ON THE ROLES OF COMPLEMENTARY AND ADMISSIBLE BOUNDARY CONSTRAINTS IN FOURIER SOLUTIONS TO THE BOUNDARY VALUE PROBLEMS OF COMPLETELY COUPLED r TH ORDER PDES

A heretofore unavailable double Fourier series based approach, for obtaining non-separable solution to a system of completely coupled linear r th order partial differential equations with constant coefficients and subjected to general (completely coupled) boundary conditions, has been presented. The method has been successfully implemented to solve a class of hitherto unsolved boundary-value problems, pertaining to free and forced vibrations of arbitrarily laminated anisotropic doubly curved thin panels of rectangular planform, with arbitrarily prescribed (both symmetric and asymmetric with respect to the panel centerlines) admissible boundary conditions and subjected to general transverse loading.Existing solutions such as those due to Navier or Levy are based on the well-known method of separation of variables. Such solutions represent particular solutions whenever the method of separation of variables work, and when these particular solution functions fortuitously satisfy the boundary conditions. For derivation of the complementary solution, the complementary boundary constraints are introduced through boundary discontinuities of some of the particular solution functions and their partial derivatives. Such discontinuities form sets of measure zero.Various cases of lamination, geometry and dynamic response (forced and free vibrations) of a class of thin anisotropic laminated shells (curved panels) have been shown to follow from the above. Six sets of boundary conditions are used to illustrate the present method for the derivation of complementary solutions. Navier-type solutions whenever available form special cases of the present general solution.     

RELIABILITY EVALUATIONS OF 3-D FRAME SUBJECTED TO NON-STATIONARY EARTHQUAKE

The objective of the present work is to evaluate the integrated reliability of multistoried space frame subjected to random earthquake. The stochastic ground motion is described by fully non-stationary sigma-oscillatory model. The stochastic dynamic analysis is performed in the frequency domain to obtain the power spectral density function of random response. Finally, the reliability formulations are developed based on computed random response through the solution of first passage problem. A building frame idealized as a space frame in finite element modelling is considered for reliability analysis. Simple modal analysis is also performed for comparison of results.     

Spin squeezing and quantum correlations

We discuss the notion of spin squeezing considering two mutually exclusive classes of spin-s states, namely, oriented and non-oriented states. Our analysis shows that the oriented states are not squeezed while non-oriented states exhibit squeezing. We also present a new scheme for construction of spin-s states using 2s spinors oriented along different axes. Taking the case of s=1, we show that the ‘non-oriented’ nature and hence squeezing arise from the intrinsic quantum correlations that exist among the spinors in the coupled state.     

An economic production lot-size model with shortages and time-dependent demand

In the present article, a production-inventory model is developedover an infinite plan ning horizon where the demand varies linearlywith time, unit production cost is taken as a function of theproduction rate, and shortages in inventory are permitted andare fully back-ordered. The machine production rate, which isassumed to be flexible, is treated as a decision variable. Theassociated nonlinear programming problem is modified by usingthe barrier-function method, and then a search technique isused to find the solution numerically. The analysis of the presentmodel of the production system points to optimality under conditionsthat are commonly recognized as ‘just in time’.     

Nuclear multifragmentation: Basic concepts

We present a brief overview of nuclear multifragmentation reaction. Basic formalism of canonical thermodynamical model based on equilibrium statistical mechanics is described. This model is used to calculate basic observables of nuclear multifragmentation like mass distribution, fragment multiplicity, isotopic distribution and isoscaling. Extension of canonical thermodynamical model to a projectile fragmentation model is outlined. Application of the projectile fragmentation model for calculating average number of intermediate mass fragments and the average size of the largest cluster at different Z _bound, differential charge distribution and cross-section of neutron-rich nuclei of different projectile fragmentation reactions at different energies are described. Application of nuclear multifragmentation reaction in basic research as well as in other domains is outlined.     

Theory of sheath in a collisional multi-component plasma

The aim of this brief report is to study the behaviour of sheath structure in a multi-component plasma with dust-neutral collisions. The plasma consists of electrons, ions, micron size negatively charged dust particles and neutrals. The sheath-edge potential and sheath width are calculated for collisionally dominated sheath. Comparison of collisionless and collisionally dominated sheath are made.     

Analysis of a shielded TE011 mode composite dielectric resonator for stable frequency reference

Analysis of a TE₀₁₁ mode composite sapphire-rutile dielectric resonator has been carried out to study the temperature variation of resonance frequency, close to the Cs atomic clock hyperfine frequency of 9.192 GHz. The complementary behavior of dielectric permittivity with temperature of the composite has been exploited to obtain the desired turning point in the resonant frequency. The frequency of the composite structure is found to be independent of the shield diameter beyond four times the puck diameter.     

ON SELECTIVE HARVESTING OF TWO COMPETING FISH SPECIES IN THE PRESENCE OF ENVIRONMENTAL FLUCTUATION

ABSTRACT. The present paper deals with a problem of selective harvesting of two competing fish species in a randomly fluctuating environment. The environmental parameters are assumed to be perturbed by white noise characterized by a Gaussian distribution with mean zero and unit spectral density. The dynamic behavior of the stochastic system is studied and the fluctuations in population are measured both analytically and numerically by computer simulation.     

Hydration-induced conformational changes in protonated 2,4-pentanedione in the gas phase

Starting with H⁺[CH₃C(O)CH₂C(O)CH₃] (denoted H⁺PD), the protonated diketone-water clusters H⁺PD(H₂O) _n (n = 1–3) have been characterized by density functional theory calculations in combination with vibrational predissociation spectroscopy to explore the conformational changes of a protonated bifunctional ion solvated by water in the gas phase. Theoretical calculations for H⁺PD revealed that the ion contains an intramolecular hydrogen bond (IHB), with two oxygen atoms bridged by the extra proton in an O—H⁺ … O form. Attachment of one water molecule to it readily ruptures this IHB, replacing the H⁺ by the H₃O⁺ moiety. Further replacement of the IHB by two water molecules occurs at n = 2 and the ?C(O)CH₂C(O)- chain is fully opened (or unfolded) after transfer of the extra proton to the water trimer at n = 3. To verify the computational findings, infrared spectroscopic measurements were performed using a vibrational predissociation ion trap spectrometer to identify cluster isomers from the signatures of hydrogen bonded and non-hydrogen bonded OH stretching spectra of H⁺PD(H₂O)_2,3 produced in a corona discharge supersonic expansion. Besides open form isomers, evidence for the formation of water-bridged structures has been found for H⁺PD(H₂O)₃ at an estimated temperature of 200 K. A detailed illustration of the unfolding steps as well as the energy profiles for the evolution of a two-water bridge isomer from the protonated H⁺PD monomer are analysed pictorially (including both stable intermediates and transition states) in the present investigation.