The Poisson-Helmholtz-Boltzmann model

We present a mean-field model of a one-component electrolyte solution where the mobile ions interact not only via Coulomb interactions but also through a repulsive non-electrostatic Yukawa potential. Our choice of the Yukawa potential represents a simple model for solvent-mediated interactions between ions. We employ a local formulation of the mean-field free energy through the use of two auxiliary potentials, an electrostatic and a non-electrostatic potential. Functional minimization of the mean-field free energy leads to two coupled local differential equations, the Poisson-Boltzmann equation and the Helmholtz-Boltzmann equation. Their boundary conditions account for the sources of both the electrostatic and non-electrostatic interactions on the surface of all macroions that reside in the solution. We analyze a specific example, two like-charged planar surfaces with their mobile counterions forming the electrolyte solution. For this system we calculate the pressure between the two surfaces, and we analyze its dependence on the strength of the Yukawa potential and on the non-electrostatic interactions of the mobile ions with the planar macroion surfaces. In addition, we demonstrate that our mean-field model is consistent with the contact theorem, and we outline its generalization to arbitrary interaction potentials through the use of a Laplace transformation.     

A scalar-mode representation of stochastic, planar, electromagnetic sources

A very useful theoretical tool for investigating coherence properties of stochastic scalar sources and stochastic scalar fields is the so-called coherent-mode representation. We introduce a somewhat similar new representation for planar, secondary stochastic electromag netic sources which generate beams. It consists of three expansions for the three independent elements of the 2 × 2 electric cross-spectral density matrix of the beam. The expansion of the diagonal elements of the matrix are coherent-mode representations in the sense of the scalar theory. The third one, for each off-diagonal element, is a bi-modal expansion, expressed in terms of the coherent modes of the diagonal elements.     

Self-consistent nonlocal potentials near planar surfaces

A new derivation of the self-consistent dynamically screened nonlocal Coulomb potential near a planar surface is presented, based on the integral equation approach. The exact solution is obtained without restrictions on the dynamical response of the solid (e.g. RPA in metals), the type of surface potential or electronic density profile, and without additional matching or boundary conditions. This makes the present approach particularly useful e.g. in the general discussion of model-independent screening phenomena at metal surfaces. The application to the calculation of matrix elements for electron and ion excitation of collective modes and electron-hole pairs is formulated, and the connection with the previous results discussed.     

Higher order representation of the beam cross section deformation in large displacement finite element analysis

Most existing beam formulations assume that the cross section of the beam remains rigid regardless of the amplitude of the displacement. The absolute nodal coordinate formulation (ANCF); however, allows for the deformation of the cross section and leads to a more general beam models that capture the coupling between different modes of displacement. This paper examines the effect of the order of interpolation on the modes of deformation of the beam cross section using ANCF finite elements. To this end, a new two-dimensional shear deformable ANCF beam element is developed. The new finite element employs a higher order of interpolation, and allows for new cross section deformation modes that cannot be captured using previously developed shear deformable ANCF beam elements. The element developed in this study relaxes the assumption of planar cross section; thereby allowing for including the effect of warping as well as for different stretch values at different points on the element cross section. The displacement field of the new element is assumed to be cubic in the axial direction and quadratic in the transverse direction. Using this displacement field, more expressions for the element extension, shear and the cross section stretch can be systematically defined. The change in the cross section area is measured using Nanson’s formula. Measures of the shear angle, extension, and cross section stretch can also be systematically defined using coordinate systems defined at the element material points. Using these local coordinate systems, expressions for a nominal shear angle are obtained. The differences between the cross section deformation modes obtained using the new higher order element and those obtained using the previously developed lower order elements are highlighted. Numerical examples are presented in order to compare the results obtained using the new finite element and the results obtained using previously developed ANCF finite elements.     

Gaussian-DPSM (G-DPSM) and Element Source Method (ESM) modifications to DPSM for ultrasonic field modeling

In the last few years, Distributed Point Source Method (DPSM) a mesh-free semi-analytical technique has been developed. In spite of its many advantages, one shortcoming of the conventional DPSM method is that the field obtained by conventional DPSM method needs to be scaled to match the theoretical solutions. Two modification techniques called Gaussian-DPSM (G-DPSM) and Element Source Method (ESM) are developed here to avoid the scaling need. G-DPSM technique introduces additional fictitious point sources around every parent point source. Gaussian weight functions determine the strength of these additional fictitious point sources that are denoted as child point sources. ESM replaces discrete point sources used in the conventional DPSM by continuous sources. In the ESM formulation individual point sources are denoted as nodes. Special elements are formed on the boundary by connecting these nodes. The source strength inside the element can vary linearly or non-linearly depending on the order of the interpolation function used inside the element. Results generated by both these methods are compared with the conventional DPSM solution and analytical solution. It is shown that the ultrasonic field in front of the transducer computed by G-DPSM and ESM matches very well with the theory without using any scaling factor.     

