Similarities between 2D and 3D convection for large Prandtl number

Using direct numerical simulations of Rayleigh–Bénard convection (RBC), we perform a comparative study of the spectra and fluxes of energy and entropy, and the scaling of large-scale quantities for large and infinite Prandtl numbers in two (2D) and three (3D) dimensions. We observe close similarities between the 2D and 3D RBC, in particular, the kinetic energy spectrum E_u(k)～k^?13/3, and the entropy spectrum exhibits a dual branch with a dominant k^?2 spectrum. We showed that the dominant Fourier modes in 2D and 3D flows are very close. Consequently, the 3D RBC is quasi-two-dimensional, which is the reason for the similarities between the 2D and 3D RBC for large and infinite Prandtl numbers.     

Review of dark matter direct detection experiments

Matter, as we know it, makes up less than 5% of the Universe. Various astrophysical observations have confirmed that one quarter of the Universe and most of the matter content in the Universe is made up of dark matter. The nature of dark matter is yet to be discovered and is one of the biggest questions in physics. Particle physics combined with astrophysical measurements of the abundance gives rise to a dark matter candidate called weakly interacting massive particle (WIMP). The low density of WIMPs in the galaxies and the extremely weak nature of the interaction with ordinary matter make detection of the WIMP an extraordinarily challenging task, with abundant fakes from various radioactive and cosmogenic backgrounds with much stronger electromagnetic interaction. The extremely weak nature of the WIMP interaction dictates detectors that have extremely low naturally occurring radioactive background, a large active volume (mass) of sensitive detector material to maximize statistics, a highly efficient detector-based rejection mechanism for the dominant electromagnetic background and sophisticated analysis techniques to reject any residual background. This paper reviews currently available major technologies being pursued by various collaborations, with special emphasis on the cryogenic Ge detector technology used by the Cryogenic Dark Matter Search Collaboration (CDMS).     

Value functions for certain class of Hamilton Jacobi equations

We consider a class of Hamilton Jacobi equations (in short, HJE) of type

$ u_t + \frac{1}{2}\big(|u_{x_1}|^2+ \cdots +|u_{x_{n-1}}|^2\big) + \frac{\mathrm{e}^u}{m}|u_{x_n}|^m=0, $

in ? ⁿ ×?_?+? and m?>?1, with bounded, Lipschitz continuous initial data. We give a Hopf-Lax type representation for the value function and also characterize the set of minimizing paths. It is shown that the minimizing paths in the representation of value function need not be straight lines. Then we consider HJE with Hamiltonian decreasing in u of type

$ u_t + H_1\big(u_{x_1},\ldots,u_{x_i}\big) + \mathrm{e}^{-u}H_2\big(u_{x_{i+1}},\ldots, u_{x_n}\big)=0 $

where H ₁,H ₂ are convex, homogeneous of degree n,m?>?1 respectively and the initial data is bounded, Lipschitz continuous. We prove that there exists a unique viscosity solution for this HJE in Lipschitz continuous class. We also give a representation formula for the value function.

     

The Hoyle state in nuclear lattice effective field theory

We review the calculation of the Hoyle state of ¹²C in nuclear lattice effective field theory (NLEFT) and its anthropic implications in the nucleosynthesis of ¹²C and ¹⁶O in red giant stars. We also analyse the extension of NLEFT to the regime of medium-mass nuclei, with emphasis on the determination of the ground-state energies of the α nuclei ¹⁶O, ²⁰Ne, ²⁴Mg, and ²⁸Si by Euclidean time projection. Finally, we discuss recent NLEFT results for the spectrum, electromagnetic properties, and α-cluster structure of ¹⁶O.     

Exciplex parameters: key factors in the dielectric behaviour of magnetodynamics

Photoinduced electron transfer reactions in solution produce two primary geminate radical ion pairs: contact ion pair or exciplex and solvent-separated ion pair. The magnetodynamics of radical ion pairs involves suppression of the spin-evolution between singlet and triplet states of a fraction of solvent-separated ion pairs, the partners of which undergo prior diffusion to attain the distance where exchange interaction is negligible, in the presence of an external low magnetic field of the order of the hyperfine interactions present in the system. This results in an increase in geminate recombination of the singlet solvent-separated ion pairs and enhancement in exciplex luminescence since the precursor radical ion pair is singlet. Although seemingly magnetodynamics is a diffusion-controlled phenomenon that should depend mainly on the dielectric constant of the medium (keeping viscosity almost constant), it is not true for all the exciplex systems since the nature of the magnetic field effect versus medium dielectric curves differ from each other in peak positions, peak heights and onset points. To investigate this differential nature, magnetic field effects among exciplex systems consisting of different derivatives of carbazole as electron donors are compared with a universal acceptor, 1,4-dicyano-benzene, with the pyrene—N,N-dimethylaniline exciplex system as reference. It was found that, apart from the solvent dielectric, the exciplex energy and the bulk effect of the steric constraints present on either donor or acceptor site, regulating the optimum inter-radical distance in the initially formed radical ion pair, are the key factors in controlling the magnetodynamic behaviour.     

Goos–Hänchen shift for higher-order Hermite–Gaussian beams

We study the reflection of a Hermite–Gaussian beam at an interface between two dielectric media. We show that unlike Laguerre–Gaussian beams, Hermite–Gaussian beams undergo no significant distortion upon reflection. We report Goos–H?nchen shift for all the spots of a higher-order Hermite–Gaussian beam near the critical angle. The shift is shown to be insignificant away from the critical angle. The calculations are carried out neglecting the longitudinal component along the direction of propagation for a spatially finite, s-polarized, full 3D vector beam. We briefly discuss the difficulties associated with the paraxial approximation pertaining to a vector Gaussian beam.     

SUSY formalism for the symmetric double well potential

Using first- and second-order supersymmetric Darboüx formalism and starting with symmetric double well potential barrier we have obtained a class of exactly solvable potentials subject to moving boundary condition. The eigenstates are also obtained by the same technique.