Quasiparticle states in disordered superfluids

A model for disordered superfluids and superconductors is considered in terms of the Bogoliubov-de Gennes equation with a random order parameter field. Two characteristic cases are distinguished: model I with a real order parameter (time reversal invariant system) and model II with a complex order parameter (broken time reversal invariance). The fluctuations of the order parameter close the gap in both models, and we investigate the states at the center of the filled gap. The two models have distinctive properties in terms of the quasiparticle states due to different symmetries. Model II exhibits only localized quasiparticle states at the band center. In contrast, the fluctuations of the real order parameter of model I can be described by a nonlinear sigma model which leads to a transition from localized to extended states for dimensionsd>2.     

Prediction of displacement and stress fields of a notched panel with geometric nonlinearity by reduced order modeling

The focus of this investigation is on a first assessment of the predictive capabilities of nonlinear geometric reduced order models for the prediction of the large displacement and stress fields of panels with localized geometric defects, the case of a notch serving to exemplify the analysis. It is first demonstrated that the reduced order model of the notched panel does indeed provide a close match of the displacement and stress fields obtained from full finite element analyses for moderately large static and dynamic responses (peak displacement of 2 and 4 thicknesses). As might be expected, the reduced order model of the virgin panel would also yield a close approximation of the displacement field but not of the stress one. These observations then lead to two “enrichment” techniques seeking to superpose the notch effects on the virgin panel stress field so that a reduced order model of the latter can be used. A very good prediction of the full finite element stresses, for both static and dynamic analyses, is achieved with both enrichments.     

An Euler solver based on locally adaptive discrete velocities

A new discrete-velocity model is presented to solve the three-dimensional Euler equations. The velocities in the model are of an adaptive nature—both the origin of the discrete-velocity space and the magnitudes of the discrete velocities are dependent on the local flow—and are used in a finite-volume context. The numerical implementation of the model follows the near-equilibrium flow method of Nadiga and Pullin and results in a scheme which is second order in space (in the smooth regions and between first and second order at discontinuities) and second order in time. (The three-dimensional code is included.) For one choice of the scaling between the magnitude of the discrete velocities and the local internal energy of the flow, the method reduces to a flux-splitting scheme based on characteristics. As a preliminary exercise, the result of the Sod shock-tube simulation is compared to the exact solution.     

Role of hybridization in phase transition in the Falicov-Kimball model

Extended Falicov-Kimball model has been considered for samarium-chalcogenides where, (a) f-f interactions are considered to be quite large, (b) periodicity of the system has been taken into account, (c) f-d interactions are considered within mean field approximation and (d) the unperturbed conduction bandwidth is taken to be non-zero. We observe both continuous as well as discontinuous transitions and hence conclude that “extended Falicov-Kimball model” is a suitable model which can describe both a first order transition and a suitable intermediate valence phase in Sm-chalcogenides.     

Peierls transition in the quantum spin-Peierls model

We use the density matrix renormalization group method to investigate the role of longitudinal quantized phonons on the Peierls transition in the spin-Peierls model. For both the XY and Heisenberg spin-Peierls model we show that the staggered phonon order parameter scales as sqrt[lambda] (and the dimerized bond order scales as lambda) as lambda-->0 (where lambda is the electron-phonon interaction). This result is true for both linear and cyclic chains. Thus, we conclude that the Peierls transition occurs at lambda=0 in these models. Moreover, for the XY spin-Peierls model we show that the quantum predictions for the bond order follow the classical prediction as a function of inverse chain size for small lambda. We therefore conclude that the zero lambda phase transition is of the mean-field type.     

Replica symmetry breaking in the Ising spin glass model on Bethe-like lattices with loop

The Ising spin glass model on Bethe-like lattices (cactus lattices) is studied using replicas in the presence of a magnetic field. Parisi's order parameter function and the de Almeida–Thouless (AT) line are obtained close to the spin glass transition temperature. The results are compared with those for the Bethe lattice to see the effects of loops. The slope of the order parameter function diminishes considerably for both lattices compared with that for the Sherrington–Kirkpatrick (SK) model. The loci of the AT line for the cactus lattices and the Bethe lattice are above and below that for the SK model, respectively.     

Two nonlinear Dicke models

We consider two simple classes of nonlinear extensions of the Dicke model in order to understand how sensitive the presence of the phase transition is to the structural form of the model Hamiltonian. In both classes, second order phase transitions can occur for sufficiently large values of the coupling constant λ. Gap equations are derived for both classes of nonlinear extensions. Second order phase transitions cannot occur in these classes of models unless the model Hamiltonian contains a bilinear interaction term of the form originally proposed by Dicke.     

