Journal articles on the topic 'Free-discontinuity energie'

We establish new lower semicontinuity results for energy functionals containing a very general volume term of polyconvex type and a surface term depending on the spatial variable in a discontinuous way.

We provide a variational approximation for quasiconvex energies with linear growth, defined on vector valued generalized functions with bounded variation, in the framework of free-discontinuity problems.

We provide an approximation of some free discontinuity problems by local functionals with a singular perturbation of higher order. More precisely, we study the limiting behaviour of energies of the form where Hu denotes the Hessian matrix of u.

We provide a variational approximation for quasiconvex energies defined on vector valued special functions with bounded variation. We extend the Ambrosio–Tortorelli's construction to the vectorial case.

The mechanism of slow positron annihilation at polymeric surfaces has been discussed in terms of positron diffusion at the surface and trapping of positrons and positronium in free volume holes. The one-dimensional diffusion equation has been solved and the rate equations have been set up to describe the various processes supposed to occur when a thermalized positron encounters the polymeric surface. The model has been used to calculate the Doppler broadening of the line shape parameter (S parameter) in polyurethane and polystyrene as a function of incident positron energy and temperature. The results have been compared with the available experimental data. The S parameter vs temperature curves show a remarkable discontinuity at the glass transition temperature (Tg). Large variation in the S parameter has been observed at low energies, suggesting a significant structure of free volume holes near the surface.

A minimization problem for partially wetting droplet profiles is considered, in which Van der Waal's forces have been taken into account via a singular ‘disjoining pressure’. When the singular disjoining pressure is neglected, energy minimization leads to Laplace's equation and Young's equation; once the singular disjoining pressure is included, this is no longer the case. Indeed, the free energy is no longer bounded from below. Introducing the notion of overtaking to compare the energies of configurations whose energies are arbitrarily large and negative, we demonstrate that if a configuration is not convex then it cannot be an absolute minimizer. If profiles are allowed to ‘double-over’ then there does not exist an absolute minimizer. Within the class of profiles which do not double-over, absolute minimizers are shown to exist; these minimizing profiles are not single-valued. The singular minimization problem is shown to be discontinuously dependent on the definition of the wetting profile in the neighbourhood of the contact points; the implications of this discontinuity are discussed.

Transport and structural properties of heavily doped ceria can reveal subtle details of the interplay between conductivity and defects aggregation in this material, widely studied as solid electrolyte in solid oxide fuel cells. The ionic conductivity of heavily Gd-doped ceria samples (Ce1−xGdxO2−x/2 with x ranging between 0.31 and 0.49) was investigated by impedance spectroscopy in the 600–1000 K temperature range. A slope change was found in the Arrhenius plot at ~723 K for samples with x = 0.31 and 0.34, namely close to the compositional boundary of the CeO2-based solid solution. The described discontinuity, giving rise to two different activation energies, points at the existence of a threshold temperature, below which oxygen vacancies are blocked, and above which they become free to move through the lattice. This conclusion is well supported by Raman spectroscopy, due to the discontinuity revealed in the Raman shift trend versus temperature of the signal related to defects aggregates which hinder the vacancies movement. This evidence, observable in samples with x = 0.31 and 0.34 above ~750 K, accounts for a weakening of Gd–O bonds within blocking microdomains, which is compatible with the existence of a lower activation energy above the threshold temperature.

An one-matrix model of singularities on the torus has been investigated. We calculate the value of discontinuity of free energy asymptotics which tends to an infinity number of lattice sites at the critical point.

By taking the massless limit of linearized massive conformal gravity coupled to a source, we show that the theory is free from the vDVZ discontinuity. This result is confirmed when we take the massless limit of the gravitational potential of the theory, which is shown to be finite at the origin.

We study the thermodynamic consistency of phase-field models, which include gradient terms of the density ρ in the free-energy functional such as the van der Waals–Cahn–Hilliard model. It is well known that the entropy inequality admits gradient and higher-order gradient terms of ρ in the free energy only if either the energy flux or the entropy flux is represented by a non-classical form. We identify a non-classical entropy flux, which is not restricted to isothermal processes, so that gradient contributions are possible.We then investigate equilibrium conditions for the van der Waals–Cahn–Hilliard phase-field model in the sharp interface limit. For a single substance thermodynamics provides two jump conditions at the sharp interface, namely the continuity of the Gibbs free energies of the adjacent phases and the discontinuity of the corresponding pressures, which is balanced by the mean curvature. We show that these conditions can be also extracted from the van der Waals–Cahn–Hilliard phase-field model in the sharp interface limit. To this end we prove an asymptotic expansion of the density up to the first order. The results are based on local energy estimates and uniform convergence results for the density.

