Showing papers in "Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences in 2011"
TL;DR: The class post-IQP of languages decided with bounded error by uniform families of IQP circuits with post-selection is introduced, and it is proved first that post- IQP equals the classical class PP, and that if the output distributions of uniform IQP circuit families could be classically efficiently sampled, then the infinite tower of classical complexity classes known as the polynomial hierarchy would collapse to its third level.
Abstract: We consider quantum computations comprising only commuting gates, known as IQP computations, and provide compelling evidence that the task of sampling their output probability distributions is unli...
417 citations
TL;DR: This paper presents a simpler implementation of genuinely high-order accurate finite volume and discontinuous Galerkin schemes satisfying a strict maximum principle for scalar conservation laws, which will result in a significant reduction of computational cost especially for weighted essentially non-oscillatory finite-volume schemes.
Abstract: In an earlier study (Zhang & Shu 2010 b J. Comput. Phys. 229 , 3091–3120 ([doi:10.1016/j.jcp.2009.12.030][1])), genuinely high-order accurate finite volume and discontinuous Galerkin schemes satisfying a strict maximum principle for scalar conservation laws were developed. The main advantages of such schemes are their provable high-order accuracy and their easiness for generalization to multi-dimensions for arbitrarily high-order schemes on structured and unstructured meshes. The same idea can be used to construct high-order schemes preserving the positivity of certain physical quantities, such as density and pressure for compressible Euler equations, water height for shallow water equations and density for Vlasov–Boltzmann transport equations. These schemes have been applied in computational fluid dynamics, computational astronomy and astrophysics, plasma simulation, population models and traffic flow models. In this paper, we first review the main ideas of these maximum-principle-satisfying and positivity-preserving high-order schemes, then present a simpler implementation which will result in a significant reduction of computational cost especially for weighted essentially non-oscillatory finite-volume schemes.
[1]: http://dx.doi.org/10.1016/j.jcp.2009.12.030
310 citations
TL;DR: In this article, it was shown that for a large class of SDEs with non-globally Lipschitz continuous drift and diffusion coefficients, Euler's approximation converges neither in the strong mean-square sense nor in the numerically weak sense to the exact solution at a finite time point.
Abstract: The stochastic Euler scheme is known to converge to the exact solution of a stochastic differential equation (SDE) with globally Lipschitz continuous drift and diffusion coefficients. Recent results extend this convergence to coefficients that grow, at most, linearly. For superlinearly growing coefficients, finite-time convergence in the strong mean-square sense remains. In this article, we answer this question to the negative and prove, for a large class of SDEs with non-globally Lipschitz continuous coefficients, that Euler’s approximation converges neither in the strong mean-square sense nor in the numerically weak sense to the exact solution at a finite time point. Even worse, the difference of the exact solution and of the numerical approximation at a finite time point diverges to infinity in the strong mean-square sense and in the numerically weak sense.
299 citations
TL;DR: In this paper, the concept of cointegration is introduced for the analysis of non-stationary time series, as a promising new approach for dealing with the problem of environmental variation in monitored features.
Abstract: Before structural health monitoring (SHM) technologies can be reliably implemented on structures outside laboratory conditions, the problem of environmental variability in monitored features must be first addressed. Structures that are subjected to changing environmental or operational conditions will often exhibit inherently non-stationary dynamic and quasi-static responses, which can mask any changes caused by the occurrence of damage. The current work introduces the concept of cointegration , a tool for the analysis of non-stationary time series, as a promising new approach for dealing with the problem of environmental variation in monitored features. If two or more monitored variables from an SHM system are cointegrated, then some linear combination of them will be a stationary residual purged of the common trends in the original dataset. The stationary residual created from the cointegration procedure can be used as a damage-sensitive feature that is independent of the normal environmental and operational conditions.
177 citations
TL;DR: In this article, a surface integral formulation based on the convective wave equation, which takes into account the presence of a mean flow, was derived to be easy to implement as a numerical post-processing tool for computational fluid dynamics codes.
