Feshbach modulation spectroscopy of the Fermi-Hubbard model

In the vicinity of a Feshbach resonance, a system of ultracold atoms in an optical lattice undergoes rich physical transformations which involve molecule formation and hopping of molecules on the lattice and thus goes beyond a single-band Hubbard model description. We explore theoretically the response of this system to a harmonic modulation of the magnetic field, and thus of the scattering length, across the Feshbach resonance. In the regime in which the single-band Hubbard model is still valid, we provide results for the doublon production as a function of the various parameters, such as frequency, amplitude, etc., that characterize the field modulation, as well as the lattice depth. The method may uncover a route towards the efficient creation of ultracold molecules and also provide an alternative to conventional lattice-depth-modulation spectroscopy.

ASYMPTOTIC PRESERVING SCHEME FOR A KINETIC MODEL DESCRIBING IN COMPRESSIBLE FLUIDS

The kinetic theory of fluid turbulence modeling developed by Degond and Lemou in 7] is considered for further study, analysis and simulation. Starting with the Boltzmann like equation representation for turbulence modeling, a relaxation type collision term is introduced for isotropic turbulence. In order to describe some important turbulence phenomenology, the relaxation time incorporates a dependency on the turbulent microscopic energy and this makes difficult the construction of efficient numerical methods. To investigate this problem, we focus here on a multi-dimensional prototype model and first propose an appropriate change of frame that makes the numerical study simpler. Then, a numerical strategy to tackle the stiff relaxation source term is introduced in the spirit of Asymptotic Preserving Schemes. Numerical tests are performed in a one-dimensional framework on the basis of the developed strategy to confirm its efficiency.

Convective heat dissipation with lattice-frame materials

This paper presents experimental results on heat transfer and pressure drop for a compact heat sink made of fully triangulated, lightweight (porosity∼0.938), aluminum lattice-frame materials (LFMs). Due to the inherent structural anisotropy of the LFMs, two mutually perpendicular orientations were selected for the measurements. Constant heat flux was applied to the heat sink under steady state conditions, and dissipated by forced air convection. The experimental data were compared with those predicted from an analytical model based on fin analogy. The experimental results revealed that pressure drop is strongly dependent upon the orientation of the structure, due mainly to the flow blockage effect. For heat transfer measurements, typical local temperature distributions on the substrate under constant heat flux conditions were captured with infrared camera. The thermal behavior of LFMs was found to follow closely that of cylinder banks, with early transition Reynolds number (based on strut diameter) equal to about 300. The Nusselt number prediction from the fin-analogy correlates well with experimental measurements, except at low Reynolds numbers where a slightly underestimation is observed. Comparisons with empty channels and commonly used heat exchanger media show that the present LFM heat sink can remove heat approximately seven times more efficient than an empty channel and as efficient as a bank of cylinders at the same porosity level. The aluminum LFMs are extremely stiff and strong, making them ideal candidates for multifunctional structures requiring both heat dissipation and mechanical load carrying capabilities. © 2003 Elsevier Ltd. All rights reserved.

Lattice instability at a fast moving crack tip

A molecular dynamics method is used to analyze the dynamic propagation of an atomistic crack tip. The simulation shows that the crack propagates at a relatively constant global velocity which is well below the Rayleigh wave velocity. However the local propagation velocity oscillates violently, and it is limited by the longitudinal wave velocity. The crack velocity oscillation is caused by a repeated process of crack tip blunting and sharpening. When the crack tip opening displacement exceeds a certain critical value, a lattice instability takes place and results in dislocation emissions from the crack tip. Based on this concept, a criterion for dislocation emission from a moving crack tip is proposed. The simulation also identifies the emitted dislocation as a source for microcrack nucleation. A simple method is used to examine this nucleation process. (C) 1996 American Institute of Physics.

Phase relaxation model for 2-phase flows

A phase relaxation model (PRM) for 2-phase flows is presented in this paper on the basis of three principal assumptions. The basic equations for PRM arc derived from the Boltzmann equations for gas-partlcle mixture, The general characteristics and solving process of the PRM's basic equations are also presented and discussed. Many terms in the PRM's basic equations contain a factor ε= ρgρp/ρg+ρp2 which is an intrinsic small parameter for 2-phase mixture, with ρg and ρp being respectively the densities of gas and particle phases.This makes it possible to simplify the computation of the PRM's basic equations. The model is applied to for example, studying file steady propagation of shock waves in gas-particle mixture. The analysis shows that with an increase of shock wave strength the relaxation process behind a gasdynamics shock front becomes a kind of dynamics relaxation instead of the standard exponential relaxation process. A method of determining experimentally the velocity and tem...更多perature relaxation rates (or times) of gas-particle flows is suggested and analyzed.