We show that minimal models coupled to quantum gravity have special type of resonant correlations defined by the free field representations and are explicitly computable. The key phenomena in these models are shown to be discontinuity of the number of degrees of freedom at exceptional values of momenta and incomplete decoupling of the spurious states.

A layer-wise finite element approach is adopted to analyse the hollow cylindrical shell made of functionally graded material with piezoelectric rings as sensor/actuator, under dynamic load. The mechanical properties of the substrate are regulated by volume fraction as a function of radial coordinate. The thickness of functionally graded material shell and piezo-rings is divided into mathematical sub-layers and then the general layer-wise laminate theory is formulated through introducing piecewise continuous approximations across the thickness, accounting for any discontinuity in derivatives of the displacement at the interface between the ring and cylinder. The virtual work statement including structural and electrical potential energies yields the three-dimensional governing equations which are reduced to two-dimensional differential equations, using layer-wise method. For axisymmetric case, the resulted equations are solved with one-dimensional finite element method in the axial direction. By assembling stiffness and mass matrices, the required stress and displacement continuities at each interface and between the two adjacent elements are forced. The results for free vibration and static loading are applied to study the convergence and verified by comparing them to solutions of similar existing problems. The induced deformation by piezoelectric actuators as well as the effect of rings on functionally graded material shell is investigated.

Electronic structure calculations are used to study the bonding at diamond/BeO interfaces. The {110} interface between zinc blende BeO and diamond is used as a representative model for general reconstructed interfaces characterized by an equal amount of Be–C and O–C bonds. The interface energy is calculated to be 2 J/m2 and combined with the estimated free surface energies to obtain an estimate of the adhesion energy. It is found to be close to the adhesion of BeO to itself, but somewhat lower than that of diamond to itself. The effects of the 7% lattice mismatch on the total energy and the band structure for a biaxially strained pseudomorphic diamond film are investigated. The effect of misfit dislocations, expected to occur for thicker films, on the adhesion energy is estimated to be lower than 10%. The bulk properties, such as equilibrium lattice constant, bulk modulus, cohesive energy, and band gap of BeO are shown to be in good agreement with experimental values and previous calculations. The valence-band offset is calculated to be 3.9 eV and found to take up most of the large band gap discontinuity. The nature of the bonding is discussed in terms of the local densities of states near the interface. The interface localized features are identified in terms of Be–C and O–C bonding and antibonding states.

We study the thermodynamics of a q-fermion gas for complex values of q on the unit circle. Special emphasis is given to the study of the virial coefficients and the specific heat of this gas. In particular, it is shown that if any state can accommodate up to p q-fermions, then the first p virial coefficients of such a gas are the same as that of a gas of free bosons. Explicit expressions for the deviation of higher virial coefficients from the corresponding values for a Bose gas are obtained. Further, as for ordinary fermions, it is shown that the specific heat of a q-fermion gas at low temperature is proportional to T. Numerical computations show that the derivative of the specific heat as a function of T has no discontinuity.

In this paper we further develop our matrix element and complex angular momentum summation techniques, in order to calculate both the one-loop free field and two-loop interacting vacuum diagrams in field theory on a four-sphere. In the case of the free field diagrams, we show how the sums may be evaluated by integrating over an analytic function with both poles and branch cuts where the discontinuity across the cuts determines the result. We then extend the matrix element formalism to multiple angular momenta involving the addition of angular momenta and the associated Clebsch-Gordon type selection rules. This then allows us to evaluate the matrix elements of two-loop diagrams in spherical QED as a function of the three angular momenta in the diagram. The selection rules allow us to cast the triple angular momentum sum into a form which enables evaluation again by contour integration. The result is obtained in analytic form using dimensional regularization for the previously obtained spinor case, and also for scalar QED, which we believe is a new result. Finally, we discuss the applicability of this method for calculations in non-Abelian field theory which we believe cannot be performed using earlier methods.

Starting with the representation of the Wilson average in the Euclidean 4D compact QED as a partition function of the universal confining string theory, we derive the corresponding loop equation, an alternative to the familiar one. In the functional momentum representation the obtained equation decouples into two independent ones, which describe the dynamics of the transverse and longitudinal components of the area derivative of the Wilson loop. At some critical value of the momentum discontinuity, which can be determined from a certain equation, the transverse component does not propagate. Next, we derive the equation for the momentum Wilson loop, where the left-hand side represents the sum of the squares of the momentum discontinuities, multiplied by the loop, which describes its free propagation, while the right-hand side describes the interaction of the loop with the functional vorticity tensor current. Finally, using the method of inversion of the functional Laplacian, we obtain for the Wilson loop in the coordinate representation a simple Volterra type-II linear integral equation, which can be treated perturbatively.

