Repulsive fermions in optical lattices: Phase separation versus coexistence of antiferromagnetism and d-wave superfluidity

We investigate a system of fermions on a two-dimensional optical square lattice in the strongly repulsive coupling regime. In this case, the interactions can be controlled by laser intensity as well as by Feshbach resonance. We compare the energetics of states with resonating valence bond d-wave superfluidity, antiferromagnetic long-range order, and a homogeneous state with coexistence of superfluidity and antiferromagnetism. Using a variational formalism, we show that the energy density of a hole e(hole)(x) has a minimum at doping x = x(c) that signals phase separation between the antiferromagnetic and d-wave paired superfluid phases. The energy of the phase-separated ground state is, however, found to be very close to that of a homogeneous state with coexisting antiferromagnetic and superfluid orders. We explore the dependence of the energy on the interaction strength and on the three-site hopping terms and compare with the nearest-neighbor hopping t-J model.

A Flexible Crypto-system Based upon the REDEFINE Polymorphic ASIC Architecture

The highest levels of security can be achieved through the use of more than one type of cryptographic algorithm for each security function. In this paper, the REDEFINE polymorphic architecture is presented as an architecture framework that can optimally support a varied set of crypto algorithms without losing high performance. The presented solution is capable of accelerating the advanced encryption standard (AES) and elliptic curve cryptography (ECC) cryptographic protocols, while still supporting different flavors of these algorithms as well as different underlying finite field sizes. The compelling feature of this cryptosystem is the ability to provide acceleration support for new field sizes as well as new (possibly proprietary) cryptographic algorithms decided upon after the cryptosystem is deployed.

Geometrically non-linear dynamics of composite four-bar mechanisms

This work intends to demonstrate the importance of a geometrically nonlinear cross-sectional analysis of certain composite beam-based four-bar mechanisms in predicting system dynamic characteristics. All component bars of the mechanism are made of fiber reinforced laminates and have thin rectangular cross-sections. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. They are linked to each other by means of revolute joints. We restrict ourselves to linear materials with small strains within each elastic body (beam). Each component of the mechanism is modeled as a beam based on geometrically non-linear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and non-linear 1-D analyses along the three beam reference curves. For the thin rectangular cross-sections considered here, the 2-D cross-sectional non-linearity is also overwhelming. This can be perceived from the fact that such sections constitute a limiting case between thin-walled open and closed sections, thus inviting the non-linear phenomena observed in both. The strong elastic couplings of anisotropic composite laminates complicate the model further. However, a powerful mathematical tool called the Variational Asymptotic Method (VAM) not only enables such a dimensional reduction, but also provides asymptotically correct analytical solutions to the non-linear cross-sectional analysis. Such closed-form solutions are used here in conjunction with numerical techniques for the rest of the problem to predict multi-body dynamic responses more quickly and accurately than would otherwise be possible. The analysis methodology can be viewed as a three-step procedure: First, the cross-sectional properties of each bar of the mechanism is determined analytically based on an asymptotic procedure, starting from Classical Laminated Shell Theory (CLST) and taking advantage of its thin strip geometry. Second, the dynamic response of the non-linear, flexible four-bar mechanism is simulated by treating each bar as a 1-D beam, discretized using finite elements, and employing energy-preserving and -decaying time integration schemes for unconditional stability. Finally, local 3-D deformations and stresses in the entire system are recovered, based on the 1-D responses predicted in the previous step. With the model, tools and procedure in place, we identify and investigate a few four-bar mechanism problems where the cross-sectional non-linearities are significant in predicting better and critical system dynamic characteristics. This is carried out by varying stacking sequences (i.e. the arrangement of ply orientations within a laminate) and material properties, and speculating on the dominating diagonal and coupling terms in the closed-form non-linear beam stiffness matrix. A numerical example is presented which illustrates the importance of 2-D cross-sectional non-linearities and the behavior of the system is also observed by using commercial software (I-DEAS + NASTRAN + ADAMS). (C) 2012 Elsevier Ltd. All rights reserved.

