Modified T-matrix formulation for multiple scattering of acoustic waves

Abstract

In studying the multiple scattering of acoustic waves by distributed discrete scatterers, the ‘two-exterior’ T-matrix or the modified T-matrix is needed. In this paper, the modified T-matrix formulae for a scatterer of arbitrary shape are derived, based on Huygen's principle and the method of optimal truncation (MOOT), respectively. Analytical expressions are given for the modified T-matrix elements of a spheroid in the low-frequency limit. The agreement with the existing results is shown to be exact to the given order of ka. It is also shown that the results based on Huygen's principle are merely the special cases of those based on MOOT.     

Density functionals for nondynamical correlation constructed from an upper bound to the exact exchange energy density

ABSTRACT

Hyper-generalised-gradient approximations (hGGAs) for the exact exchange-correlation functional are increasingly popular in density functional theory. HGGAs model nondynamical correlation using a flexible local combination of exact (Hartree–Fock, HF) exchange and approximate exchange. We present a simplified ‘Rung 3.5’ upper bound to the HF exchange energy density, the essential ingredient of hGGAs. We also present a nonempirical generalised gradient approximation for this upper bound. Both upper bounds go to zero in the high-density and density tail limits, facilitating the construction of hGGAs that recover HF exchange in these limits. The ‘Rung 3.5’ construction enables facile evaluation of analytic derivatives and calculations in periodic boundary conditions. Extensive numerical tests show that the upper bounds capture the critical difference between HF and approximate exchange, showing these ingredients' promise for building simple hGGAs. The tests also indicate a need for more sophisticated semi-local upper bounds.     

High pressure dynamic XAS studies using an energy-dispersive spectrometer

ABSTRACT

We present in this paper recent advances in the high pressure domain provided by the introduction of time-resolved energy-dispersive XAS (EDXAS) techniques at synchrotrons. We highlight technical aspects and describe two modes of acquisition: the ‘movie’ mode, where the time resolution is given by the detector acquisition speed and the ‘pump-and-probe’ mode, where the time resolution is given by the delay between the pump and the probe. These two modes define a frontier in the time resolution, respectively above and below the ～10?μs regime. In the former, examples of applications are chemical stability and reactions at high pressure and high temperature or probing the warm dense matter regime using rapid current ramps. In the latter, an example is given on studies of dynamically compressed matter, by coupling single-bunch EDXAS at high-brilliance synchrotron to a nanosecond high-power laser.     

The use of fast field cycling to evaluate the time domain relaxation of starches from tropical fruit seeds

ABSTRACT

A proton NMR relaxation study of the molecular dynamics in flour samples of ‘Eugenia uniflora’ (‘Pitanga’), ’Citrus reticulate’ (‘Tangerine’), ‘Prunus persica’ (‘Peach’), ‘Vitis vinifera’ (‘Grape’), and ‘Cucumis melo’ (‘Honeydew melon’) seeds is presented. The spin–lattice relaxation time was obtained over a broad frequency range from 100?kHz to 100?MHz using both conventional and fast field-cycling NMR techniques. This relaxometry study made possible a comparison between the molecular dynamics behaviour of starch from different fruit seeds and from potatoes. I was possible to conclude that the spin–lattice dispersion presents slightly differences for all samples, in particular at low frequencies. All relaxation dispersions could be well interpreted in terms of power-law relaxation models and domains with different power-law relaxation exponents. For the Peach seeds flour the relaxation dispersion at low frequencies was very similar to that observed for potato’s starch incorporated with 5% organoclay Viscogel B8 nanoparticles.     

Comportement non lorentzien de la raie Rayleigh dépolarisée dans quelques liquides. Discussion des théories ‘à trois variables’

Nous considérons en général le spectre Rayleigh dépolarisé des liquides simples constitués de molécules anisotropes comme la superposition d'une raie lorentzienne de réorientation, comportant une structure fine dûe au couplage entre orientation et modes hydrodynamiques, et d'une aile lointaine d'origine collisionnelle. Par une analyse détaillée des spectres d'un certain nombre de liquides constitués de molécules isotropes (CCl₄) ou anisotropes (benzène, pyridine, cyanopropyne, 2-butyne, iodopropyne), cet article met en évidence pour ces derniers une quatrième ‘composante’, bien représentée par une lorentzienne de demi-largeur comprise entre 3 et 10 cm^-1. Cette deuxième lorentzienne peut représenter jusqu'à 30 pour cent de l'intensité totale du spectre. Nous montrons qu'elle ne peut être dûe à une simple anisotropie réorientationnelle décrite par la variable tensorielle i. Elle implique donc l'existence d'une seconde variable tensorielle d'anisotropie locale g, attribuée à l'anisotropie d'ordre translationnel.