Algorithm for simulating fracture processes in concrete by lattice modeling

To simulate fracture behaviors in concrete more realistically, a theoretical analysis on the potential question in the quasi-static method is presented, then a novel algorithm is proposed which takes into account the inertia effect due to unstable crack propagation and meanwhile requests much lower computational efforts than purely dynamic method. The inertia effect due to load increasing becomes less important and can be ignored with the loading rate decreasing, but the inertia effect due to unstable crack propagation remains considerable no matter how low the loading rate is. Therefore, results may become questionable if a fracture process including unstable cracking is simulated by the quasi-static procedure excluding completely inertia effects. However, it requires much higher computational effort to simulate experiments with not very high loading rates by the dynamic method. In this investigation which can be taken as a natural continuation, the potential question of quasi-static method is analyzed based on the dynamic equations of motion. One solution to this question is the new algorithm mentioned above. Numerical examples are provided by the generalized beam (GB) lattice model to show both fracture processes under different loading rates and capability of the new algorithm.

A simple method to simulate shrinkage-induced cracking in cement-based composites by lattice-type modeling

A new numerical procedure is proposed to investigate cracking behaviors induced by mismatch between the matrix phase and aggregates due to matrix shrinkage in cement-based composites. This kind of failure processes is simplified in this investigation as a purely spontaneous mechanical problem, therefore, one main difficulty during simulating the phenomenon lies that no explicit external load serves as the drive to propel development of this physical process. As a result, it is different from classical mechanical problems and seems hard to be solved by using directly the classical finite element method (FEM), a typical kind of "load -> medium -> response" procedures. As a solution, the actual mismatch deformation field is decomposed into two virtual fields, both of which can be obtained by the classical FEM. Then the actual response is obtained by adding together the two virtual displacement fields based on the principle of superposition. Then, critical elements are detected successively by the event-by-event technique. The micro-structure of composites is implemented by employing the generalized beam (GB) lattice model. Numerical examples are given to show the effectiveness of the method, and detailed discussions are conducted on influences of material properties.

Displacive To Order-Disorder Two-Step Phase Transition Model For Para-Ferroelectric Transition

Two-step phase transition model, displacive to order-disorder, is proposed. The driving forces for these two transitions are fundamentally different. The displacive phase transition is one type of the structural phase transitions. We clearly define the structural phase transition as the symmetry broking of the unit cell and the electric dipole starts to form in the unit cell. Then the dipole-dipole interaction takes place as soon as the dipoles in unit cells are formed. We believe that the dipole-dipole interaction may cause an order-disorder phase transition following the displacive phase transition. Both structural and order-disorder phase transition can be first-order or second-order or in between. We found that the structural transition temperatures can be lower or equal or higher than the order-disorder transition temperature. The para-ferroelectric phase transition is the combination of the displacive and order-disorder phase transitions. It generates a variety of transition configurations along with confusions. In this paper, we discuss all these configurations using our displacive to order-disorder two-step phase transition model and clarified all the confusions.

Asymptotic scaling in the two-dimensional O(3) Nonlinear sigma model: a Monte Carlo study on parallel computers

We investigate the 2d O(3) model with the standard action by Monte Carlo simulation at couplings β up to 2.05. We measure the energy density, mass gap and susceptibility of the model, and gather high statistics on lattices of size L ≤ 1024 using the Floating Point Systems T-series vector hypercube and the Thinking Machines Corp.'s Connection Machine 2. Asymptotic scaling does not appear to set in for this action, even at β = 2.10, where the correlation length is 420. We observe a 20% difference between our estimate m/Λ^─_(Ms) = 3.52(6) at this β and the recent exact analytical result . We use the overrelaxation algorithm interleaved with Metropolis updates and show that decorrelation time scales with the correlation length and the number of overrelaxation steps per sweep. We determine its effective dynamical critical exponent to be z' = 1.079(10); thus critical slowing down is reduced significantly for this local algorithm that is vectorizable and parallelizable.

We also use the cluster Monte Carlo algorithms, which are non-local Monte Carlo update schemes which can greatly increase the efficiency of computer simulations of spin models. The major computational task in these algorithms is connected component labeling, to identify clusters of connected sites on a lattice. We have devised some new SIMD component labeling algorithms, and implemented them on the Connection Machine. We investigate their performance when applied to the cluster update of the two dimensional Ising spin model.