Existence of Value in Stochastic Differential Games of Mixed Type

In this article, we address stochastic differential games of mixed type with both control and stopping times. Under standard assumptions, we show that the value of the game can be characterized as the unique viscosity solution of corresponding Hamilton-Jacobi-Isaacs (HJI) variational inequalities.

VAM applied to dimensional reduction of non-linear hyperelastic plates

This work aims at dimensional reduction of non-linear isotropic hyperelastic plates in an asymptotically accurate manner. The problem is both geometrically and materially non-linear. The geometric non-linearity is handled by allowing for finite deformations and generalized warping while the material non-linearity is incorporated through hyperelastic material model. The development, based on the Variational Asymptotic Method (VAM) with moderate strains and very small thickness to shortest wavelength of the deformation along the plate reference surface as small parameters, begins with three-dimensional (3-D) non-linear elasticity and mathematically splits the analysis into a one-dimensional (1-D) through-the-thickness analysis and a two-dimensional (2-D) plate analysis. Major contributions of this paper are derivation of closed-form analytical expressions for warping functions and stiffness coefficients and a set of recovery relations to express approximately the 3-D displacement, strain and stress fields. Consistent with the 2-D non-linear constitutive laws, 2-D plate theory and corresponding finite element program have been developed. Validation of present theory is carried out with a standard test case and the results match well. Distributions of 3-D results are provided for another test case. (c) 2012 Elsevier Ltd. All rights reserved.

3-MANIFOLD GROUPS, KÄHLER GROUPS AND COMPLEX SURFACES

Let G be a Kahler group admitting a short exact sequence 1 -> N -> G -> Q -> 1 where N is finitely generated. (i) Then Q cannot be non-nilpotent solvable. (ii) Suppose in addition that Q satisfies one of the following: (a) Q admits a discrete faithful non-elementary action on H-n for some n >= 2. (b) Q admits a discrete faithful non-elementary minimal action on a simplicial tree with more than two ends. (c) Q admits a (strong-stable) cut R such that the intersection of all conjugates of R is trivial. Then G is virtually a surface group. It follows that if Q is infinite, not virtually cyclic, and is the fundamental group of some closed 3-manifold, then Q contains as a finite index subgroup either a finite index subgroup of the three-dimensional Heisenberg group or the fundamental group of the Cartesian product of a closed oriented surface of positive genus and the circle. As a corollary, we obtain a new proof of a theorem of Dimca and Suciu in Which 3-manifold groups are Kahler groups? J. Eur. Math. Soc. 11 (2009) 521-528] by taking N to be the trivial group. If instead, G is the fundamental group of a compact complex surface, and N is finitely presented, then we show that Q must contain the fundamental group of a Seifert-fibered 3-manifold as a finite index subgroup, and G contains as a finite index subgroup the fundamental group of an elliptic fibration. We also give an example showing that the relation of quasi-isometry does not preserve Kahler groups. This gives a negative answer to a question of Gromov which asks whether Kahler groups can be characterized by their asymptotic geometry.

Radial Deformation of Cylinders Due to Torsion

Classical literature on solid mechanics claims existence of radial deformation due to torsion but there is hardly any literature on analytic solutions capturing this phenomenon. This paper tries to solve this problem in an asymptotic sense using the variational asymptotic method (VAM). The method makes no ad hoc assumptions and hence asymptotic correctness is assured. The VAM splits the 3D elasticity problem into two parts: A 1D problem along the length of the cylinder which gives the twist and a 2D cross-sectional problem which gives the radial deformation. This enables closed form solutions, even for some complex problems. Starting with a hollow cylinder, made up of orthotropic but transversely isotropic material, the 3D problem has been formulated and solved analytically despite the presence of geometric nonlinearity. The general results have been specialized for particularly useful cases, such as solid cylinders and/or cylinders with isotropic material. DOI: 10.1115/1.4006803]

Sensory-organ-like response determines the magnetism of zigzag-edged honeycomb nanoribbons