Abstract: Acoustic analogy methods are used as post-processing tools to predict aerodynamically generated sound from numerical solutions of unsteady flow. The Ffowcs Williams–Hawkings (FW–H) equation and related formulations, such as Farassat’s Formulations 1 and 1A, are among the commonly used analogies because of their relative low computation cost and their robustness. These formulations assume the propagation of sound waves in a medium at rest. The present paper describes a surface integral formulation based on the convective wave equation, which takes into account the presence of a mean flow. The formulation was derived to be easy to implement as a numerical post-processing tool for computational fluid dynamics codes. The new formulation constitutes one possible extension of Farassat’s Formulation 1 and 1A based on the convective form of the FW–H equation.
176 citations
TL;DR: In this article, the elastic ground states of a flat sheet of material are analyzed and a method for reversibly inducing non-developable surfaces from flat sheets of material at the micro-scale all the way to macroscopic objects is discussed.
Abstract: We discuss methods of reversibly inducing non-developable surfaces from flat sheets of material at the micro-scale all the way to macroscopic objects. We analyse the elastic ground states of a nema...
154 citations
TL;DR: In this article, the authors define effective fields for a randomly inhomogeneous material, which guarantee automatic satisfaction of the equations of motion in the case of a medium with periodic microstructure.
Abstract: Definitions of ‘effective fields’ for a randomly inhomogeneous material are offered, which guarantee automatic satisfaction of the equations of motion. The important case of a medium with periodic microstructure is included. In this special case, the definitions are completely explicit and can be applied without reference to random media. The presentation is mostly expressed in terms of electromagnetic waves. The reasoning is applicable also to other types of waves and its realization for elastodynamics is briefly outlined towards the end. Some of the effective fields are defined directly as ensemble averages, ensuring the exact satisfaction of the equations of motion, but the effective ‘kinematic’ fields to which they are related are defined more generally, as weighted averages. The main result of this work is an explicit formula for the tensor of effective properties. The important issue of uniqueness (or not) of the effective properties is explained and resolved. Self-adjointness of the original problem is not assumed. An attractive feature of the formulation is that self-adjointness at the local level implies self-adjointness at the level of the ‘effective medium’.
143 citations
TL;DR: In this article, a novel excitability type where a large excitable response appears when a system's parameter is varied gradually, or ramped, above some critical rate is studied, even though there is a unique stable quiescent state for any fixed setting of the ramped parameter.
Abstract: The paper studies a novel excitability type where a large excitable response appears when a system’s parameter is varied gradually, or ramped, above some critical rate. This occurs even though there is a (unique) stable quiescent state for any fixed setting of the ramped parameter. We give a necessary and a sufficient condition for the existence of a critical ramping rate in a general class of slow–fast systems with folded slow (critical) manifold. Additionally, we derive an analytical condition for the critical rate by relating the excitability threshold to a canard trajectory through a folded saddle singularity. The general framework is used to explain a potential climate tipping point termed the ‘compost-bomb instability’—an explosive release of soil carbon from peatlands into the atmosphere occurs above some critical rate of global warming even though there is a unique asymptotically stable soil carbon equilibrium for any fixed atmospheric temperature.
135 citations
TL;DR: In this article, a maximum likelihood estimate of damage location for guided-wave structural health monitoring (GWSHM) using a minimally informed, Rayleigh-based statistical model of scattered wave measurements is presented.
Abstract: This paper describes the formulation of a maximum-likelihood estimate of damage location for guided-wave structural health monitoring (GWSHM) using a minimally informed, Rayleigh-based statistical model of scattered wave measurements. Also introduced are two statistics-based methods for evaluating localization performance: the localization probability density function estimate and the localizer operating characteristic curve. Using an ensemble of measurements from an instrumented plate with stiffening stringers, the statistical performance of the so-called Rayleigh maximum-likelihood estimate (RMLE) is compared with that of seven previously reported localization methods. The RMLE proves superior in all test cases, and is particularly effective in localizing damage using very sparse arrays consisting of as few as three transducers. The probabilistic basis used for modelling the complicated wave scattering behaviour makes the algorithm especially suited for localizing damage in complicated structures, with the potential for improved performance with increasing structure complexity.
