Supersymmetry In The Two-Anyon Problem

We show that the problem of two anyons interacting through a simple harmonic potential or a Coulomb potential is supersymmetric. The supersymmetry operators map a theory described by statistics parameter θ to one described by π+θ. Thus fermions and bosons go into each other, while semions are supersymmetric by themselves. The simple harmonic problem has a Sp(4) symmetry for any value of θ which explains the energy degeneracies.

Spin and charge density waves in the extended Hubbard model: A slave-boson approach

We use the extended Hubbard model to investigate the properties of the charge- and spin-density-wave phases in the presence of a nearest-neighbors repulsion term in the framework of the slave-boson technique. We show that, contrary to Hartree-Fock results, an instablity may occur for sufficiently high values of the Hubbard repulsion, both in the spin- and charge-density-wave phase, which makes the system discontinuously jump to a phase with a smaller or zero wave amplitude. The limits of applicability of our approach are discussed and our results are compared with previous numerical analysis. The phase diagram of the model at half-filling is determined.

Extended Muskingum method for flood routing

Routing of floods is essential to control the flood flow at the flood control station such that it is within the specified safe limit. In this paper, the applicability of the extended Muskingum method is examined for routing of floods for a case study of Hirakud reservoir, Mahanadi river basin, India. The inflows to the flood control station are of two types-one controllable which comprises of reservoir releases for power and spill and the other is uncontrollable which comprises of inflow from lower tributaries and intermediate catchment between the reservoir and the flood control station. Muskingum model is improved to incorporate multiple sources of inflows and single outflow to route the flood in the reach. Instead of time lag and prismoidal flow parameters, suitable coefficients for various types of inflows were derived using Linear Programming. Presently, the decisions about operation of gates of Hirakud dam are being taken once in 12 h during floods. However, four time intervals of 24, 18, 12 and 6 h are examined to test the sensitivity of the routing time interval on the computed flood flow at the flood control station. It is observed that mean relative error decreases with decrease in routing interval both for calibration and testing phase. It is concluded that the extended Muskingum method can be explored for similar reservoir configurations such as Hirakud reservoir with suitable modifications. (C) 2010 International Association of Hydro-environment Engineering and Research. Asia Pacific Division. Published by Elsevier By. All rights reserved.

Simulation of the infrared spectra of thioacetamide by the extended molecular mechanics method

The infrared spectrum of the matrix-isolated species of thioacetamide has been simulated using the extended molecular mechanics method. The equilibrium structure, vibrational frequencies, dipole moment and infrared absorption intensities of thioacetamide have been calculated in good agreement with the experiment. The vibrational frequencies and infrared absorption intensities for the isotopic molecules (CH2CSNH2)-C-13, (CH3CSNH2)-N-15 and (CH2CSND2)-C-13 have also been calculated consistent with the experiment. The infrared spectra of the matrix isolated species of N- and C- deuterated isotopomers of thioacetamide, CH3CSND2 and CD3CSNH2 have also been simulated in satisfactory agreement with the experimental spectra.

An extended Cahn-Hilliard model for interfaces with cubic anisotropy

For studying systems with a cubic anisotropy in interfacial energy sigma, we extend the Cahn-Hilliard model by including in it a fourth-rank term, namely, gamma (ijlm) [partial derivative (2) c/(partial derivativex(i) partial derivativex(j))] [partial derivative (2) c/(partial derivativex(l) partial derivativex(m))]. This term leads to an additional linear term in the evolution equation for the composition parameter field. It also leads to an orientation-dependent effective fourth-rank coefficient gamma ([hkl]) in the governing equation for the one-dimensional composition profile across a planar interface. The main effect of a non-negative gamma ([hkl]) is to increase both sigma and interfacial width w, each of which, upon suitable scaling, is related to gamma ([hkl]) through a universal scaling function. In this model, sigma is a differentiable function of interface orientation (n) over cap, and does not exhibit cusps; therefore, the equilibrium particle shapes (Wulff shapes) do not contain planar facets. However, the anisotropy in the interfacial energy can be large enough to give rise to corners in the Wulff shapes in two dimensions. In particles of finite sizes, the corners become rounded, and their shapes tend towards the Wulff shape with increasing particle size.

The extended Enskog operator for simple fluids with continuous potentials: single particle and collective properties

We generalized the Enskog theory originally developed for the hard-sphere fluid to fluids with continuous potentials, such as the Lennard–Jones. We derived the expression for the k and ω dependent transport coefficient matrix which enables us to calculate the transport coefficients for arbitrary length and time scales. Our results reduce to the conventional Chapman–Enskog expression in the low density limit and to the conventional k dependent Enskog theory in the hard-sphere limit. As examples, the self-diffusion of a single atom, the vibrational energy relaxation, and the activated barrier crossing dynamics problem are discussed.

