The transport equation in optically thick media

The photon transport equation is transformed into a new form by considering the deviation of the specific intensity from the local equilibrium field. We call the new form of the equations the difference formulation. It is rigorously equivalent to the original transport equation. The difference formulation is particularly suited for thick media, where the radiation field approaches local equilibrium and the deviations from the Planck distribution are small. The difference formulation for photon transport also clarifies the diffusion limit. Preliminary results confirm our expectations of a substantial advantage for accurate numerical calculations in optically thick media.     

A moving medium formulation for prediction of propeller noise at incidence

This paper presents a time domain formulation for the sound field radiated by moving bodies in a uniform steady flow with arbitrary orientation. The aim is to provide a formulation for prediction of noise from body so that effects of crossflow on a propeller can be modeled in the time domain. An established theory of noise generation by a moving source is combined with the moving medium Green's function for derivation of the formulation. A formula with Doppler factor is developed because it is more easily interpreted and is more helpful in examining the physic of systems. Based on the technique presented, the source of asymmetry of the sound field can be explained in terms of physics of a moving source. It is shown that the derived formulation can be interpreted as an extension of formulation 1 and 1A of Farassat based on the Ffowcs Williams and Hawkings (FW–H) equation for moving medium problems. Computational results for a stationary monopole and dipole point source in moving medium, a rotating point force in crossflow, a model of helicopter blade at incidence and a propeller case with subsonic tips at incidence verify the formulation.     

The shadow and observation appearance of black hole surrounded by the dust field in Rastall theory

In the context of Rastall gravity, the shadow and observation intensity casted by the new Kiselev-like black hole with dust field have been numerically investigated. In this system, the Rastall parameter and surrounding dust field structure parameter have considerable consequences on the geometric structure of spacetime. Considering the photon trajectories near the black hole, we investigate the variation of the radii of photon sphere, event horizon and black hole shadow under the different related parameters. Furthermore, taking into account two different spherically symmetric accretion models as the only background light source, we also studied the observed luminosity and intensity of black holes. For the both spherical accretions background, the results show that the decrease or increase of the observed luminosity depends on the value range of relevant parameters, and the promotion effect is far less obvious than the attenuation effect on the observed intensity. One can find that the inner shadow region and outer bright region of the black hole wrapped by infalling accretion are significantly darker than those of the static model, which is closely related to the Doppler effect. In addition, the size of the shadow and the position of the photon sphere are always the same in the two accretion models, which means that the black hole shadow depend only on the geometry of spacetime, while the observation luminosity is affected by the form of accretion material and the related spacetime structure.     

Some remarks on local operators in quantum electrodynamics

We assume the existence of a conserved current which generates locally gauge transformations of first kind. We are working in a local quantum Field Theory, where the fields are defined on a vector space where indefinite metric is allowed. We show that the Maxwell equations are not consistent with the above assumptions and the vectors obtained by applying local charged operators on the vacuum cannot describe physical states. Moreover we show that, if charged fields have non-trivial expectation value on the physical states, the vector space must contain vectors with negative norm. We discuss the relation between the local formulation of QED and a formulation in terms of physical states. As an example we study the transition from Gupta-Bleuler free QED to the Coulomb-gauge formulation.     

Viscoelastic analysis of multi-body systems using the finite element method

A study of the effect of viscoelastic material damping on the dynamic response of multibody systems, consisting of interconnected rigid, elastic and viscoelastic components, is presented. The motion of each elastic or viscoelastic body is identified by using three sets of modes: rigid body, reference and normal modes. Rigid body modes describe translation and large angular rotation of a body reference. Reference modes are the result of imposing the body-axis conditions. Normal modes define the deformation of the body relative to the body reference. Constraints between different components are formulated by using a set of non-linear algebraic equations that can be introduced to the dynamic formulation by using a Lagrange multiplier technique or can be utilized to eliminate dependent co-ordinates by partitioning the constraint Jacobian matrix. In developing the system equations of motion of the viscoelastic component, an assumption of a linear viscoelastic model is made. A Kelvin-Voigt model is employed, wherein the stress is assumed to be proportional to the strain and its time derivative. The formulation yields a constant damping matrix and the damping forces depend only on the local deformation; thus, no additional coupling between the reference and elastic co-ordinates appears in the formulation when considering the viscoelastic effects. It is demonstrated, by a numerical example, that the viscoelastic material damping can have a significant effect on the dynamic response of multibody systems.     

