Energy identities in water wave theory for free-surface boundary condition with higher-order derivatives

A modified form of Green's integral theorem is employed to derive the energy identity in any water wave diffraction problem in a single-layer fluid for free-surface boundary condition with higher-order derivatives. For a two-layer fluid with free-surface boundary condition involving higher-order derivatives, two forms of energy identities involving transmission and reflection coefficients for any wave diffraction problem are also derived here by the same method. Based on this modified Green's theorem, hydrodynamic relations such as the energy-conservation principle and modified Haskind–Hanaoka relation are derived for radiation and diffraction problems in a single as well as two-layer fluid.

Affine Hall-Littlewood Functions for A(1)((1)) And Some Constant Term Identities of Cherednik-Macdonald-Mehta Type

We study t-analogs of string functions for integrable highest weight representations of the affine Kac-Moody algebra A(1)((1)). We obtain closed form formulas for certain t-string functions of levels 2 and 4. As corollaries, we obtain explicit identities for the corresponding affine Hall-Littlewood functions, as well as higher level generalizations of Cherednik's Macdonald and Macdonald-Mehta constant term identities.

SOME INFINITE SUMS IDENTITIES

We find the sum of series of the form Sigma(infinity)(i=1) f(i)/i(r) for some special functions f. The above series is a generalization of the Riemann zeta function. In particular, we take f as some values of Hurwitz zeta functions, harmonic numbers, and combination of both. These generalize some of the results given in Mezo's paper (2013). We use multiple zeta theory to prove all results. The series sums we have obtained are in terms of Bernoulli numbers and powers of pi.

Gauge theory of a group of diffeomorphisms. I. General principles

Any (N+M)-parameter Lie group G with an N-parameter subgroup H can be realized as a global group of diffeomorphisms on an M-dimensional base space B, with representations in terms of transformation laws of fields on B belonging to linear representations of H. The gauged generalization of the global diffeomorphisms consists of general diffeomorphisms (or coordinate transformations) on a base space together with a local action of H on the fields. The particular applications of the scheme to space-time symmetries is discussed in terms of Lagrangians, field equations, currents, and source identities. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

State Dependent Attempt Rate Modeling of Single Cell IEEE 802.11 WLANs with Homogeneous Nodes and Poisson Arrivals

Analytical models of IEEE 802.11-based WLANs are invariably based on approximations, such as the well-known mean-field approximations proposed by Bianchi for saturated nodes. In this paper, we provide a new approach for modeling the situation when the nodes are not saturated. We study a State Dependent Attempt Rate (SDAR) approximation to model M queues (one queue per node) served by the CSMA/CA protocol as standardized in the IEEE 802.11 DCF. The approximation is that, when n of the M queues are non-empty, the attempt probability of the n non-empty nodes is given by the long-term attempt probability of n saturated nodes as provided by Bianchi's model. This yields a coupled queue system. When packets arrive to the M queues according to independent Poisson processes, we provide an exact model for the coupled queue system with SDAR service. The main contribution of this paper is to provide an analysis of the coupled queue process by studying a lower dimensional process and by introducing a certain conditional independence approximation. We show that the numerical results obtained from our finite buffer analysis are in excellent agreement with the corresponding results obtained from ns-2 simulations. We replace the CSMA/CA protocol as implemented in the ns-2 simulator with the SDAR service model to show that the SDAR approximation provides an accurate model for the CSMA/CA protocol. We also report the simulation speed-ups thus obtained by our model-based simulation.

Fournier polarography revisited

A theory for Fournier polarography and higher order harmonics is presented. This is valid for reversible systems under semi-infinite diffusion to stationary and expanding plane electrodes. The algorithm is simple, accurate and exploits the identities holding for the interfacial concentrations. The computations — minimal in nature — can be carried out easily and the results given here were evaluated taking into account the presence of harmonics to, at least, the twenty-fifth order.