Simulation of the infrared spectra of N-methylformamide and N-methylacetamide by the extended molecular mechanics method

The infrared spectra of the matrix isolated species of N-methylformamide (NMF) and N-methylacetamide (NMA) and their N-deuterated molecules have been simulated by the extended molecular mechanics method using an empirical force field which includes charges and charge fluxes as coulombic potential parameters. The structural parameters and dipole. moments of NMF and NMA have. also been computed in satisfactory agreement with the experiment. Good agreement between experimental and calculated vibrational frequencies and infrared absorption band intensities for NMF and NMA and their deuterated molecules has been obtained. The vibrational assignments of NMF and NMA are-discussed taking also into account the infrared absorption intensities.

Two-Stage Extended Kalman Filters with Derivative-Free Local Linearizations

This paper proposes a derivative-free two-stage extended Kalman filter (2-EKF) especially suited for state and parameter identification of mechanical oscillators under Gaussian white noise. Two sources of modeling uncertainties are considered: (1) errors in linearization, and (2) an inadequate system model. The state vector is presently composed of the original dynamical/parameter states plus the so-called bias states accounting for the unmodeled dynamics. An extended Kalman estimation concept is applied within a framework predicated on explicit and derivative-free local linearizations (DLL) of nonlinear drift terms in the governing stochastic differential equations (SDEs). The original and bias states are estimated by two separate filters; the bias filter improves the estimates of the original states. Measurements are artificially generated by corrupting the numerical solutions of the SDEs with noise through an implicit form of a higher-order linearization. Numerical illustrations are provided for a few single- and multidegree-of-freedom nonlinear oscillators, demonstrating the remarkable promise that 2-EKF holds over its more conventional EKF-based counterparts. DOI: 10.1061/(ASCE)EM.1943-7889.0000255. (C) 2011 American Society of Civil Engineers.

Bounds on fourth generation induced lepton flavour violating double insertions in supersymmetry

We derive bounds on leptonic double mass insertions of the type delta(l)(i4)delta(l)(4j) in four generational MSSM, using the present limits on l(i) -> l(j) + gamma. Two main features distinguish the rates of these processes in MSSM4 from MSSM3: (a) tan beta is restricted to be very small less than or similar to 3 and (b) the large masses for the fourth generation leptons. In spite of small tan beta, there is an enhancement in amplitudes with LLRR (4 delta(ll)(i4)delta(rr)(4j)) type insertions which pick up the mass of the fourth generation lepton, m(tau'). We find these bounds to be at least two orders of magnitude more stringent than those in MSSM3. (C) 2011 Elsevier B.V. All rights reserved.

Fermion Electric Dipole Moments in R-parity violating Supersymmetry

In this talk I discuss some aspects of the study of electric dipole moments (EDMs) of the fermions, in the context of R-parity violating (\rpv) Supersymmetry (SUSY). I will start with a brief general discussion of how dipole moments, in general, serve as a probe of physics beyond the Standard Model (SM) and an even briefer summary of \rpv SUSY. I will follow by discussing a general method of analysis for obtaining the leading fermion mass dependence of the dipole moments and present its application to \rpv SUSY case. Then I will summarise the constraints that the analysis of $e,n$ and $Hg$ EDMs provide for the case of trilinear \rpv SUSY couplings and make a few comments on the case of bilinear \rpv, where the general method of analysis proposed by us does not work.

Determinant: Old algorithms, new insights (Extended Abstract)

In this paper we approach the problem of computing the characteristic polynomial of a matrix from the combinatorial viewpoint. We present several combinatorial characterizations of the coefficients of the characteristic polynomial, in terms of walks and closed walks of different kinds in the underlying graph. We develop algorithms based on these characterizations, and show that they tally with well-known algorithms arrived at independently from considerations in linear algebra.

The inhomogeneous extended Bose-Hubbard model: A mean-field theory

We develop an inhomogeneous mean-field theory for the extended Bose-Hubbard model with a quadratic, confining potential. In the absence of this potential, our mean-field theory yields the phase diagram of the homogeneous extended Bose-Hubbard model. This phase diagram shows a superfluid (SF) phase and lobes of Mott-insulator (MI), density-wave (DW), and supersolid (SS) phases in the plane of the chemical potential mu and on-site repulsion U; we present phase diagrams for representative values of V, the repulsive energy for bosons on nearest-neighbor sites. We demonstrate that, when the confining potential is present, superfluid and density-wave order parameters are nonuniform; in particular, we obtain, for a few representative values of parameters, spherical shells of SF, MI, DW, and SS phases. We explore the implications of our study for experiments on cold-atom dipolar condensates in optical lattices in a confining potential.