Les théories dites ‘à trois variables’, supposant g directe (primaire) ou indirecte (secondaire), sont comparées à la lumière de ces résultats expérimentaux, sans qu'il soit possible de trancher définitivement cette question. En particulier, nous montrons que dans le cas le plus général — g à la fois directe et indirecte-il existe plus de paramètres théoriques que de paramètres déductibles de l'expérience.     

Kinetics of the geometric isomerization of cyclohexene in a stochastic bath

Rare-events molecular dynamics techniques are used to study the interconversion between the two half-chair isomers of cyclohexene (C₆H₁₀), in a solvent modelled through a stochastic bath, in order to investigate dynamic solvent effects on the isomerization rate. Adopting the torsional angle around the C-C sigma bond opposite to the double bond as the reaction coordinate, we calculate the equilibrium distribution of this coordinate (using umbrella sampling), and estimate the isomerization rate, including the transmission coefficient κ. The paper also contains methodological developments. A variant of Andersen's stochastic collision method (canonical ensemble sampling) is developed for molecules with constraints: by resampling Cartesian velocities of a localized subgroup of atoms of the molecule and leaving all other atomic velocity components unchanged, one mimics the collision of a virtual gas molecule with a subpart of the molecule of interest. To evaluate the transmission coefficient κ, the initial conditions for trajectories ‘crossing the top’ are automatically generated during the run, using a biased potential to obtain the probability of being at the saddle point.     

State-to-state quantum dynamics studies of the H + LiH+ → Li+ + H2 reaction

ABSTRACT

Quantum dynamical calculations of the H?+?LiH⁺?→?Li⁺?+?H₂ reaction were performed based on the potential energy surface (PES) reported by Dong et al. (RSC Adv. 7, 7008 (2017)) using the time-dependent quantum wave packet method in collision energy range from 0.01 to 1.0?eV. Dynamics properties such as reaction probability, integral cross section, differential cross section (DCS), and thermal rate constant of the H?+?LiH⁺?→?Li⁺?+?H₂ reaction were reported at the state-to-state level of theory and compared with available theoretical calculations. The results indicated that present values are in good agreement with results obtained from the quasi-classical trajectory method. However, large differences can be found between present values and previous quantum results. This can be attributed to the different PESs used in the calculation and the CS approximation was adopted in previous theoretical studies. In addition, the ‘rebound’ reaction mechanism was proposed in previous theoretical studies in a high collision energy range. However, the DCS scattering signals calculated in the present work indicated that complex-forming and direct abstract reaction mechanisms are dominant in low and high collision energies, respectively.     

Giving birth to the refined unambiguous statement of Snell's law in ray optics

This paper reports on the ambiguity present in the long-running Snell's law of refraction of light, which is based on the traditional ambiguous definitions of the angles of incidence and refraction in ray optics. To get rid of the said ambiguity, the refined unambiguous definitions of angles of incidence and refraction reported earlier by the author have been employed to give birth to the refined unambiguous statement of Snell's law of refraction. The most interesting physical insights that resulted from the refined unambiguous statement of Snell's law are: (i) in case of refraction of light of a particular colour while passing from one optical medium to another, the ratio of the sine of the angle of incidence and the sine of the angle of refraction is approximately equal to the refractive index of the second optical medium with respect to the first optical medium and (ii) the refractive index of an optical medium ‘b’ with respect to another optical medium ‘a’ is approximately equal to the reciprocal of the refractive index of the optical medium ‘a’ with respect to the optical medium ‘b’, and vice versa. These results are entirely novel and different from those existing in the traditional literature of ray optics.     

Correlation characteristics of waves in lossy media with smooth fluctuations of the refractive index with oblique incidence on boundary

Abstract

The features of coherence function (and angular spectrum) and also the fluctuation of amplitude and phase of wavefield in a random strongly absorptive medium are investigated in the case of arbitrary angle of incidence at the surface.

In this paper it is elucidated that with oblique incidence a dissipation in the random medium can accelerate the accumulation of wave fluctuations and its incoherence. This effect strongly depends on the rate of decrease of the ‘wings’ of the scattering indicatrix. An analytical theory (Rytov's approximation and modified method of parabolic equation) has been modelled by Monte Carlo simulation of wave propagation, and also by numerical solution of the model transfer equation. It is revealed that the width of an angle spectrum can nonmonotonically change with the immersion to the absorptive medium.     

