Exact spectral functions of a non-Fermi liquid in one dimension

We study the exact one-electron propagator and spectral function of a solvable model of interacting electrons due to Schulz and Shastry. The solution previously found for the energies and wave functions is extended to give spectral functions that turn out to be computable, interesting, and nontrivial. They provide one of the few examples of cases where the spectral functions are known asymptotically as well as exactly.

Quantum spin models with exact dimer ground states

Inspired by the exact solution of the Majumdar-Ghosh model, a family of one-dimensional, translationally invariant spin Hamiltonians is constructed. The exchange coupling in these models is antiferromagnetic, and decreases linearly with the separation between the spins. The coupling becomes identically zero beyond a certain distance. It is rigorously proved that the dimer configuration is an exact, superstable ground-state configuration of all the members of the family on a periodic chain. The ground state is twofold degenerate, and there exists an energy gap above the ground state. The Majumdar-Ghosh Hamiltonian with a twofold degenerate dimer ground state is just the first member of the family. The scheme of construction is generalized to two and three dimensions, and illustrated with the help of some concrete examples. The first member in two dimensions is the Shastry-Sutherland model. Many of these models have exponentially degenerate, exact dimer ground states.

Three-Component Self-Assembly of a Series of Triply Interlocked Pd12 Coordination Prisms and Their Non-Interlocked Pd6 Analogues

Template-assisted formation of multicomponent Pd6 coordination prisms and formation of their self-templated triply interlocked Pd12 analogues in the absence of an external template have been established in a single step through Pd?N/Pd?O coordination. Treatment of cis-[Pd(en)(NO3)2] with K3tma and linear pillar 4,4'-bpy (en=ethylenediamine, H3tma=benzene-1,3,5-tricarboxylic acid, 4,4'-bpy=4,4'-bipyridine) gave intercalated coordination cage [{Pd(en)}6(bpy)3(tma)2]2[NO3]12 (1) exclusively, whereas the same reaction in the presence of H3tma as an aromatic guest gave a H3tma-encapsulating non-interlocked discrete Pd6 molecular prism [{Pd(en)}6(bpy)3(tma)2(H3tma)2][NO3]6 (2). Though the same reaction using cis-[Pd(NO3)2(pn)] (pn=propane-1,2-diamine) instead of cis-[Pd(en)(NO3)2] gave triply interlocked coordination cage [{Pd(pn)}6(bpy)3(tma)2]2[NO3]12 (3) along with non-interlocked Pd6 analogue [{Pd(pn)}6(bpy)3(tma)2](NO3)6 (3'), and the presence of H3tma as a guest gave H3tma-encapsulating molecular prism [{Pd(pn)}6(bpy)3(tma)2(H3tma)2][NO3]6 (4) exclusively. In solution, the amount of 3' decreases as the temperature is decreased, and in the solid state 3 is the sole product. Notably, an analogous reaction using the relatively short pillar pz (pz=pyrazine) instead of 4,4'-bpy gave triply interlocked coordination cage [{Pd(pn)}6(pz)3(tma)2]2[NO3]12 (5) as the single product. Interestingly, the same reaction using slightly more bulky cis-[Pd(NO3)2(tmen)] (tmen=N,N,N',N'-tetramethylethylene diamine) instead of cis-[Pd(NO3)2(pn)] gave non-interlocked [{Pd(tmen)}6(pz)3(tma)2][NO3]6 (6) exclusively. Complexes 1, 3, and 5 represent the first examples of template-free triply interlocked molecular prisms obtained through multicomponent self-assembly. Formation of the complexes was supported by IR and multinuclear NMR (1H and 13C) spectroscopy. Formation of guest-encapsulating complexes (2 and 4) was confirmed by 2D DOSY and ROESY NMR spectroscopic analyses, whereas for complexes 1, 3, 5, and 6 single-crystal X-ray diffraction techniques unambiguously confirmed their formation. The gross geometries of H3tma-encapsulating complexes 2 and 4 were obtained by universal force field (UFF) simulations.

Combination of similarity measures for time series classification using genetic algorithms

Time series classification deals with the problem of classification of data that is multivariate in nature. This means that one or more of the attributes is in the form of a sequence. The notion of similarity or distance, used in time series data, is significant and affects the accuracy, time, and space complexity of the classification algorithm. There exist numerous similarity measures for time series data, but each of them has its own disadvantages. Instead of relying upon a single similarity measure, our aim is to find the near optimal solution to the classification problem by combining different similarity measures. In this work, we use genetic algorithms to combine the similarity measures so as to get the best performance. The weightage given to different similarity measures evolves over a number of generations so as to get the best combination. We test our approach on a number of benchmark time series datasets and present promising results.