Finally we use a Monte Carlo Renormalization Group method to directly measure the couplings of block Hamiltonians at different blocking levels. For the usual averaging block transformation we confirm the renormalized trajectory (RT) observed by Okawa. For another improved probabilistic block transformation we find the RT, showing that it is much closer to the Standard Action. We then use this block transformation to obtain the discrete β-function of the model which we compare to the perturbative result. We do not see convergence, except when using a rescaled coupling β_E to effectively resum the series. For the latter case we see agreement for m/ Λ^─_(Ms) at , β = 2.14, 2.26, 2.38 and 2.50. To three loops m/Λ^─_(Ms) = 3.047(35) at β = 2.50, which is very close to the exact value m/ Λ^─_(Ms) = 2.943. Our last point at β = 2.62 disagrees with this estimate however.

A model for energy and morphology of crystalline grain boundaries with arbitrary geometric character

It has been well-established that interfaces in crystalline materials are key players in the mechanics of a variety of mesoscopic processes such as solidification, recrystallization, grain boundary migration, and severe plastic deformation. In particular, interfaces with complex morphologies have been observed to play a crucial role in many micromechanical phenomena such as grain boundary migration, stability, and twinning. Interfaces are a unique type of material defect in that they demonstrate a breadth of behavior and characteristics eluding simplified descriptions. Indeed, modeling the complex and diverse behavior of interfaces is still an active area of research, and to the author's knowledge there are as yet no predictive models for the energy and morphology of interfaces with arbitrary character. The aim of this thesis is to develop a novel model for interface energy and morphology that i) provides accurate results (especially regarding "energy cusp" locations) for interfaces with arbitrary character, ii) depends on a small set of material parameters, and iii) is fast enough to incorporate into large scale simulations.

In the first half of the work, a model for planar, immiscible grain boundary is formulated. By building on the assumption that anisotropic grain boundary energetics are dominated by geometry and crystallography, a construction on lattice density functions (referred to as "covariance") is introduced that provides a geometric measure of the order of an interface. Covariance forms the basis for a fully general model of the energy of a planar interface, and it is demonstrated by comparison with a wide selection of molecular dynamics energy data for FCC and BCC tilt and twist boundaries that the model accurately reproduces the energy landscape using only three material parameters. It is observed that the planar constraint on the model is, in some cases, over-restrictive; this motivates an extension of the model.

In the second half of the work, the theory of faceting in interfaces is developed and applied to the planar interface model for grain boundaries. Building on previous work in mathematics and materials science, an algorithm is formulated that returns the minimal possible energy attainable by relaxation and the corresponding relaxed morphology for a given planar energy model. It is shown that the relaxation significantly improves the energy results of the planar covariance model for FCC and BCC tilt and twist boundaries. The ability of the model to accurately predict faceting patterns is demonstrated by comparison to molecular dynamics energy data and experimental morphological observation for asymmetric tilt grain boundaries. It is also demonstrated that by varying the temperature in the planar covariance model, it is possible to reproduce a priori the experimentally observed effects of temperature on facet formation.

Finally, the range and scope of the covariance and relaxation models, having been demonstrated by means of extensive MD and experimental comparison, future applications and implementations of the model are explored.

Um método SN híbrido direto para cálculos de sistemas combustível-moderador em geometria unidimensional

Desenvolvemos nesta dissertação um método híbrido direto para o cálculo do fator de desvantagem e descrição da distribuição do fluxo de nêutrons em sistemas combustível-moderador. Na modelagem matemática, utilizamos a equação de transporte de Boltzmann independente do tempo, considerando espalhamento linearmente anisotrópico no modelo monoenergético e espalhamento isotrópico no modelo multigrupo, na formulação de ordenadas discretas (SN), em geometria unidimensional. Desenvolvemos nesta dissertação um método híbrido direto para o cálculo do fator de desvantagem e descrição da distribuição do fluxo de nêutrons em sistemas combustível-moderador. Na modelagem matemática, utilizamos a equação de transporte de Boltzmann independente do tempo, considerando espalhamento linearmente anisotrópico no modelo monoenergético e espalhamento isotrópico no modelo multigrupo, na formulação de ordenadas discretas (SN), em geometria unidimensional. Descrevemos uma análise espectral das equações de ordenadas discretas (SN)a um grupo e a dois grupos de energia, onde seguimos uma analogia com o método de Case. Utilizamos, neste método, quadraturas angulares diferentes no combustível (NC) e no moderador (NM), onde em geral assumimos que NC > NM . Condições de continuidade especiais que acoplam os fluxos angulares que emergem do combustível (moderador) e incidem no moderador (combustível), foram utilizadas com base na equivalência entre as equações SN e PN-1, o que caracteriza a propriedade híbrida do modelo proposto. Sendo um método híbrido direto, utilizamos as NC + NM equações lineares e algébricas constituídas pelas (NC + NM)/2 condições de contorno reflexivas e (NC + NM)/2 condições de continuidade para determinarmos as NC + NM constantes. Com essas constantes podemos calcular os valores dos fluxos angulares e dos fluxos escalares em qualquer ponto do domínio. Apresentamos resultados numéricos para ilustrar a eficiência e a precisão do método proposto.