Dilepton and vector meson production in heavy-ion reactions

We present a nonperturbative dynamical study of dilepton and vector meson production in heavy-ion collisions from 1 to 2 GeV/A bombarding energies incorporating all known sources relevant in this energy range. The dynamical evolution of the nucleus-nucleus collision is described by a transport equation of the Boltzmann-Uehling-Uhlenbeck type evolving phase-space distribution functions for nucleons, baryon resonances, pions,η’s,ρ’s andσ’s with their isospin degrees of freedom. We investigate in particular the sensitivity of the calculated yields to predicted changes of theρ andω mesons in dense matter.     

Linear and angular velocity autocorrelation functions for two-dimensional systems of repulsive and Lennard-Jones diatomics

The method of molecular dynamics has been employed to study the autocorrelation functions (ACF's) of the linear velocity and of the angular momentum for two two-dimensional systems of diatomic molecules. The anisotropic potential used is built from four atom-atom interactions. These are either purely repulsive (R), or repulso-attractive (LJ). Emphasis has been put on the long-time behaviour; for this we have used large systems (1600 molecules). The density lies in the intermediate range.

The linear velocity ACF exhibits, for system R, an initial decay which is exponential and whose characteristic time has been checked to be of the order of the mean ‘collision’ time. For system LJ (where collisions cannot be usefully defined) the decay does not follow a simple law, and lies above a single exponential. After an intermediate regime which lasts a long time-span for both systems, the ACF's adopt a t ^-1 decay in agreement with theoretical predictions based on hydrodynamics or other approaches.

The mean square displacement has also been extracted from the data. Its ratio to time, i.e. the apparent coefficient of diffusion, increases logarithmically with time, so that the two kinds of data are in accord. This asymptotic regime starts after about 11 collision times for the repulsive system, and about as soon for the other one.

The angular momentum ACF's, after an initial decay which is closer to an exponential for system R than for system LJ, adopt a t ^-3 behaviour for a very long time-span; this possibly masks a final t ^-2 decay predicted by several theories based on the coupling of the intrinsic momentum with the vorticity of the fluid.     

From transistor to nanotube

We present here the main steps in the evolution of the transistor, since the tremendous invention of such a device and the introduction of the integrated circuit. We will then recall the main steps of Moore's law development. Nanotechnology began at the very beginning of the 21st century. Two aspects are presented in this article: the first, called ‘More Moore’, consists in continuing the laws of scale up to the physical limits; the second aspect, called ‘beyond CMOS’ explores new concepts such as spintronics, moletronics, nanotronics and other types of molecular electronics. To cite this article: J.-C. Boudenot, C. R. Physique 9 (2008).     

Homogenization of multicoated inclusion-reinforced linear elastic composites with eigenstrains: Application to thermoelastic behavior

A new micromechanical approach for arbitrary multicoated ellipsoidal elastic inclusions with general eigenstrains is developed. We start from the integral equation of the linear elastic medium with eigenstrains adopting the Green's function technique and we apply an ‘(n+1)-phase’ model with a self-consistent condition to determine the homogenized behavior of multicoated inclusion-reinforced composites. The effective elastic moduli and eigenstrains are obtained as well as the residual stresses through the local stress concentration equations. The effective eigenstrains are determined either with the concentration tensors obtained here by the present model, or, more classically, with Levin's formula. In order to assess our micromechanical model, some applications to the isotropic thermoelastic behavior of composites with and without interphase are given. In particular, ‘four-phase’ and ‘three-phase’ models are derived for isotropic homothetic spherical inclusion-reinforced materials, and the results are successfully compared to exact analytical solutions regarding the effective elastic moduli and the effective thermal expansion.     

Dynamic pruned-enriched Rosenbluth method

Recently, Grassberger [1997, Phys. Rev. E, 56, 3682] has presented a new algorithm (‘PERM’) for simulating flexible polymer chains. This algorithm has been shown to have a good efficiency and has been used in a wide class of systems. A drawback of this algorithm is that it is static: it is therefore not suited for Markov-chain Monte Carlo simulations. Here, we present a dynamic generalization of the PERM algorithm. For a specific example, we compare the efficiency of DPERM to that of other Monte Carlo algorithms. In the case studied, we find that DPERM is only marginally more efficient. However, this result may depend on the details of the implementation.     

