Rigid Rotor as a Toy Model for Hodge Theory

We apply the superfield approach to the toy model of a rigid rotor and show the existence of the nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations, under which, the kinetic term and action remain invariant. Furthermore, we also derive the off-shell nilpotent and absolutely anticommuting (anti-) co-BRST symmetry transformations, under which, the gauge-fixing term and Lagrangian remain invariant. The anticommutator of the above nilpotent symmetry transformations leads to the derivation of a bosonic symmetry transformation, under which, the ghost terms and action remain invariant. Together, the above transformations (and their corresponding generators) respect an algebra that turns out to be a physical realization of the algebra obeyed by the de Rham cohomological operators of differential geometry. Thus, our present model is a toy model for the Hodge theory.Comment: LaTeX file, 22 page

Absolutely anticommuting (anti-)BRST symmetry transformations for topologically massive Abelian gauge theory

We demonstrate the existence of the nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the four (3 + 1)-dimensional (4D) topologically massive Abelian U(1) gauge theory that is described by the coupled Lagrangian densities (which incorporate the celebrated (B \wedge F) term). The absolute anticommutativity of the (anti-) BRST symmetry transformations is ensured by the existence of a Curci-Ferrari type restriction that emerges from the superfield formalism as well as from the equations of motion that are derived from the above coupled Lagrangian densities. We show the invariance of the action from the point of view of the symmetry considerations as well as superfield formulation. We discuss, furthermore, the topological term within the framework of superfield formalism and provide the geometrical meaning of its invariance under the (anti-) BRST symmetry transformations.Comment: LaTeX file, 22 pages, journal versio

Superfield Approach to (Non-)local Symmetries for One-Form Abelian Gauge Theory

We exploit the geometrical superfield formalism to derive the local, covariant and continuous Becchi-Rouet-Stora-Tyutin (BRST) symmetry transformations and the non-local, non-covariant and continuous dual-BRST symmetry transformations for the free Abelian one-form gauge theory in four $(3 + 1)$-dimensions (4D) of spacetime. Our discussion is carried out in the framework of BRST invariant Lagrangian density for the above 4D theory in the Feynman gauge. The geometrical origin and interpretation for the (dual-)BRST charges (and the transformations they generate) are provided in the language of translations of some superfields along the Grassmannian directions of the six ($4 + 2)$-dimensional supermanifold parametrized by the four spacetime and two Grassmannian variables.Comment: LaTeX file, 23 page

Linear stability, transient energy growth and the role of viscosity stratification in compressible plane Couette flow

Linear stability and the non-modal transient energy growth in compressible plane Couette flow are investigated for two prototype mean flows: (a) the {\it uniform shear} flow with constant viscosity, and (b) the {\it non-uniform shear} flow with {\it stratified} viscosity. Both mean flows are linearly unstable for a range of supersonic Mach numbers ($M$). For a given $M$, the critical Reynolds number ($Re$) is significantly smaller for the uniform shear flow than its non-uniform shear counterpart. An analysis of perturbation energy reveals that the instability is primarily caused by an excess transfer of energy from mean-flow to perturbations. It is shown that the energy-transfer from mean-flow occurs close to the moving top-wall for ``mode I'' instability, whereas it occurs in the bulk of the flow domain for ``mode II''. For the non-modal analysis, it is shown that the maximum amplification of perturbation energy, $G_{\max}$, is significantly larger for the uniform shear case compared to its non-uniform counterpart. For $\alpha=0$, the linear stability operator can be partitioned into ${\cal L}\sim \bar{\cal L} + Re^2{\cal L}_p$, and the $Re$-dependent operator ${\cal L}_p$ is shown to have a negligibly small contribution to perturbation energy which is responsible for the validity of the well-known quadratic-scaling law in uniform shear flow: $G(t/{\it Re}) \sim {\it Re}^2$. A reduced inviscid model has been shown to capture all salient features of transient energy growth of full viscous problem. For both modal and non-modal instability, it is shown that the {\it viscosity-stratification} of the underlying mean flow would lead to a delayed transition in compressible Couette flow

