Verifications of the Scattering Theory on Manifolds

Scattering theory plays the main role in the study of manifolds and the Laplacian spectrum. In this article, we process justifying the continuous Laplacian spectrum and on a complete Riemannian manifold. (M,gi) is categorized by the use of bounded curvature of the metric. In particular, the covariant derivative is limitedly considered as an application in the geodesic distance from a fixed point.

A NEW APPROXIMATE SOLUTION TO THE MULTIPLE SCATTERING THEORY FOR THE ELASTIC PROPERTIES OF HETEROGENEOUS MATERIALS

The multiple scattering theory has been a powerful tool in determining the effective properties of heterogeneous materials. In this paper , a simple relationship between the scattering theory and the micromechanics theory based on the Eshelby principle has been suggested. According to the relationship, a new and simple approximate solution to the exact multiple scattering theory has been given in terms of Eshelby' s S-tensor. The solution easily shows those known results for isotropic composites with spherical inclusions and for tracnsversely isotropic composites, and first gives non-setf-consistent (average t-matrix) and symmetric self-consistent (effective medium or coherent potential) approximate results for isotropic composites with spheroidal inclusions.

The Scattering Theory of Nonlinear Schroedinger Equations with Interaction Terms

In this paper, we give a simplified proof on the energy scattering for the nonlinear Schroedinger equations with interaction terems by use of the interaction Morawetz estimate, which is originally introduced in [4].

MULTIPLE SCATTERING THEORY OF EFFECTIVE MECHANICAL PROPERTIES OF INHOMOGENEOUS MEDIA

The rate of hydrothermal reaction of SiO_2 and/or A1_2O_3 in the system of CaO-Al_2O_3-SiO_2-H_2O at 200℃ and the factors which influence the reactions are investigated by determining the reaction ratio.The rate of reactions depends on the reactive activities of raw materials, initial composition of mixture and relative activity of SiO_2 and A12O3. The hydrothermal reaction can be accelerated by sodium hydroxide,in the case of silica,which has low activity, this is quite obvious.

Non-unitary Scattering Theory against Generalized Unitary Scattering Theory

Comparison of non-unitary and generalized unitary scattering theories is done by means of nuclear monodromy （equivalence of Schrodinger and Maxwell time-independent equations）, tunneling and radioactivity. Radioactivity is important part of physics and our life. Its importance stretches from medicine as far as to war strategies. We present theoretical approach to achieve better understanding of the radioactive decay when modified quantum theory is applied. It can be done by updating existing codes to understand better construction of the world and terms and conditions of our existence. The theory modifications are strictly connected with the unimodular M matrix and Wronskian matrices （i.e. their determinants named Wronskians） which create underpinning of so called monodromy being two track wave-function evolution.

Scattering Theory of Current Noise in Nanoscale Devices with Electron-electron and Electron-phonon Interactions

In this paper, we derive a unified scattering theory model for current noise based on the equivalent contact model of the scattering region. Our model seamlessly covers the whole range of transport regimes from coherent transport to incoherent transport and it also includes the effects of Pauli exclusion and Coulomb interaction on shot noise.

Single-photon scattering and quantum entanglement of two giant atoms with azimuthal angle differences in a waveguide system

We theoretically investigate coherent scattering of single photons and quantum entanglement of two giant atoms with azimuthal angle differences in a waveguide system.Using the real-space Hamiltonian,analytical expressions are derived for the transport spectra scattered by these two giant atoms with four azimuthal angles.Fano-like resonance can be exhibited in the scattering spectra by adjusting the azimuthal angle difference.High concurrence of the entangled state for two atoms can be implemented in a wide angle-difference range,and the entanglement of the atomic states can be switched on/off by modulating the additional azimuthal angle differences from the giant atoms.This suggests a novel handle to effectively control the single-photon scattering and quantum entanglement.

Relation between singularity expansion method (SEM) and resonance scattering theory (RST)

In recent years there are two theories for the acoustic scattering, one is the Singularity Expansion Method (SEM) , the other is the Resonance Scattering Theory (RST). In this paper, relation between these two theories was established. For the examples of the acoustic scattering from the solid elastic cylinder and sphere immersed in water, we prove that the RST can be directly derived from the SEM, so that these two theories are equivalent. By use of the Mittag- Leffler theorem we expand the pure elastic scattering wave, which is extracted by isolating the rigid background from the total scattering wave, in an exact resonance expansion. We specially prove that the reradiation efficiency and the resonance width are nearly proportional to the imaginary part of the corresponding pole for most solid objects immersed in water. This shows that the resonance scattering behavious can be entirely determined by the complex frequency poles. For the cases of an aluminum cylinder and a tungsten carbide sphere immersed in water, we calculate the partial-wave form functions by using the new resonance formulae. The results agree with the exact calculation well.