Associative and non-associative automorphisms of Newtonian space-time

In this article, an algebraic study of the transformations $$(x,t) \mapsto \left( {Rx + \sum\limits_{i = 0}^m {A_i t^i /i!,t + t'} } \right)$$ of Newtonian space-time onto itself is presented. The study is carried out within the framework of Eilenberg and Maclane's co-homology theory of group prolongations, a generalisation of the theory of group extensions (Eilenberg & Maclane, 1947a-d). The ‘loops’ or non-associative groups involving ‘m’ from 0 to 5 are placed in classes of decreasing associativity described in the text. We also discuss the physical applications of the cup-product of co-chains and the vector bundle structure of Newtonian space-time.     

Etude ENDOR d'un radical HAsO3 - dans la phase anti-ferroélectrique du cristal d'arséniate d'ammonium NH4H2AsO4

L'identification par ENDOR d'un centre radicalaire HAsO₃ ^- créé par irradiation gamma d'un monocristal de NH₄H₂AsO₄ a été réalisée à 1,5 K. En particulier, les interactions hyperfines correspondant aux protons des trois liaisons hydrogène O-H … O reliant le radical à des tétraèdres AsO₄ ^3- sont déterminées. Un de ces protons est en position ‘proche’ par rapport à un oxygène du radical, en accord avec la formule HAsO₃ ^-, tandis que les deux autres protons sont en position ‘éloignée’. Les parties isotropes des interactions des protons ‘éloignés’ sont trouvées négatives, comme le veut un mécanisme de polarisation de spin à travers une liaison hydrogène partiellement covalente; les protons ‘éloignés’ sont trouvés être en configuration de Slater latérale, ce qui correspond au niveau du défaut à l'ordre antiferroélectrique des protons proposé par Nagamiya.     

A hybrid level set method for modelling detonation and combustion problems in complex geometries

We present an accurate and fast wave tracking method that uses parametric representations of tracked fronts, combined with modifications of level set methods that use narrow bands. Our strategy generates accurate computations of the front curvature and other geometric properties of the front. We introduce data structures that can store discrete representations of the location of the moving fronts and boundaries, as well as the corresponding level set fields, that are designed to reduce computational overhead and memory storage. We present an algorithm we call stack sweeping to efficiently sort and store data that is used to represent orientable fronts. Our implementation features two reciprocal procedures, a forward ‘front parameterization’ that constructs a parameterization of a front given a level set field and a backward ‘field construction’ that constructs an approximation of the signed normal distance to the front, given a parameterized representation of the front. These reciprocal procedures are used to achieve and maintain high spatial accuracy. Close to the front, precise computation of the normal distance is carried out by requiring that displacement vectors from grid points to the front be along a normal direction. For front curves in two dimensions, a cubic interpolation scheme is used, and G ¹ surface parameterization based on triangular patches is used for the three-dimensional implementation to compute the distances from grid points near the front. To demonstrate this new, high accuracy method we present validations and show examples of combustion-like applications that include detonation shock dynamics, material interface motions in a compressible multi-material simulation and the Stephan problem associated with dendrite solidification.     

Approximating moments of acoustic fields in random media

Abstract

Starting from a path integral representation of the fourth moment of an acoustic field, two types of approximations are considered in detail: a ‘zero-kink’ approximation and a ‘single-kink’ approximation. The expressions ‘zero-kink’ and ‘single-kink’ describe families of paths which are used to approximate path integrals over all continuous paths. The single-kink approximation reduces the propagation problem to a phase screen problem with fluctuations on the phase screen containing information about fluctuations along entire paths from source to receiver.     

Recent advances with association models for practical applications

ABSTRACT

Association models like Cubic Plus Association (CPA) equation of state and other Statistical Associating Fluid Theory variants have found widespread use, especially over the recent 30 or so years, and this is not limited anymore to universities and researchers. Industry is beginning slowly to adopt such models for some applications and a few of the association models are now provided by commercial simulators. Association models account explicitly for hydrogen bonding (and other complex) phenomena, and for this reason, they are potentially more useful and more successful than traditional models like cubic equations of state and activity coefficient models. Still, for practical applications, all models are judged by their results and these depend on the availability of experimental data, the number and type of adjustable parameters and the performance of the models for phase equilibria and occasionally also for other properties. We will consider four case studies in this work which, will illustrate some of the capabilities and limitations of these association models in different applications. We will offer a ‘model developer’s’ point of view showing in several cases all stages of model development in order to illustrate what worked, what did not and how it was corrected (when possible). The ‘physics’ and ‘application’ aspects of the models will be in all cases discussed. All results will be shown with the CPA equation of state, although we expect that the overall conclusions will be the same for a wide range of association models.