131 citations
TL;DR: In this paper, a hydrologically coupled flowband model of higher order ice dynamics is used to explore perturbations in response to supraglacial water drainage and subglacial flooding.
Abstract: A hydrologically coupled flowband model of ‘higher order’ ice dynamics is used to explore perturbations in response to supraglacial water drainage and subglacial flooding. The subglacial drainage system includes interacting ‘fast’ and ‘slow’ drainage elements. The fast drainage system is assumed to be composed of ice-walled conduits and the slow system of a macroporous water sheet. Under high subglacial water pressures, flexure of the overlying ice is modelled using elastic beam theory. A regularized Coulomb friction law describes basal boundary conditions that enable hydrologically driven acceleration. We demonstrate the modelled interactions between hydrology and ice dynamics by means of three observationally inspired examples: (i) simulations of meltwater drainage at an Alpine-type glacier produce seasonal and diurnal variability, and exhibit drainage evolution characteristic of the so-called ‘spring transition’; (ii) horizontal and vertical diurnal accelerations are modelled in response to summer meltwater input at a Greenland-type outlet glacier; and (iii) short-lived perturbations to basal water pressure and ice-flow speed are modelled in response to the prescribed drainage of a supraglacial lake. Our model supports the suggestion that a channelized drainage system can form beneath the margins of the Greenland ice sheet, and may contribute to reducing the dynamic impact of floods derived from supraglacial lakes.
122 citations
TL;DR: In this article, the shape of and stresses in an elastic plate with incompatible or residual strains are derived from a range of causes: inhomogeneous growth, plastic deformation, swelling or shrinkage driven by solvent absorption.
Abstract: We provide a derivation of the Foppl-von Karman equations for the shape of and stresses in an elastic plate with incompatible or residual strains. These might arise from a range of causes: inhomogeneous growth, plastic deformation, swelling or shrinkage driven by solvent absorption. Our analysis gives rigorous bounds on the convergence of the three-dimensional equations of elasticity to the low-dimensional description embodied in the plate-like description of laminae and thus justifies a recent formulation of the problem to the shape of growing leaves. It also formalizes a procedure that can be used to derive other low-dimensional descriptions of active materials with complex non-Euclidean geometries.
TL;DR: In this article, the authors presented the numerical modeling of the cross-shore propagation of infragravity waves induced by a transient focused short wave group over a sloping bottom, proving the high accuracy in the reproduction of surf zone hydrodynamics.
Abstract: This paper presents the numerical modelling of the cross shore propagation of infragravity waves induced by a transient focused short wave group over a sloping bottom. A dataset obtained through new laboratory experiments in the wave flume of the University of Cantabria is used to validate the Reynolds averaged Navier–Stokes type model IH-2VOF. A new boundary condition based on the wave maker movement used in the experiments is implemented in the model. Shoaling and breaking of short waves as well as the enhancement of long waves and the energy transfer to low-frequency motion are well addressed by the model, proving the high accuracy in the reproduction of surf zone hydrodynamics. Under the steep slope regime, a long wave trough is radiated offshore from the breakpoint. Numerical simulations conducted for different bottom slopes and short wave steepness suggest that this low-frequency breakpoint generated wave is controlled by both the bed slope parameter and the Iribarren number. Moreover, the numerical model is used to investigate the influence that a large flat bottom induces on the propagation pattern of long waves.
TL;DR: Novel PWC denoising methods are introduced, and comparisons between these methods performed on synthetic and real signals are compared, showing that the new understanding of the problem gained in part I leads to new methods that have a useful role to play.
Abstract: Removing noise from piecewise constant (PWC) signals is a challenging signal processing problem arising in many practical contexts. For example, in exploration geosciences, noisy drill hole records need to be separated into stratigraphic zones, and in biophysics, jumps between molecular dwell states have to be extracted from noisy fluorescence microscopy signals. Many PWC denoising methods exist, including total variation regularization, mean shift clustering, stepwise jump placement, running medians, convex clustering shrinkage and bilateral filtering; conventional linear signal processing methods are fundamentally unsuited. This paper (part I, the first of two) shows that most of these methods are associated with a special case of a generalized functional, minimized to achieve PWC denoising. The minimizer can be obtained by diverse solver algorithms, including stepwise jump placement, convex programming, finite differences, iterated running medians, least angle regression, regularization path following and coordinate descent. In the second paper, part II, we introduce novel PWC denoising methods, and comparisons between these methods performed on synthetic and real signals, showing that the new understanding of the problem gained in part I leads to new methods that have a useful role to play.