Stochastic radiative transfer in a finite plane-parallel medium with general boundary conditions

The time-independent radiative transfer problem in a scattering and absorbing planar random medium with general boundary conditions and internal energy source is considered. The medium is assumed to consist of two randomly mixed immiscible fluids, with the mixing statistics described as a two-state homogeneous Markov process. The problem is solved in terms of the solution of the corresponding free-source problem with simple boundary conditions which is solved using Pomraning-Eddington approximation in the deterministic case. A formalism, developed to treat radiative transfer in statistical mixtures, is used to obtain the ensemble-averaged solution. The average partial heat fluxes are calculated in terms of the albedoes of the source-free problem. Results are obtained for isotropic and anisotropic scattering for specular and diffused reflecting boundaries.     

A general solution procedure for vibrations of systems with cubic nonlinearities and nonlinear/time-dependent internal boundary conditions

The subject of this paper is the development of a general solution procedure for the vibrations (primary resonance and nonlinear natural frequency) of systems with cubic nonlinearities, subjected to nonlinear and time-dependent internal boundary conditions—this is a commonly occurring situation in the vibration analysis of continuous systems with intermediate elements. The equations of motion form a set of nonlinear partial differential equations with nonlinear, time-dependent, and coupled internal boundary conditions. The method of multiple timescales, an approximate analytical method, is applied directly to each partial differential equation of motion as well as coupled boundary conditions (i.e. on each sub-domain and the corresponding internal boundary conditions for a continuous system with intermediate elements) which ultimately leads to approximate analytical expressions for the frequency-response relation and nonlinear natural frequencies of the system. These closed-form solutions provide direct insight into the relationship between the system parameters and vibration characteristics of the system. Moreover, the suggested solution procedure is applied to a sample problem which is discussed in detail.     

Finite element approach for radiative transfer in multi-layer graded index cylindrical medium with Fresnel surfaces

Because the optical plane defined by the incidence and reflection direction at a cylindrical surface has a complicated relation with the local azimuthal angle and zenith angle in the traditional cylindrical coordinate system, it is difficult to deal with the specular reflective boundary condition in the solution of the traditional radiative transfer equation for cylindrical system. In this paper, a new radiative transfer equation for graded index medium in cylindrical system (RTEGCN) is derived based on a newly defined cylindrical coordinate system. In this new cylindrical coordinate system, the optical plane defined by the incidence and reflection direction is just the isometric plane of the local azimuthal angle, which facilitates the RTEGCN in dealing with cylindrical specular reflective boundaries. A least squares finite element method (LSFEM) is developed for solving radiative transfer in single and multi-layer cylindrical medium based on the discrete ordinates form of the RTEGCN. For multi-layer cylindrical medium, a radial basis function interpolation method is proposed to couple the radiative intensity at the interface between two adjacent layers. Various radiative transfer problems in both single and multi-layer cylindrical medium are tested. The results show that the present finite element approach has good accuracy to predict the radiative heat transfer in multi-layer cylindrical medium with Fresnel surfaces.     

Exact results in modeling planetary atmospheres—I. Gray atmospheres

An exact model is proposed for a gray, isotropically scattering planetary atmosphere in radiative equilibrium. The slab is illuminated on one side by a collimated beam and is bounded on the other side by an emitting and partially reflecting ground. We provide expressions for the incident and reflected fluxes on both boundary surfaces, as well as the temperature of the ground and the temperature distribution in the atmosphere, assuming the latter to be in local thermodynamic equilibrium. Tables and curves of the temperature distribution are included for various values of the optical thickness. Finally, semi-infinite atmospheres illuminated from the outside or by sources at infinity is dealt with.     

