Nonlinear tunneling in two-dimensional lattices

We present thorough analysis of the nonlinear tunneling of Bose-Einstein condensates in static and accelerating two-dimensional lattices within the framework of the mean-field approximation. We deal with nonseparable lattices considering different initial atomic distributions in the highly symmetric states. For analytical description of the condensate before instabilities are developed, we derive several few-mode models, analyzing both essentially nonlinear and quasi-linear regimes of tunneling. By direct numerical simulations, we show that two-mode models provide accurate description of the tunneling when either initially two states are populated or tunneling occurs between two stable states. Otherwise a two-mode model may give only useful qualitative hints for understanding tunneling but does not reproduce many features of the phenomenon. This reflects crucial role of the instabilities developed due to two-body interactions resulting in non-negligible population of the higher bands. This effect becomes even more pronounced in the case of accelerating lattices. In the latter case we show that the direction of the acceleration is a relevant physical parameter which affects the tunneling by changing the atomic rates at different symmetric states and by changing the numbers of bands involved in the atomic transfer

Finite strains fully coupled analysis of a horizontal wellbore drilled through a porous rock formation

Wellbore instability, in particular in deep perforations, continues to be one of the major problem in the oil and gas industry, that can dramatically increase production costs. Eventual instabilities may be prevented supporting temporarily the wellbore with mud circulation. If instability may occur, the value of the mud pressure needs to be sufficiently high to prevent compressional failure, but it should also be lower than a critical value that would cause tensile failure and unintentional hydraulic fracturing. Predicting faithfully the stress distribution around a borehole, and moreover the yielding and failure zones, is a challenging but fundamental task, essential to estimate the correct mud pressure and hence to prevent instabilities and sand production. This study focuses on quantifying the pressure distribution, stress field and plastic zones around a horizontal borehole drilled at great depth through a highly porous rock formation. The perforation of a wellbore in a saturated porous material is a coupled problem, which involves deformations of the solid phase and simultaneous diffusion of the fluid phase. A fully coupled finite element method is adopted, considering both material non linearity (elastoplasticity) and geometric nonlinearity (finite deformations) in the solid matrix, resulting in a so called u−p formulation. The variation of porosity and permeability, as consequence of the finite deformations of the solid matrix, is taken into account. The model adopts an elastoplastic constitutive law characterized by two yield surfaces, that is able to capture the dilatant and compactant plastic mechanism. The simulations investigate the quasi-static transient phenomenon associated with the perforation, until the steady state condition is reached. The model describes the evolution of the stress and pressure distribution, and moreover the propagation of the plastic zones around the borehole. The work demonstrates the capability of the finite deformations coupled approach to simulate the whole process, giving an instrument to determine the stability and sand production of the wellbore

Measurement of geophysical effects on the large-scale gravitational-wave interferometer

Geophysical application of large free-mass laser interferometers, which had been designed merely for the detection of gravitational radiation of an astrophysical nature, are considered. Despite the suspended mass-mirrors, these interferometers can be considered as two coordinate meters even at very low frequency ([Formula: see text][Formula: see text]Hz) are rather accurate two-coordinate distance meters. In this case, the measurement of geodynamic deformations looks like a parallel product of long-term observations dictated by the task of the blind search for gravitational waves (GW) of extraterrestrial origin. Compared to conventional laser strain meters, gravitational interferometers have the advantage of an increased absolute value of the deformation signal due to the 3–4[Formula: see text]km baseline. The magnitude of the tidal variations of the baseline is 150–200[Formula: see text]microns, leading to conceive the observation of the fine structure of geodynamic disturbances. This paper presents the results of processing geophysical measurements made on a Virgo interferometer during test (technical) series of observations in 2007–2009. The specific design of mass-mirrors suspensions in the Virgo gravitational interferometer also creates a unique possibility of separating gravitational and deformation perturbations through a recording mutual angular deviations of the suspensions of its central and end mirrors. It gives a measurement of the spatial derivative of the gravity acceleration along with the geoid of the Earth. In this mode, the physics of the interferometer is considered with estimates of the achievable sensitivity in the application to the classical problem of registration of oscillations of the inner Earth's core

Aggregate behaviour in concrete materials under high temperature conditions

Concrete under high temperature conditions is a topic of wide interest for applications in several engineering fields, from nuclear to civil as well as building engineering

An Euler-Bernoulli beam element with lumped plasticity applied on RC framed structures