TL;DR: In this paper, a model made from different-sized rigid rectangles, which rotate relative to each other, was proposed and discussed, which can be used to describe the properties of very different systems ranging from silicates and zeolites to liquid-crystalline polymers.
Abstract: Auxetic materials exhibit the unusual property of becoming fatter when uniaxially stretched and thinner when uniaxially compressed (i.e. they exhibit a negative Poisson ratio; NPR), a property that may result in various enhanced properties. The NPR is the result of the manner in which particular geometric features in the micro- or nanostructure of the materials deform when they are subjected to uniaxial loads. Here, we propose and discuss a new model made from different-sized rigid rectangles, which rotate relative to each other. This new model has the advantage over existing models that it can be used to describe the properties of very different systems ranging from silicates and zeolites to liquid-crystalline polymers. We show that such systems can exhibit scale-independent auxetic behaviour for stretching in particular directions, with Poisson’s ratios being dependent on the shape and relative size of different rectangles in the model and the angle between them.
TL;DR: In this paper, the effect of the so-called "adscititious inequalities" on the behavior of hyperelastic materials subject to shear was investigated, and the authors concluded that these inequalities must not be imposed when such materials are described.
Abstract: Motivated by recent experiments on biopolymer gels whereby the reverse of the usual (positive) Poynting effect was observed, we investigate the effect of the so-called ‘adscititious inequalities’ on the behaviour of hyperelastic materials subject to shear. We first demonstrate that for homogeneous isotropic materials subject to pure shear, the resulting deformation consists of a triaxial stretch combined with a simple shear in the direction of the shear force if and only if the Baker–Ericksen inequalities hold. Then for a cube deformed under pure shear, the positive Poynting effect occurs if the ‘sheared faces spread apart’, whereas the negative Poynting effect is obtained if the ‘sheared faces draw together’. Similarly, under simple shear deformation, the positive Poynting effect is obtained if the ‘sheared faces tend to spread apart’, whereas the negative Poynting effect occurs if the ‘sheared faces tend to draw together’. When the Poynting effect occurs under simple shear, it is reasonable to assume that the same sign Poynting effect is obtained also under pure shear. Since the observation of the negative Poynting effect in semiflexible biopolymers implies that the (stronger) empirical inequalities may not hold, we conclude that these inequalities must not be imposed when such materials are described.
TL;DR: In this article, the three-dimensional compressible magnetohydrodynamic equation in the whole space is studied and the global classical solution is established when the initial data are small perturbations of some given constant state.
Abstract: The three-dimensional compressible magnetohydrodynamic equation in the whole space are studied in this paper. The global classical solution is established when the initial data are small perturbations of some given constant state. Moreover, the optimal decay rate of the solution is also obtained.
TL;DR: In this paper, the number and types of all possible rotational symmetries for flexoelectric tensors and the number of independent material parameters contained in a flexible tensor belonging to a given symmetry class were determined.
Abstract: Flexoelectricity is due to the electric polarization generated by a non-zero strain gradient in a dielectric material without or with centrosymmetric microstructure. It is characterized by a fourth-order tensor, referred to as flexoelectric tensor, which relates the electric polarization vector to the gradient of the second-order strain tensor. This paper solves the fundamental problem of determining the number and types of all possible rotational symmetries for flexoelectric tensors and specifies the number of independent material parameters contained in a flexoelectric tensor belonging to a given symmetry class. These results are useful and even indispensable for experimentally identifying or theoretically/numerically estimating the flexoelectric coefficients of a dielectric material.
TL;DR: A quantitative structure–property relationship model similar to those used in biology and drug discovery not only predicts the authors' new chemistries but also validates published reports.