Thermal and mechanical finite element modeling of laser-generated ultrasound in coating–substrate system

Thermal and mechanical finite element modeling of laser-generated ultrasound in coating–substrate system is presented, which entails a numerical formulation for the transient responses in terms of the characteristics of the source that originated the waves in the thermoelastic regime. The formulation takes into account the temperature dependence of the material parameters and thermal diffusion from the source. Numerical results show that the temperature gradient field is equivalent to the body force source, namely, vertical forces propagate downward and horizontal forces outward in the specimen. Waveforms at the epicenter present fast oscillations immediately after the precursor, which are produced by multiple reflections of the longitudinal in the coating, the thickness of the coating has remarkable influence on the waveforms at the epicenter.     

Is Teleparallel Gravity Really Equivalent to General Relativity?

An axiomatization of the so‐called Teleparallel Equivalent to General Relativity is presented. A set of formal and semantic postulates are elaborated from where the physical meaning of various key concepts of the theory are clarified. These concepts include those of inertia, Lorentz and diffeomorphism invariance, and reference frame. It is shown that Teleparallel Gravity admits a wider representation of space‐time than General Relativity, allowing to define properties of the gravitational field such as energy and momentum that are usually considered problematic. In this sense, although the dynamical equations of both theories are equivalent, their inequivalence from a physical point of view is demonstrated. Finally, the axiomatic formulation is used to compare Teleparallel Gravity with other theories of gravity based on absolute parallelism such as non‐local and f(T) gravity.     

The non-equilibrium Marshak wave problem

An analytic solution to a particular Marshak wave problem is given. The radiative transfer model used is the gray, non-equilibrium diffusion approximation which allows the radiation and material fields to be out of equilibrium. This solution should be useful as a reference problem for validating time-dependent radiative transfer computer codes, as well as investigating the convergence, as a function of space and time step size, for such codes. The coupling of the radiation field to the material field in a multigroup code, a difficult numerical problem, can also be tested against this solution. Typical numerical results are given for surface quantities, integral quantities, and the distribution of radiative energy and material temperature as a function of space and time.     

Direct numerical simulation of turbulence/radiation interaction in premixed combustion systems

An important fundamental issue in chemically reacting turbulent flows is turbulence/radiation interaction (TRI); TRI arises from highly nonlinear coupling between temperature and composition fluctuations. Here, a photon Monte Carlo method for the solution of the radiative transfer equation has been integrated into a turbulent combustion direct numerical simulation (DNS) code. DNS has been used to investigate TRI in a canonical configuration with systematic variations in optical thickness. The formulation allows for nongray gas properties, scattering, and general boundary treatments, although in this study, attention has been limited to gray radiation properties, no scattering, and black boundaries. Individual contributions to emission and absorption TRI have been isolated and quantified. Of particular interest are intermediate values of optical thickness where, for example, the smallest hydrodynamic and chemical scales are optically thin while the largest turbulence scales approach an optically thick behavior. In the configuration investigated, the temperature self-correlation contribution (emission) is primarily a function of the ratio of burned-gas temperature to unburned-gas temperature, and is the dominant contribution to TRI only in the optically thin limit. Even in the most optically thin case considered, the absorption coefficient–Planck function correlation and absorption coefficient–intensity correlation are not negligible. At intermediate values of optical thickness, contributions from all three correlations are significant.     

基于激光旋转加热的非导电材料高温光谱发射率测试方法与装置

光谱发射率是表征材料热物理性能的重要参数。对于非导电材料的高温光谱发射率测试,一般采用高温加热炉加热或辐射加热的方式来进行发射率测试,存在的问题是采用高温石墨炉加热时,样品可能会与高温石墨发生化学反应,从而破坏材料原有物性;采用辐射加热,一般是单向静止加热,会存在样品温场梯度非均匀分布的问题。基于激光旋转加热和样品/黑体整体一体化设计,提出了一种“样品动中测”的非导电材料高温光谱发射率测试新方法,建立了相应的测量模型,突破了传统的 “样品静中测”的局限,样品与参考黑体共形一体化设计,采用微区域光谱辐射成像方法,同时测量参考黑体和样品的光谱辐射能量与温度。建立了激光旋转加热状态下的热传导方程,对典型样品材料的温度分布进行了仿真计算,结果表明旋转样品温场分布较为均匀,分析了温场分布与红外光谱发射率测量误差间的关系,给出了适用于本测试方法的材料的热导率下限值。基于该方法,搭建了相应的测量装置,对典型材料碳化硅在1 000 K时的光谱发射率进行了测试,在4 μm处对各个典型高温温度点的光谱发射率进行了测试,得到了碳化硅材料在红外波段的光谱发射率波长变化和温度变化规律特性。与国外的测量结果进行了比对,结果较为一致,验证了激光旋转加热光谱发射率测试方法的可行性。采用此方法,不破坏样品本身的理化特性,样品加热升温速度快,测量温度范围上限高,有效减小了激光静止单向加热带来的温度不均匀性,可同时测量出样品和参考黑体的光谱辐射亮度及温度,无需另外再设计标准高温黑体,解决了现有非导电材料高温光谱发射率测试中非均匀加热和辐射能量同步比对测量的问题,可应用于多种非导电材料高温光谱发射率的测试。     

