Non-linear effects on the holographic free energy and thermodynamic geometry

We have analytically investigated the effects of non-linearity on the free energy and thermodynamic geometry of holographic superconductors in $2+1 -$dimensions. The non-linear effect is introduced by considering the coupling of the massive charged scalar field with Born-Infeld electrodynamics. We then calculate the relation between critical temperature and charge density from two different methods, namely, the matching method and the divergence of the scalar curvature which is obtained by investigating the thermodynamic geometry of the model. The two results are slightly different from numerical values but the effects of non-linearity gets captured in our analysis.Comment: 11 pages Latex, some corrections made in the manuscrip

Development and stability of gyrotactic plumes in bioconvection

Using the continuum model of Pedley, Hill and Kessler (1988) for bioconvection in a suspension of swimming, gyrotactic micro-organisms, we investigate the existence and stability of a two-dimensional plume in tall, narrow chambers with stress-free sidewalls. The system is governed by the Navier–Stokes equations for an incompressible fluid coupled with a micro-organism conservation equation. These equations are solved numerically using a conservative finite-difference scheme. In sufficiently deep chambers, the plume is always unstable to both varicose and meandering modes. A linear stability analysis for an infinitely long plume predicts the growth rates of these instabilities, explains the mechanisms, and is in good agreement with the numerical results

Higher dimensional holographic superconductors in Born-Infeld electrodynamics with backreaction

In this paper, we analytically investigate the properties of holographic superconductors in higher dimensions in the framework of Born-Infeld electrodynamics taking into account the backreaction of the spacetime using the Sturm-Liouville eigenvalue method. In the background of pure Einstein and Gauss-Bonnet gravity, based on a perturbative approach, we obtain the relation between the critical temperature and the charge density. Higher value of the backreaction and Born-Infeld parameters result in a harder condensation to form in both cases. The analytical results are found to agree with the existing numerical results. We also derive an expression for the condensation operator in $d$-dimensions which yields the critical exponent to be $1/2$.Comment: 21 pages Latex, To appear in Eur.Phys.J.

Determination of neutron flux distribution by using ANISN, a one-dimensional discrete S sub n ordinates transport code with anisotropic scattering

The purpose of this project was to use a one-dimensional discrete coordinates transport code called ANISN in order to determine the energy-angle-spatial distribution of neutrons in a 6-feet cube rock box which houses a D-T neutron generator at its center. The project was two-fold. The first phase of the project involved adaptation of the ANISN code written for an IBM 360/75/91 computer to the UNIVAC system at JSC. The second phase of the project was to use the code with proper geometry, source function and rock material composition in order to determine the neutron flux distribution around the rock box when a 14.1 MeV neutron generator placed at its center is activated

Path integral action of a particle in κ\kappa-Minkowski spacetime

In this letter, we derive the path integral action of a particle in $\kappa$-Minkowski spacetime. The equation of motion for an arbitrary potential due to the $\kappa$-deformation of the Minkowski spacetime is then obtained. The action contains a dissipative term which owes its origin to the $\kappa$-Minkowski deformation parameter $a$. We take the example of the harmonic oscillator and obtain the frequency of oscillations in the path integral approach as well as operator approach upto the first order in the deformation parameter $a$. For studying this, we start with the $\kappa$-deformed dispersion relation which is invariant under the undeformed $\kappa$-Poincar$\acute{e}$ algebra and take the non-relativistic limit of the $\kappa$-deformed dispersion relation to find the Hamiltonian. The propagator for the free particle in the $\kappa$-Minkowski spacetime is also computed explicitly. In the limit, $a\rightarrow 0$, the commutative results are recovered.Comment: 5 pages, To appear in Euro.Phys. Let

Determination of the parameters of Heine and Abarenkov model potential in hcp crystals

Parameters of Heine and Abarenkov potential has been computed in this paper for twenty two hexagonal closed pack (hcp) crystals. From the minimization of structure dependent energy of the pure crystal the inter-relation between the two parameters of the potential is first determined. Calculation uses pseudopotential technique with nine different exchange and correlation functions and either only available experimental value of vacancy formation energy (E1vF) or that obtained from an empirical relation based on other experimental parameters (Melting temperature, cohesive energy or activation energy) as tool. The variation of E1vF with parameter A of HAP and different exchange and correlation functions (ECF) show sharp fall in E1vF near very small value of A after which it shows constancy for all hcp crystals. Comparison is made with parameter of Ashcroft model also. For Aschroft this variation is almost flat showing averageness while for Heine and Abarenkov sharp variations are there from one hcp crystal to other

Holographic entanglement thermodynamics for higher dimensional charged black hole

In this paper, we have investigated the entanglement thermodynamics for $d$-dimensional charged $AdS$ black hole by studying the holographic entanglement entropy in different cases. We have first computed the holographic entanglement entropy in extremal and non-extremal cases in two different regimes, namely, the low temperature and high temperature limits. We then obtain the first law of entanglement thermodynamics for boundary field theory in the low temperature regime in $d$-dimensions.Comment: 28 pages Late

Asymptotic security of continuous-variable quantum key distribution with a discrete modulation

We establish a lower bound on the asymptotic secret key rate of continuous-variable quantum key distribution with a discrete modulation of coherent states. The bound is valid against collective attacks and is obtained by formulating the problem as a semidefinite program. We illustrate our general approach with the quadrature phase-shift keying (QPSK) modulation scheme and show that distances over 100 km are achievable for realistic values of noise. We also discuss the application to more complex quadrature amplitude modulations (QAM) schemes. This work is a major step towards establishing the full security of continuous-variable protocols with a discrete modulation in the finite-size regime and opens the way to large-scale deployment of these protocols for quantum key distribution.Comment: 11 pages, 5 figures; v2: added discussion of more general quadrature amplitude modulation schemes, v3: close to published versio