Abstract: This paper develops a statistical learning approach to identify potentially new hightemperature ferroelectric piezoelectric perovskite compounds. Unlike most computational studies on crystal chemistry, where the starting point is some form of electronic structure calculation, we use a data-driven approach to initiate our search. This is accomplished by identifying patterns of behaviour between discrete scalar descriptors associated with crystal and electronic structure and the reported Curie temperature (TC) of known compounds; extracting design rules that govern critical structure–property relationships; and discovering in a quantitative fashion the exact role of these materials descriptors. Our approach applies linear manifold methods for data dimensionality reduction to discover the dominant descriptors governing structure–property correlations (the ‘genes’) and Shannon entropy metrics coupled to recursive partitioning methods to quantitatively assess the specific combination of descriptors that govern the link between crystal chemistry and TC (their ‘sequencing’). We use this information to develop predictive models that can suggest new structure/chemistries and/or properties. In this manner, BiTmO3–PbTiO3 and BiLuO3–PbTiO3 are predicted to have a TC of 730 ◦ C and 705 ◦ C, respectively. A quantitative structure–property relationship model similar to those used in biology and drug discovery not only predicts our new chemistries but also validates published reports.
TL;DR: In this paper, the tempering of two-phase mixtures of bainitic ferrite and carbon-enriched retained austenite has been investigated in an effort to separate the reactions that occur at elevated temperatures from any transformation during cooling to ambient conditions.
Abstract: The tempering of two-phase mixtures of bainitic ferrite and carbon-enriched retained austenite has been investigated in an effort to separate the reactions that occur at elevated temperatures from any transformation during cooling to ambient conditions. It is demonstrated using synchrotron X-radiation measurements that the residue of austenite left at the tempering temperature partly decomposes by martensitic transformation when the sample is cooled. It is well established in the published literature that films of retained austenite are better able to resist stress or strain-induced martensitic transformation than any coarser particles of austenite. In contrast, the coarser austenite is more resistant to the precipitation of cementite during tempering than the film form because of its lower carbon concentration.
TL;DR: In this paper, the authors investigated the directionality of the Draupner wave and concluded it might have resulted from two wave-groups crossing, whose mean wave directions were separated by about 90° or more.
Abstract: The ‘New Year Wave’ was recorded at the Draupner platform in the North Sea and is a rare high-quality measurement of a ‘freak’ or ‘rogue’ wave. The wave has been the subject of much interest and numerous studies. Despite this, the event has still not been satisfactorily explained. One piece of information that was not directly measured at the platform, but which is vital to understanding the nonlinear dynamics is the wave’s directional spreading. This paper investigates the directionality of the Draupner wave and concludes it might have resulted from two wave-groups crossing, whose mean wave directions were separated by about 90° or more. This result has been deduced from a set-up of the low-frequency second-order difference waves under the giant wave, which can be explained only if two wave systems are propagating at such an angle. To check whether second-order theory is satisfactory for such a highly nonlinear event, we have run numerical simulations using a fully nonlinear potential flow solver, which confirm the conclusion deduced from the second-order theory. This is backed up by a hindcast from European Centre for Medium-Range Weather Forecasts that shows swell waves propagating at approximately 80° to the wind sea. Other evidence that supports our conclusion are the measured forces on the structure, the magnitude of the second-order sum waves and some other instances of freak waves occurring in crossing sea states.
TL;DR: In this paper, the authors examined the validity of the entransy-based irreversibility measurement and its use as the optimization criterion in heat transfer, both the conserved and non-conservative quantities during a heat transfer process.
Abstract: Entropy generation is recognized as a common measurement of the irreversibility in diverse processes, and entropy generation minimization has thus been used as the criterion for optimizing various heat transfer cases. To examine the validity of such entropy-based irreversibility measurement and its use as the optimization criterion in heat transfer, both the conserved and non-conservative quantities during a heat transfer process are analysed. A couple of irreversibility measurements, including the newly defined concept entransy , in heat transfer process are discussed according to different objectives. It is demonstrated that although thermal energy is conserved, the accompanied system entransy and entropy in heat transfer process are non-conserved quantities. When the objective of a heat transfer is for heating or cooling, the irreversibility should be measured by the entransy dissipation, whereas for heat-work conversion, the irreversibility should be described by the entropy generation. Next, in Fourier’s Law derivation using the principle of minimum entropy production, the thermal conductivity turns out to be inversely proportional to the square of temperature. Whereas, by using the minimum entransy dissipation principle, Fourier’s Law with a constant thermal conductivity as expected is derived, suggesting that the entransy dissipation is a preferable irreversibility measurement for heat transfer.