Exact internal controllability for a hyperbolic problem in a domain with highly oscillating boundary

In this paper, by using the Hilbert Uniqueness Method (HUM), we study the exact controllability problem described by the wave equation in a three-dimensional horizontal domain bounded at the bottom by a smooth wall and at the top by a rough wall. The latter is assumed to consist in a plane wall covered with periodically distributed asperities whose size depends on a small parameter epsilon > 0, and with a fixed height. Our aim is to obtain the exact controllability for the homogenized equation. In the process, we study the asymptotic analysis of wave equation in two setups, namely solution by standard weak formulation and solution by transposition method.

Analysis of an queue operated under the FCFS policy with exact admission control

In this article, we present an exact theoretical analysis of an system, with arbitrary distribution of relative deadline for the end of service, operated under the first come first served scheduling policy with exact admission control. We provide an explicit solution to the functional equation that must be satisfied by the workload distribution, when the system reaches steady state. We use this solution to derive explicit expressions for the loss ratio and the sojourn time distribution. Finally, we compare this loss ratio with that of a similar system operating without admission control, in the cases of some common distributions of the relative deadline.

Frequency Domain Based Solution for Certain Class of Wave Equations: An exhaustive study of Numerical Solutions

The paper discusses the frequency domain based solution for a certain class of wave equations such as: a second order partial differential equation in one variable with constant and varying coefficients (Cantilever beam) and a coupled second order partial differential equation in two variables with constant and varying coefficients (Timoshenko beam). The exact solution of the Cantilever beam with uniform and varying cross-section and the Timoshenko beam with uniform cross-section is available. However, the exact solution for Timoshenko beam with varying cross-section is not available. Laplace spectral methods are used to solve these problems exactly in frequency domain. The numerical solution in frequency domain is done by discretisation in space by approximating the unknown function using spectral functions like Chebyshev polynomials, Legendre polynomials and also Normal polynomials. Different numerical methods such as Galerkin Method, Petrov- Galerkin method, Method of moments and Collocation method or the Pseudo-spectral method in frequency domain are studied and compared with the available exact solution. An approximate solution is also obtained for the Timoshenko beam with varying cross-section using Laplace Spectral Element Method (LSEM). The group speeds are computed exactly for the Cantilever beam and Timoshenko beam with uniform cross-section and is compared with the group speeds obtained numerically. The shear mode and the bending modes of the Timoshenko beam with uniform cross-section are separated numerically by applying a modulated pulse as the shear force and the corresponding group speeds for varying taper parameter in are obtained numerically by varying the frequency of the input pulse. An approximate expression for calculating group speeds corresponding to the shear mode and the bending mode, and also the cut-off frequency is obtained. Finally, we show that the cut-off frequency disappears for large in, for epsilon > 0 and increases for large in, for epsilon < 0.

Microscopic description of the evolution of the local structure and an evaluation of the chemical pressure concept in a solid solution

Extended x-ray absorption fine-structure studies have been performed at the Zn K and Cd K edges for a series of solid solutions of wurtzite Zn1-xCdxS samples with x = 0.0, 0.1, 0.25, 0.5, 0.75, and 1.0, where the lattice parameter as a function of x evolves according to the well-known Vegard's law. In conjunction with extensive, large-scale first-principles electronic structure calculations with full geometry optimizations, these results establish that the percentage variation in the nearest-neighbor bond distances are lower by nearly an order of magnitude compared to what would be expected on the basis of lattice parameter variation, seriously undermining the chemical pressure concept. With experimental results that allow us to probe up to the third coordination shell distances, we provide a direct description of how the local structure, apparently inconsistent with the global structure, evolves very rapidly with interatomic distances to become consistent with it. We show that the basic features of this structural evolution with the composition can be visualized with nearly invariant Zn-S-4 and Cd-S-4 tetrahedral units retaining their structural integrity, while the tilts between these tetrahedral building blocks change with composition to conform to the changing lattice parameters according to the Vegard's law within a relatively short length scale. These results underline the limits of applicability of the chemical pressure concept that has been a favored tool of experimentalists to control physical properties of a large variety of condensed matter systems.

A modified approach to numerical solution of Fredholm integral equations of the second kind

A modified approach to obtain approximate numerical solutions of Fredholin integral equations of the second kind is presented. The error bound is explained by the aid of several illustrative examples. In each example, the approximate solution is compared with the exact solution, wherever possible, and an excellent agreement is observed. In addition, the error bound in each example is compared with the one obtained by the Nystrom method. It is found that the error bound of the present method is smaller than the ones obtained by the Nystrom method. Further, the present method is successfully applied to derive the solution of an integral equation arising in a special Dirichlet problem. (C) 2015 Elsevier Inc. All rights reserved.