We present an analytical effective theory for the magnetic phase diagram for zigzag-edge terminated honeycomb nanoribbons described by a Hubbard model with an interaction parameter U. We show that the edge magnetic moment varies as ln U and uncover its dependence on the width W of the ribbon. The physics of this owes its origin to the sensory-organ-like response of the nanoribbons, demonstrating that considerations beyond the usual Stoner-Landau theory are necessary to understand the magnetism of these systems. A first-order magnetic transition from an antiparallel orientation of the moments on opposite edges to a parallel orientation occurs upon doping with holes or electrons. The critical doping for this transition is shown to depend inversely on the width of the ribbon. Using variational Monte Carlo calculations, we show that magnetism is robust to fluctuations. Additionally, we show that the magnetic phase diagram is generic to zigzag-edge terminated nanostructures such as nanodots. Furthermore, we perform first-principles modeling to show how such magnetic transitions can be realized in substituted graphene nanoribbons. DOI: 10.1103/PhysRevB.87.085412

A generic variant of NIST’s KAS2 key agreement protocol

We propose a generic three-pass key agreement protocol that is based on a certain kind of trapdoor one-way function family. When specialized to the RSA setting, the generic protocol yields the so-called KAS2 scheme that has recently been standardized by NIST. On the other hand, when specialized to the discrete log setting, we obtain a new protocol which we call DH2. An interesting feature of DH2 is that parties can use different groups (e.g., different elliptic curves). The generic protocol also has a hybrid implementation, where one party has an RSA key pair and the other party has a discrete log key pair. The security of KAS2 and DH2 is analyzed in an appropriate modification of the extended Canetti-Krawczyk security model.

Simulation of length-preserving motions of flexible one dimensional oObjects using optimization

During the motion of one dimensional flexible objects such as ropes, chains, etc., the assumption of constant length is realistic. Moreover,their motion appears to be naturally minimizing some abstract distance measure, wherein the disturbance at one end gradually dies down along the curve defining the object. This paper presents purely kinematic strategies for deriving length-preserving transformations of flexible objects that minimize appropriate ‘motion’. The strategies involve sequential and overall optimization of the motion derived using variational calculus. Numerical simulations are performed for the motion of a planar curve and results show stable converging behavior for single-step infinitesimal and finite perturbations 1 as well as multi-step perturbations. Additionally, our generalized approach provides different intuitive motions for various problem-specific measures of motion, one of which is shown to converge to the conventional tractrix-based solution. Simulation results for arbitrary shapes and excitations are also included.

Three-dimensional acoustic analysis of an elliptical chamber muffler with a side inlet and a side outlet

The acoustical behaviour of an elliptical chamber muffler having a side inlet and side outlet port is analyzed in this paper, wherein a uniform velocity piston source is assumed to model the 3-D acoustic field in the elliptical chamber cavity. Towards this end, we consider the modal expansion of the acoustic pressure field in the elliptical cavity in terms of the angular and radial Mathieu func-tions, subjected to the rigid wall condition. Then, the Green's function due to the point source lo-cated on the side (curved) surface of the elliptical chamber is obtained. On integrating this function over the elliptical piston area on the curved surface of the elliptical chamber and subsequent divi-sion by the area of the elliptic piston, one obtains the acoustic pressure field due to the piston driven source which is equivalent to considering plane wave propagation in the side ports. Thus, one can obtain the acoustic pressure response functions, i.e., the impedance matrix (Z) parameters due to the sources (ports) located on the side surface, from which one may also obtain a progressive wave rep-resentation in terms of the scattering matrix (S). Finally, the acoustic performance of the muffler is evaluated in terms of the Transmission loss (TL) which is computed in terms of the scattering pa-rameters. The effect of the axial length of the muffler and the angular location of the ports on the TL characteristics is studied in detail. The acoustically long chambers show dominant axial plane wave propagation while the TL spectrum of short chambers indicates the dominance of the trans-versal modes. The 3-D analytical results are compared with the 3-D FEM simulations carried on a commercial software and are shown to be in an excellent agreement, thereby validating the analyti-cal procedure suggested in this work.