Relaxation dynamics of charged gravitational collapse

We study analytically the relaxation dynamics of charged test fields left outside a newly born charged black hole. In particular, we obtain a simple analytic expression for the fundamental quasinormal resonances of near-extremal Reissner-Nordström black holes. The formula is expressed in terms of the black-hole physical parameters: , where TBH and Φ are the temperature and electric potential of the black hole, and q is the charge of the field.     

A robust level set method based on local statistical information for noisy image segmentation

The paper presents an improved local region-based active contour model for image segmentation, which is robust to noise. A data fitting energy functional is defined in terms of curves and the energy terms which are based on the differences between the local average intensity and the global intensity means. Then the energy is incorporated into a level set variational formulation, from which a curve evolution equation is derived for energy minimization. And then the level set function is regularized by Gaussian filter to keep smooth and eliminate the re-initialization. By using the local statistical information, the proposed model can handle with noisy images. The proposed model is first presented as a two-phase level set formulation and then extended to a multi-phase one. Experimental results show desirable performances of the proposed model for both noisy synthetic and real images, especially with high level noise.     

Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws

In this article, we propose a new class of finite volume schemes of arbitrary accuracy in space and time for systems of hyperbolic balance laws with stiff source terms. The new class of schemes is based on a three stage procedure. First a high-order WENO reconstruction procedure is applied to the cell averages at the current time level. Second, the temporal evolution of the reconstruction polynomials is computed locally inside each cell using the governing equations. In the original ENO scheme of Harten et al. and in the ADER schemes of Titarev and Toro, this time evolution is achieved via a Taylor series expansion where the time derivatives are computed by repeated differentiation of the governing PDE with respect to space and time, i.e. by applying the so-called Cauchy–Kovalewski procedure. However, this approach is not able to handle stiff source terms. Therefore, we present a new strategy that only replaces the Cauchy–Kovalewski procedure compared to the previously mentioned schemes. For the time-evolution part of the algorithm, we introduce a local space–time discontinuous Galerkin (DG) finite element scheme that is able to handle also stiff source terms. This step is the only part of the algorithm which is locally implicit. The third and last step of the proposed ADER finite volume schemes consists of the standard explicit space–time integration over each control volume, using the local space–time DG solutions at the Gaussian integration points for the intercell fluxes and for the space–time integral over the source term. We will show numerical convergence studies for nonlinear systems in one space dimension with both non-stiff and with very stiff source terms up to sixth order of accuracy in space and time. The application of the new method to a large set of different test cases is shown, in particular the stiff scalar model problem of LeVeque and Yee [R.J. LeVeque, H.C. Yee, A study of numerical methods for hyperbolic conservation laws with stiff source terms, Journal of Computational Physics 86 (1) (1990) 187–210], the relaxation system of Jin and Xin [S. Jin, Z. Xin, The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications on Pure and Applied Mathematics 48 (1995) 235–277] and the full compressible Euler equations with stiff friction source terms.     

Squeezed thermal radiation state in a Kerr-nonlinear black body

We find that the photon system in the black body filled in its interior by a Kerr-nonlinear crystal is in a squeezed thermal radiation state, in which the photon system possesses a new kind of quasiparticles—nonpolaritons. The existence of nonpolaritons should be manifested by observing the predicted temperature dependence of the velocity and squeezing of nonpolaritons. The propagation velocity and noise properties of nonpolaritons constitute potentially novel and significant effects in solid-state quantum optics and hence these effects should have extensive application to fields of science and technology.     

Direct measurement of the photon statistics of a triggered single photon source

We studied intensity fluctuations of a single photon source relying on the pulsed excitation of the fluorescence of a single molecule at room temperature. We directly measured the Mandel parameter Q(T) over 4 orders of magnitude of observation time scale T by recording every photocount. On time scale of a few excitation periods, sub-Poissonian statistics is clearly observed and the probablility of two-photons events is 10 times smaller than Poissonian pulses. On longer times, blinking in the fluorescence, due to the molecular triplet state, produces an excess of noise.     