Targeted Molecular Therapies for SBMA

Spinal and bulbar muscular atrophy (SBMA) is a late-onset neuromuscular disease caused by a polyglutamine expansion in the androgen receptor gene which results in progressive spinal and bulbar motor neuron degeneration, and muscle atrophy. Although the causative genetic defect is known, until recently, the molecular pathogenesis of the disease was unclear, resulting in few, if any, targets for therapy development. However, over the past decade, our understanding of the pathomechanisms that play a role in SBMA has increased dramatically, and several of these pathways and mechanisms have now been investigated as possible therapeutic targets. In this review, we discuss some of the key pathomechanisms implicated in SBMA and describe some of the therapeutic strategies that have been tested in SBMA to date, which fall into four main categories: (i) gene silencing; (ii) protein quality control and/or increased protein degradation; (iii) androgen deprivation; and (iv) modulation of AR function. Finally, it is also now clear that in addition to a greater understanding of the molecular mechanisms that underlie disease, the development of an effective disease modifying therapy for SBMA will require the coordinated, collaborative effort of research teams with diverse areas of expertise, clinicians, pharmaceutical companies as well as patient groups

Detection of a Moving Rigid Solid in a Perfect Fluid

In this paper, we consider a moving rigid solid immersed in a potential fluid. The fluid-solid system fills the whole two dimensional space and the fluid is assumed to be at rest at infinity. Our aim is to study the inverse problem, initially introduced in [3], that consists in recovering the position and the velocity of the solid assuming that the potential function is known at a given time. We show that this problem is in general ill-posed by providing counterexamples for which the same potential corresponds to different positions and velocities of a same solid. However, it is also possible to find solids having a specific shape, like ellipses for instance, for which the problem of detection admits a unique solution. Using complex analysis, we prove that the well-posedness of the inverse problem is equivalent to the solvability of an infinite set of nonlinear equations. This result allows us to show that when the solid enjoys some symmetry properties, it can be partially detected. Besides, for any solid, the velocity can always be recovered when both the potential function and the position are supposed to be known. Finally, we prove that by performing continuous measurements of the fluid potential over a time interval, we can always track the position of the solid.Comment: 19 pages, 14 figure

Free Abelian 2-Form Gauge Theory: BRST Approach

We discuss various symmetry properties of the Lagrangian density of a four (3 + 1)-dimensional (4D) free Abelian 2-form gauge theory within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. The present free Abelian gauge theory is endowed with a Curci-Ferrari type condition which happens to be a key signature of the 4D non-Abelian 1-form gauge theory. In fact, it is due to the above condition that the nilpotent BRST and anti-BRST symmetries of the theory are found to be absolutely anticommuting in nature. For our present 2-form gauge theory, we discuss the BRST, anti-BRST, ghost and discrete symmetry properties of the Lagrangian densities and derive the corresponding conserved charges. The algebraic structure, obeyed by the above conserved charges, is deduced and the constraint analysis is performed with the help of the physicality criteria where the conserved and nilpotent (anti-)BRST charges play completely independent roles. These physicality conditions lead to the derivation of the above Curci-Ferrari type restriction, within the framework of BRST formalism, from the constraint analysis.Comment: LaTeX file, 21 pages, journal referenc

Magnetic and Transport Properties of Ternary Indides of type R2CoIn8 (R = Ce, Pr and Dy)

We have synthesized and investigated the magnetic and transport properties of a series of compounds, R2CoIn8 (R = rare earth). Compounds form in single phase with a tetragonal structure (space group P4/mmm, no. 162). The Ce compound shows heavy fermion behavior. The magnetic susceptibility of Pr2CoIn8 shows a marked deviation from the Curie-Weiss behavior at low temperatures, which is attributed to the crystalline electric field effects. Heat capacity and magnetization measurements show that Dy2CoIn8 undergoes a magnetic transition at 17 K and a second transition near 5 K, the latter of which may be due to spin reorientation. Magnetization of this compound shows two metamagnetic transitions approximately at 3.6 T and 8.3 T.Comment: Total 7 pages of text and figure