An Outward-Wave-Favouring Finite Element-Based Strategy for Exterior Acoustical Problems

This work presents a finite element-based strategy for exterior acoustical problems based on an assumed pressure form that favours outgoing waves. The resulting governing equation, weak formulation, and finite element formulation are developed both for coupled and uncoupled problems. The developed elements are very similar to conventional elements in that they are based on the standard Galerkin variational formulation and use standard Lagrange interpolation functions and standard Gaussian quadrature. In addition and in contrast to wave envelope formulations and their extensions, the developed elements can be used in the immediate vicinity of the radiator/scatterer. The method is similar to the perfectly matched layer (PML) method in the sense that each layer of elements added around the radiator absorbs acoustical waves so that no boundary condition needs to be applied at the outermost boundary where the domain is truncated. By comparing against strategies such as the PML and wave-envelope methods, we show that the relative accuracy, both in the near and far-field results, is considerably higher.

Bipolar Poisson Solution for Independent Double-Gate MOSFET

We propose a new set of input voltage equations (IVEs) for independent double-gate MOSFET by solving the governing bipolar Poisson equation (PE) rigorously. The proposed IVEs, which involve the Legendre's incomplete elliptic integral of the first kind and Jacobian elliptic functions and are valid from accumulation to inversion regimes, are shown to have good agreement with the numerical solution of the same PE for all bias conditions.

Evaluation of strength of component-laminates in strip-based mechanisms

This paper deals with the evaluation of the component-laminate load-carrying capacity, i.e., to calculate the loads that cause the failure of the individual layers and the component-laminate as a whole in four-bar mechanism. The component-laminate load-carrying capacity is evaluated using the Tsai-Wu-Hahn failure criterion for various lay-ups. The reserve factor of each ply in the component-laminate is calculated by using the maximum resultant force and the maximum resultant moment occurring at different time steps at the joints of the mechanism. Here, all component bars of the mechanism are made of fiber reinforced laminates and have thin rectangular cross-sections. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. They are linked to each other by means of revolute joints. We restrict ourselves to linear materials with small strains within each elastic body (strip-like beam). Each component of the mechanism is modeled as a beam based on geometrically non-linear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and non-linear 1-D analyses along the three beam reference curves. For the thin rectangular cross-sections considered here, the 2-D cross-sectional nonlinearity is also overwhelming. This can be perceived from the fact that such sections constitute a limiting case between thin-walled open and closed sections, thus inviting the non-linear phenomena observed in both. The strong elastic couplings of anisotropic composite laminates complicate the model further. However, a powerful mathematical tool called the Variational Asymptotic Method (VAM) not only enables such a dimensional reduction, but also provides asymptotically correct analytical solutions to the non-linear cross-sectional analysis. Such closed-form solutions are used here in conjunction with numerical techniques for the rest of the problem to predict more quickly and accurately than would otherwise be possible. Local 3-D stress, strain and displacement fields for representative sections in the component-bars are recovered, based on the stress resultants from the 1-D global beam analysis. A numerical example is presented which illustrates the failure of each component-laminate and the mechanism as a whole.

Chiral Mott insulator with staggered loop currents in the fully frustrated Bose-Hubbard model

Motivated by experiments on Josephson junction arrays in a magnetic field and ultracold interacting atoms in an optical lattice in the presence of a ``synthetic'' orbital magnetic field, we study the ``fully frustrated'' Bose-Hubbard model and quantum XY model with half a flux quantum per lattice plaquette. Using Monte Carlo simulations and the density matrix renormalization group method, we show that these kinetically frustrated boson models admit three phases at integer filling: a weakly interacting chiral superfluid phase with staggered loop currents which spontaneously break time-reversal symmetry, a conventional Mott insulator at strong coupling, and a remarkable ``chiral Mott insulator'' (CMI) with staggered loop currents sandwiched between them at intermediate correlation. We discuss how the CMI state may be viewed as an exciton condensate or a vortex supersolid, study a Jastrow variational wave function which captures its correlations, present results for the boson momentum distribution across the phase diagram, and consider various experimental implications of our phase diagram. Finally, we consider generalizations to a staggered flux Bose-Hubbard model and a two-dimensional (2D) version of the CMI in weakly coupled ladders.