Most of existing reinforced concrete structures suffer due to corrosion of steel and concrete degradation. In many cases existing structures reveal to be inadequate to absorb the expected seismic load and need to be rehabilitated according to the in force code. In the worst case some structures have not been designed to absorb horizontal actions. The rehabilitation process begins with the complete knowledge of its geometrical configuration and the evaluation of the vulnerability of the structure to seismic loads. This analysis permits to identify critical zones and to establish focused strengthening actions. A comparison between the behavior of the structure in the current and in the future configurations determines the goodness of adopted intervention techniques. The evaluation of the vulnerability of an RC structure to seismic loads can be done by performing nonlinear finite element analyses. In literature, three different approaches have been tuned to simulate the elastoplastic behavior of a beam/column element: lumped elastoplasticity models, distributed nonlinearity models, fiber models. Lumped models consider the constitutive nonlinearity concentrated at a section level of a frame element, usually employing nonlinear springs at the ends of beam/column elements. Distributed nonlinearity models average the nonlinearity over a finite element by considering the possibility to form plastic hinges at different evaluation points of the element and calculating weighted integrals of the section responses. Fiber models subdivide a section with a large number of finite elements and nonlinearity is related to the stress-strain relationship of a single finite element. Within lumped models, commercial finite element programs contemplate the possibility to develop plasticity at the two ends of the beam only. In the particular cases where plasticity concentrates in points different than the ends of the beam, it computationally comes in the need to proceed with a re-meshing of the model or in the definition of multiple elements before running the analysis. In the first case, it results in an increased computational cost of the analysis. In the second case, a less precision of the response is obtained especially when the exact position of the plastic hinge is not a-priori known. The present work is devoted to the implementation of a new elastoplastic 3D Euler-Bernoulli beam element including slope discontinuities, in the framework of lumped elastoplasticity models. In the new finite element, plastic hinges can appear at any position of the beam, theoretically in a priori not-established number. Multiple slope discontinuities are included in the analysis through a non uniform bending stiffness of the beam, making use of the Dirac-delta function. Fictitious springs, with a stiffness variable according to the level of plasticity in the section, transfer the correct bending moment in correspondence of plastic hinges.The nonlinear behavior of the hinge is defined in the framework of a thermo-dynamically consistent elastoplastic theory. Associated flow rules are derived in the classical manner adopting a convex activation domain known in literature and experimentally calibrated for reinforced concrete sections. The activation domain is similar to the one suggested by the Italian seismic code. It is given in a My-Mz bending moment reference system for a fixed axial force. An elastoplastic behavior is assumed for section curvatures, while deformations in the axial and shear directions are assumed elastic. The elastoplastic frame element is introduced in a finite element analysis program to run nonlinear simulations on 2D and 3D framed structures. To this end, state equations and flow rules are rewritten in a discrete manner to solve the single iteration of the Newton-Raphson procedure. A classic elastic predictor phase is followed by a plastic corrector phase in the case of activation of the inelastic phenomena. The corrector phase is based on the evaluation of return bending moments by employing the closest point projection method, in order to satisfy the loading-unloading conditions (Kuhn-Tucker relations). The formation of one or more hinges inside a finite element modifies the distribution of internal forces and its stiffness matrix. As a consequence, the global stiffness matrix is continuously modified at each plastic load step until it becomes singular. Numerical examples are furnished as validation tests of the program. The efficiency of the proposed model is demonstrated comparing the results with those available in literature

Numerical modelling of ellipsoidal inclusions

Within the framework of numerical algorithms for the threedimensional random packing of granular materials this work presents an innovative formulation for polydispersed ellipsoidal particles, including an overlapping detection algorithm for an optimized simulation of the mesostructure of geomaterials, particularly concrete. Granular composite cement-based materials can be so reconstructed with adequate precision in terms of grain size distribution. Specifically, the algorithm performance towards the assumed inclusion shape (ellipsoidal or spheric) and degree of regularity (round or irregular) is here discussed. Examples on real grading curves prove that this approach is effective. The advantages of the proposed method for computational mechanics purposes are also disclosed when properly interfaced with visualization CAD (Computer Aided Design) tools

Investigation of stress-strain behaviour in concrete materials through the aid of 3D advanced measurement techniques

This work deals with the investigation of the mechanical behaviour of cementitious materials, following a mesoscopic approach where aggregates, grains and cement paste are explicitly represented, and the strict comparison between the numerical results and the experimental results from uniaxial tests is carried out. For this purpose, solid models are created with the support of advanced techniques of measurement and detection, such as laser scanners or computer tomography (CT). The 3D laser- scanning technique in fact allows to acquire the exact shape of the grains added to the concrete mix design while, through the adoption of an ad-hoc random distribution algorithm, a realistic disposition of the inclusions is guaranteed. The industrial CT instead, is able to reproduce exactly the tested specimens; the geometry of the inclusions and their placement. Once reconstructed realistic geometries for the models, the mechanical behaviour of concrete under uniaxial compression tests is numerically studied. A specific constitutive behaviour is assigned to each component; an elasto-plastic law with damage is assumed for the cement matrix while the aggregates are conceived to behave elastically. The implemented damage-plasticity model consists in the combination of the non-associated plasticity model by Men\ue9trey-Willam, where the yield surface is described in function of the second and the third invariant of the deviatoric stress tensor and the scalar isotropic damage model by Mazars. Comparisons between numerical and experimental results fairly prove the correctness of the suggested approach

On the geometry of four qubit invariants

The geometry of four-qubit entanglement is investigated. We replace some of the polynomial invariants for four-qubits introduced recently by new ones of direct geometrical meaning. It is shown that these invariants describe four points, six lines and four planes in complex projective space ${\bf CP}^3$. For the generic entanglement class of stochastic local operations and classical communication they take a very simple form related to the elementary symmetric polynomials in four complex variables. Moreover, their magnitudes are entanglement monotones that fit nicely into the geometric set of $n$-qubit ones related to Grassmannians of $l$-planes found recently. We also show that in terms of these invariants the hyperdeterminant of order 24 in the four-qubit amplitudes takes a more instructive form than the previously published expressions available in the literature. Finally in order to understand two, three and four-qubit entanglement in geometric terms we propose a unified setting based on ${\bf CP}^3$ furnished with a fixed quadric.Comment: 19 page