TL;DR: In this article, the authors derived a compact, exact, general analytical expression for D ET, by means of an Airy function approach that uses a reflected barrier and puts the origin of coordinates at the electron's outer classical turning point.
Abstract: In field electron emission theory, evaluating the transmission coefficient D ET for an exact triangular (ET) potential energy barrier is a paradigm problem. This paper derives a compact, exact, general analytical expression for D ET , by means of an Airy function approach that uses a reflected barrier and puts the origin of coordinates at the electron’s outer classical turning point. This approach has simpler mathematics than previous treatments. The expression derived applies to both tunnelling and ‘flyover’ (wave-mechanical transmission over the barrier), and is easily evaluated by computer algebra. The outcome is a unified theory of transmission across the ET barrier. In different ranges of relevant physical parameters, the expression yields different approximate formulae. For some ranges, no simple physical dependences exist. Ranges of validity for the most relevant formulae (including the Fowler–Nordheim 1928 formula for D ET ) are explored, and a regime diagram constructed. Previous treatments are assessed and some discrepancies noted. Further approximations involved in deriving the Fowler–Nordheim 1928 equation for current density are stated. To assist testing of numerical procedures, benchmark values of D ET are stated to six significant figures. This work may be helpful background for research into transmission across barriers for which no exact analytical theory yet exists.
TL;DR: In this article, normal form analysis is carried out on second-order equations of motion for forced, damped, nonlinear vibration problems, and the invariance properties of the first-and secondorder transforms differ.
Abstract: Vibration problems are naturally formulated with second-order equations of motion. When the vibration problem is nonlinear in nature, using normal form analysis currently requires that the second-order equations of motion be put into first-order form. In this paper, we demonstrate that normal form analysis can be carried out on the second-order equations of motion. In addition, for forced, damped, nonlinear vibration problems, we show that the invariance properties of the first- and second-order transforms differ. As a result, using the second-order approach leads to a simplified formulation for forced, damped, nonlinear vibration problems.
TL;DR: This article demonstrates the use of a Gibbs-potential-based formulation as a means for developing a thermodynamically consistent model for a class of viscoelastic fluids of the rate type.
Abstract: In this article, we demonstrate the use of a Gibbs-potential-based formulation as a means for developing a thermodynamically consistent model for a class of viscoelastic fluids of the rate type. Since one cannot always use a formulation based on a Helmholtz potential to model rate-type models, the formulation takes on added significance. The salient features of this approach are the following:
— this approach provides a thermodynamical rationalization of many commonly used models that are developed on purely phenomenological grounds; furthermore, the study provides a framework for generating other classes of models and allows for a relatively straightforward means for the inclusion of thermal effects,
— the approach provides a simple means for including anisotropic effects without the need for directors or other new internal variables, and
— the approach does not use any additional variables (such as conformation tensors or elastic strains measured from stress free configurations) other than the current (or Cauchy) stress, the current mass density and the velocity gradient.
We also show how the entire structure of the theory is obtained from just two scalar functions, the Gibbs potential and the rate of dissipation function.
TL;DR: In this paper, commercial purity aluminium at true strains 25.5 was annealed in a wide temperature range (from room temperature to 220C), and the evolution of microstructure was characterized using transmission e...
Abstract: Commercial purity aluminium at true strains 25.5 was annealed in a wide temperature range (from room temperature to 220C), and the evolution of microstructure was characterized using transmission e...
TL;DR: In this paper, it was shown that the information stored in a memory device incurs an energy cost in the form of a minimum amount of mechanical work, which can be reduced to zero by paying a cost in angular momentum or any other conserved quantity.