We consider in detail the analytic behaviour of the non-interacting massless scalar field two-point function in H. S. Snyder's discretized non-commuting spacetime. The propagator we find is purely real on the Euclidean side of the complex p2 plane and goes like 1/p2 as p2→0 from either the Euclidean or Minkowski side. The real part of the propagator goes smoothly to zero as p2 increases to the discretization scale 1/a2and remains zero for p2>1/a2. This behaviour is consistent with the termination of single-particle propagation on the ultraviolet side of the discretization scale. The imaginary part of the propagator, consistent with a multiparticle-state spectral function branch discontinuity, is finite and continuous on the Minkowski side, slowly falling to zero when 1/a2<p2<∞. The multi-particle aspect of this spectral function within the Källen-Lehmann representation of the propagator leads to the interpretation that the propagation of free-fields in a quantized spacetime is analogous to propagation of interacting fields in a continuous spacetime.

We discuss the recently proposed logarithmic violation of scaling for c = 1 − 6(n − 1)2/n theories in the light of lattice models. We study for this purpose the Q state Potts model in its antiferromagnetic regime eK − 1 = −Q1/2, coupled to gravity. Setting Q1/2 = 2 cos π/t, this model is known to have a generic central charge c = 1 − 6(t − 1)2/t. Summing over all possible planar graphs allows us to make connection with Kostov's solution of IRF models, and to calculate the genus zero properties along the critical line. Except for n = 1, 2 we do not get indications of logarithmic violations. The apparent regularity of the thermodynamic properties (γ str = −(n − 1) = integer ) is explained by a discontinuity of the free energy of the Potts model when Q crosses the Beraha numbers [Formula: see text], n ≥ 3 in the antiferromagnetic region. Such behavior was recently observed for some regular lattices. The logarithmic terms for n = 2, c = −2 appear simply because a derivative with respect to Q has to be taken to define a non-vanishing partition function. Only the n = 1, c = 1 logarithmic terms seem to have a non-trivial origin.

In this talk we discuss the scenario of multigravity according to which the gravity we observe in intermediate scales (1 mm < r < 1026 cm ) is mediated by both a massless graviton and one or more of ultralight spin-2 state. We present how this can be realized in a five dimensional brane-world theory with flat branes and the complications associated with the extra polarizations of the massive gravitons (van Dam-Veltman-Zakharov discontinuity) and the ghost radions corresponding to the fluctuations of the negative tension branes present in these models. We then show how we can construct models of AdS4 branes instead with exclusively positive tension and demonstrate how the van Dam-Veltman-Zakharov no-go theorem can be circumvented in curved space. These models, although they are consistent, face phenomenological problems related to the presence of a remnant negative cosmological constant on the branes. We finally present how we can obtain the same constructions in six dimensions with flat positive tensions branes only, in a manner that they are both theoretically consistent and phenomenologically acceptable. The latter come in two copies each and offer the first problem-free realization of the multigravity scenario.

Summary Numerical optimization is an integral part of many history-matching (HM) workflows. However, the optimization performance can be affected negatively by the numerical noise existent in the forward models when the gradients are estimated numerically. As an unavoidable part of reservoir simulation, numerical noise refers to the error caused by the incomplete convergence of linear or nonlinear solvers or truncation errors caused by different timestep cuts. More precisely, the allowed solver tolerances and allowed changes of pressure and saturation imply that simulation results no longer smoothly change with changing model parameters. For HM with linear-distributed Gaussian-Newton (L-DGN), caused by the discontinuity of simulation results, the sensitivity matrix computed by linear interpolation might be less accurate, which might result in slow convergence or, even worse, failure of convergence. Recently, we have developed an HM workflow by integrating the support-vector regression (SVR) with the distributed-Gaussian-Newton (DGN) method optimization method referred to as SVR-DGN. Unlike L-DGN that computes the sensitivity matrix with a simple linear proxy, SVR-DGN computes the sensitivity matrix by taking the gradient of the SVR proxies. In this paper, we provide theoretical analysis and case studies to show that SVR-DGN can compute a more-accurate sensitivity matrix than L-DGN, and SVR-DGN is insensitive to the negative influence of numerical noise. We also propose a cost-saving training procedure by replacing bad-training points, which correspond to relatively large values of the objective function, with those training-data points (simulation data) that have smaller values of the objective function and are generated at most-recent iterations for training the SVR proxies. Both the L-DGN approach and the newly proposed SVR-DGN approach are tested first with a 2D toy problem to show the effect of numerical noise on their convergence performance. We find that their performance is comparable when the toy problem is free of numerical noise. As the numerical-noise level increases, the performance of the L-DGN degrades sharply. By contrast, the SVR-DGN performance is quite stable. Then, both methods are tested using a real-field HM example. The convergence performance of the SVR-DGN is quite robust for both the tight and loose numerical settings, whereas the performance of the L-DGN degrades significantly when loose numerical settings are applied.