New insights from a fixed-point analysis of single cell IEEE 802.11 WLANs

We study a fixed-point formalization of the well-known analysis of Bianchi. We provide a significant simplification and generalization of the analysis. In this more general framework, the fixed-point solution and performance measures resulting from it are studied. Uniqueness of the fixed point is established. Simple and general throughput formulas are provided. It is shown that the throughput of any flow will be bounded by the one with the smallest transmission rate. The aggregate throughput is bounded by the reciprocal of the harmonic mean of the transmission rates. In an asymptotic regime with a large number of nodes, explicit formulas for the collision probability, the aggregate attempt rate, and the aggregate throughput are provided. The results from the analysis are compared with ns2 simulations and also with an exact Markov model of the backoff process. It is shown how the saturated network analysis can be used to obtain TCP transfer throughputs in some cases.

Amino acid sequence of the winged bean (Psophocarpus tetragonolobus) basic lectin. Adenine binding and identification of the active-site tryptophan residue

The complete amino acid sequence of winged bean basic agglutinin (WBA I) was obtained by a combination of manual and gas-phase sequencing methods. Peptide fragments for sequence analyses were obtained by enzymatic cleavages using trypsin and Staphylococcus aureus V8 endoproteinase and by chemical cleavages using iodosobenzoic acid, hydroxylamine, and formic acid. COOH-terminal sequence analysis of WBA I and other peptides was performed using carboxypeptidase Y. The primary structure of WBA I was homologous to those of other legume lectins and more so to Erythrina corallodendron. Interestingly, the sequence shows remarkable identities in the regions involved in the association of the two monomers of E. corallodendron lectin. Other conserved regions are the double metal-binding site and residues contributing to the formation of the hydrophobic cavity and the carbohydrate-binding site. Chemical modification studies both in the presence and absence of N-acetylgalactosamine together with sequence analyses of tryptophan-containing tryptic peptides demonstrate that tryptophan 133 is involved in the binding of carbohydrate ligands by the lectin. The location of tryptophan 133 at the active center of WBA I for the first time subserves to explain a role for one of the most conserved residues in legume lectins.

Generalization of Dynkin's Identity and Some Applications

Let X(t) be a right continuous temporally homogeneous Markov pro- cess, Tt the corresponding semigroup and A the weak infinitesimal genera- tor. Let g(t) be absolutely continuous and r a stopping time satisfying E.( S f I g(t) I dt) < oo and E.( f " I g'(t) I dt) < oo Then for f e 9iJ(A) with f(X(t)) right continuous the identity Exg(r)f(X(z)) - g(O)f(x) = E( 5 " g'(s)f(X(s)) ds) + E.( 5 " g(s)Af(X(s)) ds) is a simple generalization of Dynkin's identity (g(t) 1). With further restrictions on f and r the following identity is obtained as a corollary: Ex(f(X(z))) = f(x) + k! Ex~rkAkf(X(z))) + n-1E + (n ) )!.E,(so un-1Anf(X(u)) du). These identities are applied to processes with stationary independent increments to obtain a number of new and known results relating the moments of stopping times to the moments of the stopped processes.

Stochastic models of IEEE 802.11e wireless net works with multimedia applications

We provide a survey of some of our recent results ([9], [13], [4], [6], [7]) on the analytical performance modeling of IEEE 802.11 wireless local area networks (WLANs). We first present extensions of the decoupling approach of Bianchi ([1]) to the saturation analysis of IEEE 802.11e networks with multiple traffic classes. We have found that even when analysing WLANs with unsaturated nodes the following state dependent service model works well: when a certain set of nodes is nonempty, their channel attempt behaviour is obtained from the corresponding fixed point analysis of the saturated system. We will present our experiences in using this approximation to model multimedia traffic over an IEEE 802.11e network using the enhanced DCF channel access (EDCA) mechanism. We have found that we can model TCP controlled file transfers, VoIP packet telephony, and streaming video in the IEEE802.11e setting by this simple approximation.

Minimal three-component SU(2) gadget for polarization optics

Two identities involving quarter-wave plates and half-wave plates are established. These are used to improve on an earlier gadget involving four wave plates leading to a new gadget involving just three plates, a half-wave plate and two quarter-wave plates, which can realize all SU(2) polarization transformations. This gadget is shown to involve the minimum number of quarter-wave and half-wave plates. The analysis leads to a decomposition theorem for SU (2) matrices in terms of factors which are symmetric fourth and eighth roots of the identity.