声悬浮的实验研究和数值模拟分析

介绍了自行研制的一种磁致伸缩式单轴超声悬浮装置,用此装置实现了尺寸1—7mm的若干种金属、半导体和有机物在空气中的稳定悬浮和定位,可悬浮样品的密度高达11.3g/cm³.为了优化谐振腔设计,采用边界元方法结合两类不同结构的谐振腔模型研究了谐振腔几何形状对声场分布以及悬浮定位能力和悬浮稳定性的影响. 关键词：     

Active sound control by directional sources in the free field

TheprojectissupportedbyAeronauticalScienceFoundation.I.IntroductionThecontro1ofsoundfieldbyintroducingacousticsourcesisatopicofnoisecontrolinwhichanincrcasinginterestisbeingshown.Gcnerallytherearemain1ytwoaspectsinthere-searchesonActiveNoiseContro1(ANC)--theoriesofactivesoundattenuationwhichisthebasementofthetCchnique,anddesignofthecontrolsystem.Recent1y,anewtheorywhichisconsideredtohewc11suitcdtotheanalysisofpracticalproblemshasbeenpresentedbyP.A.Nc1sonetal.[ll.Itshowsthattheminimumpowe…     

Three-dimensional fundamental solutions for one-dimensional hexagonal quasicrystal with piezoelectric effect

In this paper, a set of 3D general solutions to static problems of 1D hexagonal piezoelectric quasicrystals is obtained by introducing two displacement functions and utilizing the rigorous operator theory. All the physical quantities are expressed by five quasi-harmonic functions. Based on the general solutions and with the help of the superposition principle, fundamental solutions for infinite/half-infinite spaces are presented by trial-and-error technique. The general solutions can be conveniently used to solve the boundary value problems regarding dislocations, cracks and inhomogeneities. The fundamental solutions are of primary significance to development of numerical codes such as boundary element method.     

Can nanoscale surface charge heterogeneity really explain colloid detachment from primary minima upon reduction of solution ionic strength?

This study theoretically examined colloid detachment from primary minima with ionic strength (IS) reduction on heterogeneous collector surfaces. The chemically and physically heterogeneous collector surfaces were modeled as a planar surface carrying nanoscale patches of different zeta potentials and nanoscale pillars/hemispheroids, respectively. The surface element integration technique was used to calculate interaction energies between colloid and collector surfaces. Two boundary conditions for the double-layer interaction energy were considered, namely constant surface potential (CSP), and linear superposition approximation (LSA). In contrast to prevailing opinions in the literature, our results show that colloids attached on the chemically heterogeneous surface cannot be detached by IS reduction under CSP condition due to an increase of the adhesive force/torque with decreasing IS. Detachment from chemically heterogeneous surfaces by IS reduction can occur under LSA condition only when the flow velocity is very high. In contrast, the presence of nanoscale physical heterogeneity can cause colloid detachment from primary minima by IS reduction under both CSP and LSA conditions at flow velocities commonly used in experimental studies because of a significant reduction in the adhesive forces/torques.     

Passive IR field gradient detection of thermal objects in active Fresnel zones

A dual element Passive-Infrared (PIR) sensor is used with a rotating slit aperture to map a narrow scanning beam on the sensing elements through each lens of a Fresnel lens array. The stimuli generated due to each thermal object fall in the active Fresnel zones in a certain direction based on their locations and temperature variations on the surfaces of the sources. These signals are used to analyze the signatures of stationary thermal objects, their slight movements and thermal field gradient changes of the source surfaces provided the object projected area is less than the area of the active zone. Pattern matching is performed using Dynamic-Time-Warping (DTW) algorithm on STFT reduced length time vectors. The object space is divided into m-active zones that correspond to the Fresnel zones in a Fresnel lens array. Within passive IR region from each of the active zones, the system identifies not only the heat intensity changes but also detects the slight movement of the thermal source. The efficiency of the system is dependent on the number of active Fresnel zones and the angular separation between them. This single node PIR sensor system is designed to cover an angular view of ∼10° × 80° while horizontal Field of View (FOV) is divided into 4 active Fresnel zones. Generally costly Thermal-IR camera is used for thermal analysis. Our system is comparatively less costly and active coverage zones are easily configurable by increasing number of Fresnel lenses.     

Energy-efficient beamforming optimization for MISO communication based on reconfigurable intelligent surface

Reconfigurable intelligent surface (RIS), a planar metasurface consisting of a large number of low-cost reflecting elements, has received much attention due to its ability to improve both the spectrum and energy efficiency (EE) by reconfiguring the wireless propagation environment. In this paper, we propose a base station (BS) beamforming and RIS phase shift optimization technique that maximizes the EE of a RIS-aided multiple-input–single-output system. In particular, considering the system circuits’ energy consumption, an EE maximization problem is formulated by jointly optimizing the active beamforming at the BS and the passive beamforming at the RIS, under the constraints of each user’ rate requirement, the BS’s maximal transmit power budget and unit-modulus constraint of the RIS phase shifts. Due to the coupling of optimization variables, this problem is a complex non-convex optimization problem, and it is challenging to solve it directly. To overcome this obstacle, we divide the problem into active and passive beamforming optimization subproblems. For the first subproblem, the active beamforming is given by the maximum ratio transmission optimal strategy. For the second subproblem, the optimal phase shift matrix at the RIS is obtained by exploiting sine cosine algorithm (SCA). Moreover, for this case where each reflection element’s working state is controlled by a circuit switch, each reflection element’s switch value is optimized with the aid of particle swarm optimization algorithm. Finally, numerical results verify the effectiveness of our proposed algorithm compared to other algorithms.     