Summary This paper describes the hardware and operation of a new generation of nuclear magnetic resonance (NMR) logging tools. In the past, NMR required the logging engineer to consider the T1 relaxation times of the reservoir fluids likely to be encountered. Actual, or simply assumed, long T1's translated into slow logging speeds. The new tool generation overcomes this limitation. The key feature is that nine sensitive volumes are polarized in parallel and are read out in rapid sequence. A new sonde design speeds up the polarization process by a factor of 2. Each volume contributes equally to the result and can support identical measurements for rapid stacking and fast logging, and each can be used for individual, simultaneous measurements. Laboratory data and field-test results are presented to demonstrate both the relative simplicity of operation and the improvement in data quality. Logging speeds typically can be upgraded by a factor of 4, while data for total porosity determination and fluid typing are acquired in a single logging pass. Background Over the past few years, log analysts have become familiar with the potential and the limitations of NMR logging. Basically, an NMR tool reports the total number of hydrogen atoms that are in the liquid or gaseous state. As such, NMR is a lithology-independent porosity tool as long as the hydrogen index of the fluids can be estimated. The commercial use of modern pulsed-NMR tools (NUMAR's MRIL1,***, and Schlumberger's CMR,2,**** brought two surprises:The near-borehole zone, which was assumed to be flushed, can contain substantial amounts of native hydrocarbons, both oil and gas.The T1 relaxation times of hydrocarbons (connate fluids and filtrate from oil-based muds) under reservoir conditions are substantially longer than previously assumed. The consequence of these findings was that NMR began to be used as a hydrocarbon-detection and reservoir-quantification tool, at the expense of logging speed and wellsite efficiency.3,4 From the theory of nuclear spin relaxation in liquids by Bloembergen, Purcell, and Pound5 follows the proportionality of bulk relaxation time and self-diffusion coefficient: T1~D. The Stokes relationship between viscosity and correlation time stipulates that D~T/µ; therefore, we can expect that T1~T/µ over a certain range of temperatures. We conducted measurements of T1 and T2 in the 30 to 150°C range on oils used for oil-based mud synthesis.***** Some of our results are listed in Table 1. These oils are typically type C16/C18, with hydrogen indices close to that of water. The absence of longer chains or aromatics suggests short correlation times and long T1 relaxation times for Larmor frequencies in the low-MHz range. For all samples investigated, T1=T2. In general, our data confirm the expected temperature dependency of T1. Certain oils, however, including Oil B and Oil C in Table 1, show a sharp discontinuity at some point between 110 and 150°C. We have confirmed that no chemical change takes place in the oil because the original T1 can be restored by cooling the sample to room temperature and exposing it to the atmosphere. The most likely explanation is dissolved oxygen that becomes volatile above 110°C. Paramagnetic oxygen is a potent relaxation agent even at low concentrations, and its disappearance at high temperatures causes an additional increase in T1. The surface interaction, which is responsible for rapid relaxation/polarization in the water phase, is inefficient for oil, even in cases where rock analysis would classify the rock as oil-wet. Gas is another example of high T1's (4-5 sec and more) caused by weak internal relaxation and nonexistent interaction with the rock surface. T 1 affects data acquisition and logging speed in a direct fashion:The hydrogen atoms must be exposed to the polarizing magnetic field for a multiple of T1. A factor of 3 is considered minimum. Fig. 1 illustrates exponential polarization curves for T1's of 1 sec, 2 sec, and 4 sec. Note that 95% polarization is reached only after 12 sec for fluids with T1=4 sec.The measurement itself is contaminated by thermal noise and must be repeated a few times to bring the influence of this noise down to acceptable levels. After each measurement, a full wait time (tw) of at least 3× T1 is required. Assuming 8 repeats and T1=4 sec, we find that the wait times required for a single measurement add up to 8×4×3=96 sec. If a vertical resolution of 3 ft is acceptable, the NMR tool cannot move faster than 3×60/96˜2 ft/min. A speed limit of 120 ft/hr makes it impractical to deploy NMR on a routine basis over large openhole intervals. An undesirable option is to forego full polarization. This mode is faster but results in data that are substantially harder to interpret in a quantitative fashion. Furthermore, this mode defeats the unique capability of NMR to detect hydrocarbons independent of resistivity contrast. It is highly desirable to use an NMR tool that is virtually free of T1 effects. Current NMR applications such as total and effective porosities, pore-size distribution, permeability modeling, hydrocarbon typing, and gas detection require that all hydrogen components are equally visible; i.e., even the slowest T1 component should be fully polarized. Furthermore, these applications should run at logging speeds of 1,000-1,500 ft/hr. Lastly, a higher level of automation should reduce the amount of job planning and setup procedures required today. These requirements are met by the newest generation of MRIL tools, MRIL-Prime. The T1 problem is solved by using a large number of measurement volumes in parallel and by employing a new prepolarization scheme. New Tool Features The key feature of the new MRIL tool is the ability to rapidly polarize and to read out many identical measurement volumes. The scheme is illustrated in Fig. 2. There are nine tightly packed cylindrical shells, each 24 in. tall and each containing on average 750 mL. The tool electronics can rapidly switch back and forth between volumes by changing the operating frequency over a wide range. The magnetic field gradient translates lower operating frequencies into resonance conditions that occur farther away from the tool. The gradient is circularly symmetric, resulting in resonance shells around the tool. These shells are labeled A (innermost, diameter 14 in.) to J (outermost, diameter 16.5 in.). In an 8-in. borehole, these diameters correspond to a depth of investigation between 3 and 4 in. The individual volumes are completely separated such that concurrent measurements do not influence each other. The approximate field strength, resonance frequency, and magnetic field gradient for each measurement volume is listed in Table 2.