A Continuum Model for Slip-Twinning Interactions in Magnesium and Magnesium Alloys

Due to their high specific strength and low density, magnesium and magnesium-based alloys have gained great technological importance in recent years. However, their underlying hexagonal crystal structure furnishes Mg and its alloys with a complex mechanical behavior because of their comparably smaller number of energetically favorable slip systems. Besides the commonly studied slip mechanism, another way to accomplish general deformation is through the additional mechanism of deformation-induced twinning. The main aim of this thesis research is to develop an efficient continuum model to understand and ultimately predict the material response resulting from the interaction between these two mechanisms.

The constitutive model we present is based on variational constitutive updates of plastic slips and twin volume fractions and accounts for the related lattice reorientation mechanisms. The model is applied to single- and polycrystalline pure magnesium. We outline the finite-deformation plasticity model combining basal, pyramidal, and prismatic dislocation activity as well as a convexification based approach for deformation twinning. A comparison with experimental data from single-crystal tension-compression experiments validates the model and serves for parameter identification. The extension to polycrystals via both Taylor-type modeling and finite element simulations shows a characteristic stress-strain response that agrees well with experimental observations for polycrystalline magnesium. The presented continuum model does not aim to represent the full details of individual twin-dislocation interactions, yet it is sufficiently efficient to allow for finite element simulations while qualitatively capturing the underlying microstructural deformation mechanisms.

Lattice anomalies and magnetic states in Fe_5Si_3-Mn_5Si_3 alloys

The lattice anomalies and magnetic states in the (Fe_100-xMn_x)₅Si₃ alloys have been investigated. Contrary to what was previously reported, results of x-ray diffraction show a second phase (α') present in Fe-rich alloys and therefore strictly speaking a complete solid solution does not exist. Mössbauer spectra, measured as a function of composition and temperature, indicate the presence of two inequivalent sites, namely 6(g) site (designated as site I) and 4(d) (site II). A two-site model (TSM) has been introduced to interpret the experimental findings. The compositional variation of lattice parameters a and c, determined from the x-ray analysis, exhibits anomalies at x = 22.5 and x = 50, respectively. The former can be attributed to the effect of a ferromagnetic transition; while the latter is due to the effect of preferential substitution between Fe and Mn atoms according to TSM.

The reduced magnetization of these alloys deduced from magnetic hyperfine splittings has been correlated with the magnetic transition temperatures in terms of the molecular field theory. It has been found from both the Mössbauer effect and magnetization measurements that for composition 0 ≤ x ˂ 50 both sites I and II are ferromagnetic at liquid-nitrogen temperature and possess moments parallel to each other. In the composition range 50 ˂ x ≤ 100 , the site II is antiferromagnetic whereas site I is paramagnetic even at a temperature below the bulk Néel temperatures. In the vicinity of x = 50 however, site II is in a state of transition between ferromagnetism and antiferromagnetism. The present study also suggests that only Mn in site II are responsible for the antiferromagnetism in Mn₅Si₃ contrary to a previous report.

Electrical resistance has also been measured as a function of temperature and composition. The resistive anomalies observed in the Mn-rich alloys are believed to result from the effect of the antiferromagnetic Brillouin zone on the mobility of conduction electrons.

Non linear constitutive models for lattice materials

We use a computational homogenisation approach to derive a non linear constitutive model for lattice materials. A representative volume element (RVE) of the lattice is modelled by means of discrete structural elements, and macroscopic stress-strain relationships are numerically evaluated after applying appropriate periodic boundary conditions to the RVE. The influence of the choice of the RVE on the predictions of the model is discussed. The model has been used for the analysis of the hexagonal and the triangulated lattices subjected to large strains. The fidelity of the model has been demonstrated by analysing a plate with a central hole under prescribed in plane compressive and tensile loads, and then comparing the results from the discrete and the homogenised models. © 2013 Elsevier Ltd.

Chiral symmetry analysis and rigid rotational invariance for the lattice dynamics of single-wall carbon nanotubes

We provide a detailed expression of the vibrational potential for the lattice dynamics of single-wall carbon nanotubes (SWCNT's) satisfying the requirements of the exact rigid translational as well as rotational symmetries, which is a nontrivial generalization of the valence force model for the planar graphene sheet. With the model, the low-frequency behavior of the dispersion of the acoustic modes as well as the flexure mode can be precisely calculated. Based upon a comprehensive chiral symmetry analysis, the calculated mode frequencies (including all the Raman- and infrared-active modes), velocities of acoustic modes, and the polarization vectors are systematically fitted in terms of the chiral angle and radius, where the restrictions of various symmetry operations of SWCNT's are fulfilled.