Asymptotic Behaviour of Randomly Reflecting Billiards in Unbounded Tubular Domains

We study stochastic billiards in infinite planar domains with curvilinear boundaries: that is, piecewise deterministic motion with randomness introduced via random reflections at the domain boundary. Physical motivation for the process originates with ideal gas models in the Knudsen regime, with particles reflecting off microscopically rough surfaces. We classify the process into recurrent and transient cases. We also give almost-sure results on the long-term behaviour of the location of the particle, including a super-diffusive rate of escape in the transient case. A key step in obtaining our results is to relate our process to an instance of a one-dimensional stochastic process with asymptotically zero drift, for which we prove some new almost-sure bounds of independent interest. We obtain some of these bounds via an application of general semimartingale criteria, also of some independent interest.     

System throughput maximization in IRS-assisted phase cooperative NOMA networks

This work investigates performance of system throughput in intelligent reflecting surfaces (IRSs)-enabled phase cooperative non-orthogonal multiple access (NOMA) framework. By exploiting heterogeneous cognitive radio networks concept the aim is to maximize the sum rate of secondary users in the proposed phase cooperative downlink network configuration via optimization solutions. However, the optimization problem comes out to be NP-hard and precludes direct solution. Hence, an alternating optimization is applied at the primary network to solve the maximization problem by exploiting the transmit beamforming (BF) at the power station (PS) and phase shift optimization at the IRS. Later, sum rate maximization for secondary network is performed by utilizing phase shifts of primary network via phase cooperation. In order to find global optimal solutions for active beamformers at both PSs, a branch-reduce-and-bound (BRnB) method is used whereas, passive phase shift optimization at the primary PS is performed via a simple iterative solution, i.e., the element-wise block coordinate descent method. For the proposed framework, Monte-Carlo simulations are performed where the optimality of the global solution is compared with heuristic BF methods including minimum-mean-square-error/regularized zero-forcing-beamforming (ZFBF) and ZFBF. The BRnB algorithm sets an upper performance bound by improving the sum rate of users in comparison with the conventional heuristic BF schemes. This work signifies the utilization of phase cooperation in IRS-assisted NOMA networks for a multi-user environment.     

Two variational approaches for domain decomposition problems solved by SGBEM with nonconforming discretizations

Two original approaches for the solution of elastic boundary value problems with domain decomposition (DDBVP) using the symmetric Galerkin boundary element method (SGBEM) are presented. Each approach is based on a variational principle, a difference between them consisting in the treatment of the coupling conditions which connect the solutions through an interface. The computer codes developed are able to deal with curved interfaces in a domain decomposition problem discretized by nonmatching meshes of linear elements along the interfaces. The effectiveness of the methods is documented by a numerically solved example. The text was submitted by the authors in English.     

Fast Fourier transform and singular value decomposition formulations for patch nearfield acoustical holography

Nearfield acoustical holography (NAH) requires the measurement of the pressure field over a complete surface in order to recover the normal velocity on a nearby concentric surface, the latter generally coincident with a vibrator. Patch NAH provides a major simplification by eliminating the need for complete surface pressure scans-only a small area needs to be scanned to determine the normal velocity on the corresponding (small area) concentric patch on the vibrator. The theory of patch NAH is based on (1) an analytic continuation of the patch pressure which provides a spatially tapered aperture extension of the field and (2) a decomposition of the transfer function (pressure to velocity and/or pressure to pressure) between the two surfaces using the singular value decomposition (SVD) for general shapes and the fast Fourier transform (FFT) for planar surfaces. Inversion of the transfer function is stabilized using Tikhonov regularization and the Morozov discrepancy principle. Experimental results show that root mean square errors of the normal velocity reconstruction for a point-driven vibrator over 200-2700 Hz average less than 20% for two small, concentric patch surfaces 0.4 cm apart. Reconstruction of the active normal acoustic intensity was also successful, with less than 30% error over the frequency band.