Abstract We introduce the analog of Kramers-Kronig dispersion relations for correlators of four scalar operators in an arbitrary conformal field theory. The correlator is expressed as an integral over its “absorptive part”, defined as a double discontinuity, times a theory-independent kernel which we compute explicitly. The kernel is found by resumming the data obtained by the Lorentzian inversion formula. For scalars of equal scaling dimensions, it is a remarkably simple function (elliptic integral function) of two pairs of cross-ratios. We perform various checks of the dispersion relation (generalized free fields, holographic theories at tree-level, 3D Ising model), and get perfect matching. Finally, we derive an integral relation that relates the “inverted” conformal block with the ordinary conformal block.

Abstract Tie bolt rotors for centrifugal compressors comprise multiple shaft components that are held together by a single tie bolt. The axial connections of these rotors—including butt joints, Hirth couplings, and Curvic couplings—exhibit a contact stiffness effect, which tends to lower the shaft bending frequencies compared to geometrically identical monolithic shafts. If not accounted for in the design stage, shaft bending critical speed margins can be compromised after a rotor is built. A previous paper had investigated the effect of tie bolt force on the bending stiffness of stacked rotor assemblies with butt joint interfaces, both with and without pilot fits. This previous work derived an empirical contact stiffness model and developed a practical finite element modeling approach for simulating the axial contact surfaces, which was validated by predicting natural frequencies for several test rotor configurations. The present work built on these previous results by implementing the same contact stiffness modeling approach on a real tie bolt rotor system designed for a high pressure centrifugal compressor application. Each joint location included two axial contact faces, with contact pressures up to five times higher than previously modeled, and a locating pilot fit. The free-free natural frequencies for different amounts of tie bolt preload force were measured, and the frequencies exhibited the expected stiffening behavior with increasing preload. However, a discontinuity in the data trend indicated a step-change increase in the contact stiffness. It was shown that this was likely due to one or more of the contact faces becoming fully engaged only after sufficient tie bolt force was applied. Finally, a design calculation was presented that can be used to estimate whether contact stiffness effects may be ignored, which could simplify rotor analyses if adequate contact pressure is used.

The implementation of sandwich panel on the marine structure needs better knowledge of mechanical behaviour, primarily static and dynamic response. The static and dynamic response is investigated due to the application of a sandwich panel on the ferry ro-ro ramp door using finite element software ABAQUS. Five modification models using different sandwich thickness and stiffener configuration are compared using nonlinear static analysis to analyse a comparison of structural strength and weight saving. Additionally, the dynamic response is also investigated due to debonding problem. The influence of debonding ratio, geometry, number of debonding, debonding depth, debonding location, and boundary condition is carried out. Debonding is estimated by using free vibration analysis where Lanczos method for eigenvalues extraction is applied. Result of nonlinear static analysis shows that Model C causes an increase in strength to weight ratio compared to the existing model. Furthermore, natural frequencies are being calculated as modal parameters to investigate the debonding problem. The natural frequency of the debonded model decreases due to discontinuity in the damage area. The dynamic response using natural frequency shift can be performed as structural health monitoring technique on the ramp door model.