Effect of dynamical asymmetry on the viscosity of a random copolymer melt

The variation of the viscosity as a function of the sequence distribution in an A-B random copolymer melt is determined. The parameters that characterize the random copolymer are the fraction of A monomers f, the parameter lambda which determines the correlation in the monomer identities along a chain and the Flory chi parameter chi(F) which determines the strength of the enthalpic repulsion between monomers of type A and B. For lambda>0, there is a greater probability of finding like monomers at adjacent positions along the chain, and for lambda<0 unlike monomers are more likely to be adjacent to each other. The traditional Markov model for the random copolymer melt is altered to remove ultraviolet divergences in the equations for the renormalized viscosity, and the phase diagram for the modified model has a binary fluid type transition for lambda>0 and does not exhibit a phase transition for lambda<0. A mode coupling analysis is used to determine the renormalization of the viscosity due to the dependence of the bare viscosity on the local concentration field. Due to the dissipative nature of the coupling. there are nonlinearities both in the transport equation and in the noise correlation. The concentration dependence of the transport coefficient presents additional difficulties in the formulation due to the Ito-Stratonovich dilemma, and there is some ambiguity about the choice of the concentration to be used while calculating the noise correlation. In the Appendix, it is shown using a diagrammatic perturbation analysis that the Ito prescription for the calculation of the transport coefficient, when coupled with a causal discretization scheme, provides a consistent formulation that satisfies stationarity and the fluctuation dissipation theorem. This functional integral formalism is used in the present analysis, and consistency is verified for the present problem as well. The upper critical dimension for this type of renormaliaation is 2, and so there is no divergence in the viscosity in the vicinity of a critical point. The results indicate that there is a systematic dependence of the viscosity on lambda and chi(F). The fluctuations tend to increase the viscosity for lambda<0, and decrease the viscosity for lambda>0, and an increase in chi(F) tends to decrease the viscosity. (C) 1996 American Institute of Physics.

The algebra and geometry of SU(3) matrices

We give an elementary treatment of the defining representation and Lie algebra of the three-dimensional unitary unimodular group SU(3). The geometrical properties of the Lie algebra, which is an eight dimensional real Linear vector space, are developed in an SU(3) covariant manner. The f and d symbols of SU(3) lead to two ways of 'multiplying' two vectors to produce a third, and several useful geometric and algebraic identities are derived. The axis-angle parametrization of SU(3) is developed as a generalization of that for SU(2), and the specifically new features are brought out. Application to the dynamics of three-level systems is outlined.

Microwave cavity resonators. Some perturbation effects and their applications

Lagrange's equation is utilized to show the analogy of a lossless microwave cavity resonator with the conventional LC network. A brief discussion on the resonant frequencies of a microwave cavity resonator and the two degenerate companion modes H01 and E11 appearing in a cavity is given. The first order perturbation theory of a small deformation of the wall of a cavity is discussed. The effects of perturbation, such as the change in the resonant frequency and the Q of a cavity, the change in the electromagnetic field configurations and hence mixing of modes are also discussed. An expression for the coupling coefficient between the two degenerate modes H01 and E11 is derived with the help of the field equations. Results indicate that in the absence of perturbation the above two degenerate modes can co-exist without losing their individual identities. Several applications of the perturbation theory, such as the measurement of the dielectric properties of matter, study of ferromagnetic resonance, etc., are described.

Thermodynamics of higher spin black holes in 3D

We examine the thermodynamic properties of recently constructed black hole solutions in SL(3, R) x SL(3, R) Chern-Simons theory in the presence of a chemical potential for spin-3 charge, which acts as an irrelevant deformation of the dual CFT with W-3 X W-3 symmetry. The smoothness or holonomy conditions admit four branches of solutions describing a flow between two AdS(3) backgrounds corresponding to two different CFTs. The dominant branch at low temperatures, connected to the BTZ black hole, merges smoothly with a thermodynamically unstable branch and disappears at higher temperatures. We confirm that the UV region of the flow satisfies the Ward identities of a CFT with W-3((2)) x W-3((2)) symmetry deformed by a spin-3/2 current. This allows to identify the precise map between UV and HI thermodynamic variables. We find that the high temperature regime is dominated by a black hole branch whose thermodynamics can only be consistently inferred with reference to this W-3((2)) x W-3((2)) CFT.