dots. The complete one-particle spectrum is obtained by using group-theoretical methods. The excitonic eigenstates are then deduced in the configuration-interaction approach by fully taking into account the Coulomb direct and exchange interactions. Here we focus on ZnS/CdS, ZnS/CdS/ZnS and CdS/ZnS nanocrystals with particular emphasis on recently reported experimental data. The degree of carrier localization in the CdS well layer is analyzed as a function of its thickness. We compute the excitonic fine structure, i.e., the relative intensities of low-energy optical transitions. The calculated values of the absorption gap show a good agreement with the experimental ones. Enhanced resonant photoluminescence Stokes shifts are predicted.

cond-mat↗

arXiv2002

CdS/HgS/CdS Quantum Dot Quantum Wells: A Tight-binding Study

We study the electronic properties of spherical quantum dot quantum well nanocrystals within a symmetry-based tight-binding model. In particular, the influence of a concentric monolayer of HgS embedded in a spherical CdS nanocrystal of diameter 52.7 A is analyzed as a function of its distance from the center. The electron and hole states around the energy gap show a strong localization in the HgS well and the neighboring inner (core) interface region. Important effects on the optical properties such as the absorption gap and the fine structure of the exciton spectrum are also reported.

cond-mat.mes-hall↗

arXiv2001

Photoluminescence Stokes shift and exciton fine structure in CdTe nanocrystals

The photoluminescence spectra of spherical CdTe nanocrystals with zincblende structure are studied by size-selective spectroscopic techniques. We observe a resonant Stokes shift of 15 meV when the excitation laser energy is tuned to the red side of the absorption band at 2.236 eV. The experimental data are analyzed within a symmetry-based tight-binding theory of the exciton spectrum, which is first shown to account for the size dependence of the fundamental gap reported previously in the literature. The theoretical Stokes shift presented as a function of the gap shows a good agreement with the experimental data, indicating that the measured Stokes shift indeed arises from the electron-hole exchange interaction.

cond-mat.mes-hall↗

arXiv2001

Exciton states and optical properties of CdSe nanocrystals

The optical spectra of CdSe nanocrystals up to 55 A in diameter are analyzed in a wide range of energies from the fine structure of the low-energy excitations to the so-called high-energy transitions. We apply a symmetry-based method in two steps. First we take the tight-binding (TB) parameters from the bulk sp^{3}s^{*} TB model, extended to include the spin-orbit interaction. The full single-particle spectra are obtained from an exact diagonalization by using a group-theoretical treatment. The electron-hole interaction is next introduced: Both the Coulomb (direct) and exchange terms are considered. The high-energy excitonic transitions are studied by computing the electric dipole transition probabilities between single-particle states, while the transition energies are obtained by taking into account the Coulomb interaction. The fine structure of the lowest excitonic states is analyzed by including the electron-hole exchange interaction and the wurtzite crystal-field terms in the exciton Hamiltonian. The latter is diagonalized in the single electron-hole pair excitation subspace of progressively increasing size until convergence. The peaks in the theoretical transition spectra are then used to deduce the resonant and nonresonant Stokes shifts, which are compared with their measured values in photoluminescence experiments. We find that the final results depend on the crystal-field term, the relative size of the surface and the degree of saturation of the dangling bonds. The results show a satisfactory agreement with the available experimental data.

cond-mat.mes-hall↗

arXiv1999

Electronic structure of CdTe nanocrystals: A tight-binding study

We present a symmetry-based calculation of the electronic structure of a compound semiconductor quantum dot (QD) in the sp^3s* tight-binding model including the spin-orbit interaction. The Hamiltonian matrix is diagonalized exactly for CdTe QD sizes up to 60 Å. The surface dangling bonds are passivated by hydrogen through a careful analysis of the density of states and wave functions. The calculated size dependence of the energy gap shows a reasonable agreement with the available experimental data. Our symmetry analysis indicates that, in contrast with a reported prediction of the three-band effective-mass model, the fundamental interband transition remains dipole-allowed in CdTe nanocrystals.

cond-mat.mes-hall↗