Lattice spinor gravity

We propose a regularized lattice model for quantum gravity purely formulated in terms of fermions. The lattice action exhibits local Lorentz symmetry, and the continuum limit is invariant under general coordinate transformations. The metric arises as a composite field. Our lattice model involves no signature for space and time, describing simultaneously a Minkowski or euclidean theory. It is invariant both under Lorentz transformations and euclidean rotations. The difference between space and time arises from expectation values of composite fields. Our formulation includes local gauge symmetries beyond the generalized Lorentz symmetry. The lattice construction can be employed for formulating models with local gauge symmetries purely in terms of fermions.     

The unification of inflation and late-time acceleration in the frame of <Emphasis Type="Italic">k</Emphasis>-essence

By using the formulation of the reconstruction, we explicitly construct models of k-essence, which unify the inflation in the early universe and the late accelerating expansion of the present universe by a single scalar field. Due to the higher derivative terms, the solution describing the unification can be stable in the space of solutions, which makes the restriction for the initial condition relaxed. The higher derivative terms also eliminate tachyon. Therefore we can construct a model describing the time development, which cannot be realized by a usual inflaton or quintessence models of the canonical scalar field due to the instability or the existence of tachyon. We also propose a mechanism of the reheating by the quantum effects coming from the variation of the energy density of the scalar field.     

Arbitrary laser beam propagation in free space

The propagation of arbitrary laser beams in free space is examined. For this purpose, starting with an incident field of arbitrary field distribution, the intensity at the receiver plane is formulated via Huygens Fresnel diffraction integral. Arbitrary source field profile is produced by decomposing the source into incremental areas (pixels). The received field through the propagation in free space is found by superposing the contributions from all source incremental areas. The proposed method enables us to evaluate the received intensity originating from any type of source field. Using the arbitrary beam excitation, intensity of various laser beams such as cos-Gaussian, cosh-Gaussian, general type beams are checked to be consistent with the already existing results in literature, and the received intensity distributions are obtained for some original arbitrary beam field profiles. Our received intensity formulation for the arbitrary source field profiles presented in this paper can find application in optics communication links, reflection from rough surfaces, optical cryptography and optical imaging systems.     

Formulation and picture of quantum phase

Based on the concept of classical phase, we formulate a new explanation for the quantum phase from the quantum mechanical point of view. The quantum phase is the canonically conjugate variable of an angular momentum operator, which corresponds to the angular position φ in an actual physical space with a classical reference frame, but it takes a complex exponential form e ^iφ≡cosφ+i sinφ in the abstract Hilbert space of a quantum reference frame. This formulation is simply the famous Euler formula in a complex number field. In particular, when φ = π/2, the correlative quantum phase is a unitary pure imaginary number e ^iπ/2≡cos(π/2)+i sin(π/2) ≡ i. By using a photon state-vector function that is the general solution of photon Schr?dinger equation and can completely describe a photon’s behavior, we discuss the relationship between the angular momentum of a photon and the phase of the photon; we also analyze the intrinsic relationship between the macroscopic light wave phase and the microscopic photon phase.     

Time-reversing array retrofocusing in noisy environments

Acoustic time reversal is a robust means of retrofocusing acoustic energy, in both time and space, to the original sound-source location. However, noise may limit the performance of a time-reversing array (TRA) at long source-array ranges, or when the original-source or TRA-element power levels are low. The operation of a TRA requires two steps (reception and transmission) so both TRA-broadcast noise and ambient noise must be taken into account. In this paper, predictions are made for how a simple omnidirectional noise field influences the probability that the signal amplitude from a narrow-band TRA will exceed the noise at the TRA's retrofocus. A general formulation for the probability of TRA retrofocusing, which can be used for TRA design, is developed that includes: the variance of the noise field, the original source strength, the TRA's element output power, the number of TRA elements (N), and the propagation characteristics of the environment. This formulation predicts that a TRA's array gain (in dB) at the retrofocus may be as high as + 10log10(N) to + 20 log10(N) depending on the relative strengths of the original source and the TRA's elements. Monte Carlo simulations in both a free-space environment and a shallow-ocean sound-channel environment compare well to this probability formulation even when simple approximate parametric relationships for the appropriate Green's functions are used. The dominant deviation between theory and simulation in the sound channel is caused by acoustic absorption.