Transitions in three-dimensional XY magnets with two chiral order parameters

Two models of classic XY antiferromagnets in three dimensions are studied by Monte Carlo simulation: the model on a simple cubic lattice with two extra intralayer exchanges and the model on a stackedtriangular lattice with an extra interlayer exchange. In suggested models, the order parameters are magnetization and two chiral parameters. A transition corresponds to breaking ℤ₂ ⊗ ℤ₂ ⊗ SO(2) symmetry. A distinct first order transition is found in both models.     

New second order Mumford–Shah model based on Γ-convergence approximation for image processing

In this paper, a second order variational model named the Mumford–Shah total generalized variation (MSTGV) is proposed for simultaneously image denoising and segmentation, which combines the original Γ-convergence approximated Mumford–Shah model with the second order total generalized variation (TGV). For image denoising, the proposed MSTGV can eliminate both the staircase artefact associated with the first order total variation and the edge blurring effect associated with the quadratic H¹ regularization or the second order bounded Hessian regularization. For image segmentation, the MSTGV can obtain clear and continuous boundaries of objects in the image. To improve computational efficiency, the implementation of the MSTGV does not directly solve its high order nonlinear partial differential equations and instead exploits the efficient split Bregman algorithm. The algorithm benefits from the fast Fourier transform, analytical generalized soft thresholding equation, and Gauss–Seidel iteration. Extensive experiments are conducted to demonstrate the effectiveness and efficiency of the proposed model.     

Quasi-3D Navier–Stokes Model for a Rotating Airfoil

A quasi-3D model of the unsteady Navier–Stokes equations in a rotating frame of reference has been developed. The equations governing the flow past a rotating blade are approximated using an order of magnitude analysis on the spanwise derivatives. The model takes into account rotational effects and spanwise outflow at computing expenses in the order of what is typical for similar 2D calculations. Results are presented for both laminar and turbulent flows past blades in pure rotation. In the turbulent case the influence of small-scale turbulence is modelled by the one-equation Baldwin–Barth turbulence model. The computations demonstrate that the main influence of rotation is to increase the maximum lift.     

A comprehensive model for the quantification of linear and nonlinear regime laser-induced fluorescence of OH under A2Σ+←X2Π(1,0) excitation

An analytic model termed the ‘integrated quasi-steady-state’ (IQSS) model for the comprehensive quantification of both linear and nonlinear regime laser-induced fluorescence (LIF) is presented. The IQSS model is optimized for the hydroxyl radical (OH), subject to nanosecond A²Σ⁺←X²Π(1,0) excitation at pressures close to atmospheric. The IQSS model is particularly relevant to experimental conditions where the LIF signal is both spectrally and temporally integrated, such as in planar laser-induced fluorescence experiments. The IQSS model is based around a quasi-steady-state solution to a four-level rate-equation approximation of the OH molecule; this quasi-steady-state solution is then integrated with a triangular functional form for both the spatial and temporal variations to produce an analytic solution. In order to accurately predict LIF in the nonlinear regime, it is shown that both the temporal and the spatial variations of the laser pulse—or ‘wings’ of the laser pulse—must be adequately accounted for in the LIF model formulation. The IQSS model is successfully verified against detailed numerical simulations for variations in the laser irradiance, quenching environment and temperature. Experimentally, the IQSS model is successfully validated by comparing the predicted and measured OH LIF vs. irradiance dependence in the product gases of a methane–air laminar flame.     

An analytic study of the friedel criterion in disordered magnetic states in transition metals in the presence ofS-D hybridisation,using the cluster bethe lattice approach

In this paper we present a new theory for including both short range order and long range order simultaneously in the well known cluster Bethe lattice method for binary alloys. We have used this theory for obtaining the Friedel criterion for the appearance of magnetic moments in disordered states using the single band Hubbard model. This is followed by a study of this criterion in a two-bands-d hybridised Hubbard model, which is considered as a simulation of real transition metals. A new technique for solving this problem in the Bethe lattice network is presented, which yields an analytic solution for the critical correlation strength in the presence of hybridisation and short range order. It is found that in all cases hybridisation tends to diminish the tendency for magnetisation, which is in accord with physical expectations.     