Abstract: Landauer argued that the process of erasing the information stored in a memory device incurs an energy cost in the form of a minimum amount of mechanical work. We find, however, that this energy cost can be reduced to zero by paying a cost in angular momentum or any other conserved quantity. Erasing the memory of Maxwell’s demon in this way implies that work can be extracted from a single thermal reservoir at a cost of angular momentum and an increase in total entropy. The implications of this for the second law of thermodynamics are assessed.
TL;DR: In this paper, the Lagrangian mean flow is derived from the averaged vorticity equation, which extracts the dominant balance between wave dissipation and mean-flow dissipation.
Abstract: Acoustic streaming, the generation of mean flow by dissipating acoustic waves, provides a promising method for flow pumping in microfluidic devices. In recent years, several groups have been experimenting with acoustic streaming induced by leaky surface waves: (Rayleigh) surface waves excited in a piezoelectric solid interact with a small volume of fluid where they generate acoustic waves and, as result of the viscous dissipation of these waves, a mean flow. We discuss the computation of the corresponding Lagrangian mean flow, which controls the trajectories of fluid particles and hence the mixing properties of the flows generated by this method. The problem is formulated using the averaged vorticity equation which extracts the dominant balance between wave dissipation and mean-flow dissipation. Particular attention is paid to the thin boundary layer that forms at the solid/liquid interface, where the flow is best computed using matched asymptotics. This leads to an explicit expression for a slip velocity, which includes the effect of the oscillations of the boundary. The Lagrangian mean flow is naturally separated into three contributions: an interior-driven Eulerian mean flow, a boundary-driven Eulerian mean flow and the Stokes drift. A scale analysis indicates that the latter two contributions can be neglected in devices much larger than the acoustic wavelength but need to be taken into account in smaller devices. A simple two-dimensional model of mean flow generation by surface acoustic waves is discussed as an illustration.
TL;DR: In this article, a thermodynamic description of transient heat conduction at small length and timescales is proposed based on extended irreversible thermodynamics and the main feature of this formalism is to elevate the heat flux vector to the status of independent variable at the same level as the temperature.
Abstract: A thermodynamic description of transient heat conduction at small length and timescales is proposed. It is based on extended irreversible thermodynamics and the main feature of this formalism is to elevate the heat flux vector to the status of independent variable at the same level as the classical variable, the temperature. The present model assumes the coexistence of two kinds of heat carriers: diffusive and ballistic phonons. The behaviour of the diffusive phonons is governed by a Cattaneo-type equation to take into account the high-frequency phenomena generally present at nanoscales. To include non-local effects that are dominant in nanostructures, it is assumed that the ballistic carriers are obeying a Guyer–Krumhansl relation. The model is applied to the problem of transient heat conduction through a thin nanofilm. The numerical results are compared with those provided by Fourier, Cattaneo and other recent models.
TL;DR: In this paper, a relativistic model for heat conduction is proposed, based on a convective variational approach to multi-fluid systems where the entropy is treated as a distinct dynamical entity.
Abstract: We discuss a relativistic model for heat conduction, building on a convective variational approach to multi-fluid systems where the entropy is treated as a distinct dynamical entity. We demonstrate how this approach leads to a relativistic version of the Cattaneo equation, encoding the finite thermal relaxation time that is required to satisfy causality. We also show that the model naturally includes the non-equilibrium Gibbs relation that is a key ingredient in most approaches to extended thermodynamics. Focusing on the pure heat conduction problem, we compare the variational results with the second-order model developed by Israel and Stewart. The comparison shows that, despite the very different philosophies behind the two approaches, the two models are equivalent at first-order deviations from thermal equilibrium. Finally, we complete the picture by working out the non-relativistic limit of our results, making contact with recent work in that regime.
TL;DR: By using the model of linear-optical quantum computing and a universality theorem owing to Knill, Laflamme and Milburn, one can give a different and arguably more intuitive proof of Valiant's theorem that computing the permanent of an n×n matrix is #P-hard.
Abstract: One of the crown jewels of complexity theory is Valiant9s theorem that computing the permanent of an n × n matrix is # P -hard. Here we show that, by using the model of linear-optical quantum computing —and in particular, a universality theorem owing to Knill, Laflamme and Milburn—one can give a different and arguably more intuitive proof of this theorem.