EXACT INTERNAL CONTROLLABILITY FOR THE WAVE EQUATION IN A DOMAIN WITH OSCILLATING BOUNDARY WITH NEUMANN BOUNDARY CONDITION

In this paper, we study the exact controllability of a second order linear evolution equation in a domain with highly oscillating boundary with homogeneous Neumann boundary condition on the oscillating part of boundary. Our aim is to obtain the exact controllability for the homogenized equation. The limit problem with Neumann condition on the oscillating boundary is different and hence we need to study the exact controllability of this new type of problem. In the process of homogenization, we also study the asymptotic analysis of evolution equation in two setups, namely solution by standard weak formulation and solution by transposition method.

An Analytical Solution for Three-Dimensional Diffraction of Plane P-Waves by a Hemispherical Alluvial Valley with Saturated Soil Deposits

An analytical solution for the three-dimensional scattering and diffraction of plane P-waves by a hemispherical alluvial valley with saturated soil deposits is developed by employing Fourier-Bessel series expansion technique. Unlike previous studies, in which the saturated soil deposits were simulated with the single-phase elastic theory, in this paper, they are simulated with Biot's dynamic theory for saturated porous media, and the half space is assumed as a single-phase elastic medium. The effects of the dimensionless frequency, the incidence angle of P-wave and the porosity of soil deposits on the surface displacement magnifications of the hemispherical alluvial valley are investigated. Numerical results show that the existence of a saturated hemispherical alluvial valley has much influence on the surface displacement magnifications. It is more reasonable to simulate soil deposits with Biot's dynamic theory when evaluating the displacement responses of a hemispherical alluvial valley with an incidence of P-waves.

Perturbational Finite Volume Method For The Solution of 2-D Navier-Stokes Equations on Unstructured and Structured Colocated Meshes

Based on the first-order upwind and second-order central type of finite volume( UFV and CFV) scheme, upwind and central type of perturbation finite volume ( UPFV and CPFV) schemes of the Navier-Stokes equations were developed. In PFV method, the mass fluxes of across the cell faces of the control volume (CV) were expanded into power series of the grid spacing and the coefficients of the power series were determined by means of the conservation equation itself. The UPFV and CPFV scheme respectively uses the same nodes and expressions as those of the normal first-order upwind and second-order central scheme, which is apt to programming. The results of numerical experiments about the flow in a lid-driven cavity and the problem of transport of a scalar quantity in a known velocity field show that compared to the first-order UFV and second-order CFV schemes, upwind PFV scheme is higher accuracy and resolution, especially better robustness. The numerical computation to flow in a lid-driven cavity shows that the under-relaxation factor can be arbitrarily selected ranging from 0.3 to 0. 8 and convergence perform excellent with Reynolds number variation from 102 to 104.

Observation Of Diffusion Process Of A Water Droplet Immersed In Protein Solution In Microgravity

Pure liquid - liquid diffusion driven by concentration gradients is hard to study in a normal gravity environment since convection and sedimentation also contribute to the mass transfer process. We employ a Mach - Zehnder interferometer to monitor the mass transfer process of a water droplet in EAFP protein solution under microgravity condition provided by the Satellite Shi Jian No 8. A series of the evolution charts of mass distribution during the diffusion process of the liquid droplet are presented and the relevant diffusion coefficient is determined.

Elastodynamic stress intensity factor history for a semi-infinite crack under three-dimensional transient loading

The dynamic stress intensity factor history for a semi-infinite crack in an otherwise unbounded elastic body is analyzed. The crack is subjected to a pair of suddenly-applied point loadings on its faces at a distance L away from the crack tip. The exact expression for the mode I stress intensity factor as a function of time is obtained. The method of solution is based on the direct application of integral transforms, the Wiener-Hopf technique and the Cagniard-de Hoop method. Due to the existence of the characteristic length in loading this problem was long believed a knotty problem. Some features of the solutions are discussed and graphical result for numerical computation is presented.

Bending solution of high-order refined shear deformation-theory for rectangular composite plates

A new high-order refined shear deformation theory based on Reissner's mixed variational principle in conjunction with the state- space concept is used to determine the deflections and stresses for rectangular cross-ply composite plates. A zig-zag shaped function and Legendre polynomials are introduced to approximate the in-plane displacement distributions across the plate thickness. Numerical results are presented with different edge conditions, aspect ratios, lamination schemes and loadings. A comparison with the exact solutions obtained by Pagano and the results by Khdeir indicates that the present theory accurately estimates the in-plane responses.