An approximation for prey-predator models with time delay

A prototype prey-predator (P-D) model in which the effective size of the predator population interacting with its prey follows an instantaneous time-delay τ regarding its total size is considered here. A simplified model was derived after substituting the approximation into the above time-delay model. In order to assess the reliability of the simplified model, we performed a comparative study of both models under a wide range of parameter values, focusing on the effect of τ on two issues: (i) the boundary (in parameter space) between the regions leading either to stable fixed points characteristic of the non-delay model, both the boundary and the periods and amplitudes obtained for the time-delay model can be fairly approximated by the corresponding results for the simplified model.     

Purely quadrupolar spin-1 Ising model in a transverse field

A quantum Ising-like spin-1 model characterized by quadrupolar interaction, coupled to an external anisotropic field with both dipole and quadrupole momenta is analyzed. The general phase diagram (including temperature), as well as order parameter, specific heat, and susceptibility are evaluated in the mean-field approximation and exibit a rich structure with transitions of 2° and 1° order and tricritical points. ForT=0 the phase diagram is examined also by a recently formulated improved version of mean-field theory which has the usual mean-field theory as its zero-th order approximation.     

Continuous crystallization in hexagonally ordered materials

We demonstrate that the phase transition from columnar-hexagonal liquid crystal to hexagonal-crystalline solid falls into an unusual universality class, which in three dimensions allows for both discontinuous transitions as well as continuous transitions, characterized by a single set of exponents. We show by a renormalization group calculation (to first order in =4-d) that the critical exponents of the continuous transition are precisely those of the XY model, giving rise to a continuous evolution of elastic moduli. Although the fixed points of the present model are found to be identical to the XY model, the elastic compliance to deformations in the plane of hexagonal order, mu, is nonetheless shown to critically influence the crystallization transition, with the continuous transition being driven to first order by fluctuations as the in-plane response grows weaker, micro-->0.     

Anatomy of Gossamer superconductivity

There are many systems in which two order parameters compete with each other. Of particular interest are systems in which these order parameters are both unconventional. In this contribution, we examine the representative example of a d-wave superconductor in the presence of a d-wave density wave, which has been suggested as a model for the pseudogap phase in the high-T_c superconductors. The physical properties of unconventional superconductivity in the presence of an anisotropic charge density wave are investigated within mean field theory. This model describes many features that were anticipated by an earlier phenomenological treatment of Tallon and Loram. In addition, the quasiparticle density of states in the presence of these two order parameters is calculated, which should be accessible by scanning tunneling microscopy.     

O(N) Random Tensor Models

We define in this paper a class of three-index tensor models, endowed with \({O(N)^{\otimes 3}}\) invariance (N being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor graphs which is strictly larger than the class of Feynman graphs of both the multi-orientable model (and hence of the colored model) and the U(N) invariant models. We first exhibit the existence of a large N expansion for such a model with general interactions. We then focus on the quartic model and we identify the leading and next-to-leading order (NLO) graphs of the large N expansion. Finally, we prove the existence of a critical regime and we compute the critical exponents, both at leading order and at NLO. This is achieved through the use of various analytic combinatorics techniques.     

A cell model for liquids. II. Exact solution for the restricted cell model for hard,parallel squares

A restricted cell model for hard, parallel squares is presented both in a discrete and a continuous version. The model is solved exactly by means of a transfer matrix method and the thermodynamic properties are calculated. Some correlation functions are also obtained, which show that the long range order decays at least as fast as 1/r ².     

Mechanism of Pseudogap Detected by Electronic Raman Scattering： Phase Fluctuation or Hidden Order？

We study the electronic Raman scattering in the cuprates to distinguish the two possible scenarios of the pseudogap normal state. In one scenario, the pseudogap is assumed to be caused by phase fluctuations of the preformed Cooper pairs. We find that pair-breaking peaks appear in both the B1g and B2g Raman channels, and they axe smeared and tend to shift to the same energy with the increasing strength of phase fluctuations. Thus both channels reflect the same pairing energy scale, irrespectively of the doping level. In another scenario, the pseudogap is assumed to be caused by a hidden order that competes with the superconducting order. As an example, we assume that the hidden order is the d-density-wave （DDW） order. We find analytically and numerically that in the DDW normal state there is no Raman peak in the B2g channel in a tight-binding model up to the second nearest-neighbor hopping, while the Raman peak in the Big channel reflects the energy gap caused by the DDW order. This behavior is in agreement with experiments in the pseudogap normal state. To gain further insights, we also calculate the Raman spectra in the DDW＋SC state. We study the doping and temperature dependence of the peak energy in both channels and find a two-gap behavior, which is in agreement with recent Raman experiments. Therefore, our results shed light on the hidden order scenario for the pseudogap.