On modelling of thermodynamic interaction of particles suspended in two-dimensional medium

Analytical description of temperature distribution in a medium with foreign inclusions is difficult due to the complicated geometry of the problem, so asymptotic and numerical methods are usually used to model thermodynamic processes in heterogeneous media. To be convinced in convergence of these methods the authors consider model problem about two identical round particles in infinite planar medium with temperature gradient which is constant at infinity. Authors refine multipole expansion of the solution obtained earlier by continuing it up to higher powers of small parameter, that is nondimensional radius of thermodynamically interacting particles. Numerical approach to the problem using ANSYS software is described; in particular, appropriate choice of approximate boundary conditions is discussed. Authors ascertain that replacement of infinite medium by finite-sized domain is important source of error in FEM. To find domain boundaries in multiple inclusions’ problem the authors develop “fictituous particle” method; according to it the cloud of particles far from the center of the cloud acts approximately as a single equivalent particle of greater size and so may be replaced by it. Basing on particular quantitative data the dependence of domain size that provides acceptable accuracy on thermal conductivities of medium and of particles is explored. Authors establish series of numerical experiments confirming convergence of multipole expansions method and FEM as well; proximity of their results is illustrated, too.

Ultra Low Frequency Wave Produced by Underwater Oscillating Sphere and Its Measurement

When an underwater target moves in viscous fluid, it may cause the periodic movement of the surrounding fluid and generate ultra-low-frequency (ULF) gravity waves. The initial domain of the gravitational surface wave propagating above the moving target is named circular wave. This article studies the ULF circular wave generated by underwater oscillating sphere, which will provide basis for underwater long-range target detection. Firstly, the circular wave caused by the sphere oscillation in a finite deep fluid is studied based on the theory of linear potential flow. Meanwhile, the multipole expansion theory is established to solve the circular wave field. Secondly, the interface wave generated by the target oscillation in a two-layer fluid are numerically analyzed by comparison with the free surface fluctuation of a single-layer fluid. The results show that the amplitude of the internal interface displacement (AIID) is smaller than that of the free surface (AFSD). When the sphere is in the lower layer, the layering effect of the fluid has significant influences on the AFSD. Finally, the results of the pool experiment verified that the wave generated by the oscillating sphere is the surface gravity wave. Furthermore, the change trend of the test result is consistent with the simulation result.

Terahertz Sensing for R/S Chiral Ibuprofen via All-Dielectric Metasurface with Higher-Order Resonance

A terahertz (THz) all-dielectric metasurface with crescent cylinder arrays for chiral drug sensing has been demonstrated. Through the multipole expansion method, we theoretically found that breaking the symmetry of the metasurface can excite higher-order resonance modes and provide stronger anisotropy as well as enhanced sensitivity for the surroundings, which gives a better sensing performance than lower-order resonance. Based on the frequency shift and transmittance at higher-order resonance, we carried out the sensing experiments on (R)-(−)-ibuprofen and (S)-(+)-ibuprofen solution on the surface of this metasurface sensor. We were able to monitor the concentrations of ibuprofen solutions, and the maximum sensitivity reached 60.42 GHz/mg. Furthermore, we successfully distinguished different chiral molecules such as (R)-(−)-ibuprofen and (S)-(+)-ibuprofen in the 5 μL trace amount of samples. The maximum differentiation was 18.75 GHz/mg. Our analysis confirms the applicability of this crescent all-dielectric metasurface to enhanced sensing and detection of chiral molecules, which provides new paths for the identification of biomolecules in a trace amount.

Orientation order parameters and effective conductivity of a 2-D solid with partially disordered array of circular inhomogeneities

The paper focuses on the quantitative characterization of the microstructure of a two-dimensional heterogeneous solid with circular inhomogeneities that may vary from perfectly periodic arrangement to completely random one. This characterization is linked to the calculation of the effective conductivity of the material. The partially disordered system of disks is generated in the framework of the representative unit cell model using Metropolis algorithm. The orientation order metrics are taken as the structural parameters providing a quantitative measure of disorder, and their variation caused by the gradual disordering of the periodic system is assessed. The effective conductivity of the heterogeneous solid with partially disordered microstructure is evaluated by the multipole expansion method. It is shown that effective conductivity cannot be fully characterized by only one orientation order metric, and the required additional ones are identified.

A Multipole algorithm for solving a fractional generalization of the helmholtz equation

Рассматривается задача построения эффективного численного алгоритма решения дробно-дифференциального обобщения неоднородного уравнения Гельмгольца с дробной степенью оператора Лапласа. Построено мультипольное разложение, основанное на факторизации фундаментального решения рассматриваемого уравнения. Предложен способ нахождения значений функций Фокса, входящих в представленное мультипольное разложение. Разработана модификация мультипольного алгоритма для решения рассматриваемого дробно-дифференциального обобщения уравнения Гельмгольца. Приведены результаты вычислительных экспериментов, демонстрирующие эффективность предложенных алгоритмов. The problem of constructing an efficient numerical algorithm for solving a fractional generalization of the Helmholtz equation with the fractional Laplacian is considered. A multipole expansion based on the factorized representation of the fundamental solution of the considered equation is constructed. A numerical method for computing the values of Fox H-functions from the multipole expansion is proposed. A modification of the multipole algorithm for solving the considered fractional generalization of the Helmholtz equation is developed. Numerical results demonstrating the efficiency of the proposed algorithms are discussed.