High-Frequency Guided Wave Scattering by a Partly Through-Thickness Hole Based on 3D Theory

We present a theoretical investigation of the scattering of high frequency S0 Lamb mode from a circular blind hole defect in a plate based on the 3D theory. The SO wave is incident at the frequency above the A1 mode cut-off frequency, in which the popular approximate plate theories are inapplicable. Due to the non-symmetric blind hole defect, the scattered fields will contain higher order converted modes in addition to the fundamental SO and AO modes. The far-field scattering amplitudes of various propagating Lamb modes for different hole sizes are inspected. The results are compared with those of lower frequencies and some different phenomena are found. Two-dimensional Fourier transform （2DFT） results of transient scattered Lamb and SH wave signals agree well with the analytical dispersion curves, which check the validity of the solutions from another point of view.

Frequency-tunable single-photon router based on a microresonator containing a driven three-level emitter

We propose a frequency-tunable router of single photons with high routing efficiency, which is constructed by two waveguides mediately linked by a single-mode whispering gallery resonator with a driven three-level emitter. Quantum routing probability in the output port is obtained via the real-space Hamiltonian. By adjusting the resonator–emitter coupling and the drive, the desired continuous central frequencies for the resonance peaks of routing photons can be manipulated nearly linearly, with the assistance of Rabi splitting effect and optical Stark shift. The proposed routing system may provide potential applications in designing other frequency-modulation quantum optical devices, such as multiplexers,filters, and so on.

Exactly Solvable Two-Parameter Models of Relativistic δ′s -Sphere Interactions in Quantum Mechanics

We make a systematic study of two-parameter models of δ ′ s -sphere interaction and δ ′ s -sphere plus a Coulomb interaction. Where δ ′ s interaction denotes the δ ′ -sphere interaction of the second kind. We provide the mathematical definitions of Hamiltonians and obtain new results for both models, in particular the resolvents equations, spectral properties and some scattering quantities.

Tunable Multichannel Quantum Routing of Single Photons Based on Single-Mode Microresonators

We have suggested a novel multiport quantum router of single photons with reflection feedback, which is formed by three waveguides coupled with four single-mode microresonators. The single-photon routing probabilities of four channels in the coupled system are studied theoretically by applying the real-space approach. Numerical results indicate that unidirectional routing in these output channels can be effectively implemented, and the router is tunable to route desired frequencies into the output ports, by varying the inter-resonator detunings via spinning resonator technology. Therefore, the proposed multichannel system can provide potential applications in optical quantum communication.

Elastic Wave Scattering by Two-Dimensional Periodical Array of Cylinders

We extend the multiple-scattering theory (MST) for elastic wave scattering and propagating in two-dimensional composite. The formalism for the band structure calculation is presented by taking into account the full vector character of the elastic wave. As a demonstration of application of the formalism we calculate the band structure of elastic wave propagating in a two-dimensional periodic arrangement of cylinders. The results manifest that the MST shows great promise in complementing the plane-wave (PW) approach for the study of elastic wave.

The microwave scattering characteristics of sea ice in the Bohai Sea

Microwave remote sensing has become the primary means for sea-ice research, and has been supported by a great deal of field experiments and theoretical studies regarding sea-ice microwave scattering. However, these studies have been barely carried in the Bohai Sea. The sea-ice microwave scattering mechanism was first developed for the thin sea ice with slight roughness in the Bohai Sea in the winter of 2012, and included the backscattering coefficients which were measured on the different conditions of three bands（L, C and X）, two polarizations（HH and VV）, and incident angles of 20° to 60°, using a ground-based scatterometer and the synchronous physical parameters of the sea-ice temperature, density, thickness, salinity, and so on. The theoretical model of the sea-ice electromagnetic scattering is obtained based on these physical parameters. The research regarding the sea-ice microwave scattering mechanism is carried out through two means, which includes the comparison between the field microwave scattering data and the simulation results of the theoretical model, as well as the feature analysis of the four components of the sea-ice electromagnetic scattering. It is revealed that the sea-ice microwave scattering data and the theoretical simulation results vary in the same trend with the incident angles. Also, there is a visible variant in the sensitivity of every component to the different bands.For example, the C and X bands are sensitive to the top surface, the X band is sensitive to the scatterers, and the L and C bands are sensitive to the bottom surface, and so on. It is suggested that the features of the sea-ice surfaces and scatterers can be retrieved by the further research in the future. This experiment can provide an experimental and theoretical foundation for research regarding the sea-ice microwave scattering characteristics in the Bohai Sea.

INTERACTION MORAWETZ ESTIMATE AND A SIMPLIFIED PROOF ON THE ENERGY SCATTERING FOR HARTREE EQUAITONS

In this article, we give a simple proof on the energy scattering for the Hartree equations using the interaction Morawetz estimate that was originally introduced in [5].

ON THE DECAY AND SCATTERING FOR THE KLEIN-GORDON-HARTREE EQUATION WITH RADIAL DATA

In this paper,we study the decay estimate and scattering theory for the Klein-Gordon-Hartree equation with radial data in space dimension d≥3.By means of a compactness strategy and two Morawetz-type estimates which come from the linear and nonlinear parts of the equation,respectively,we obtain the corresponding theory for energy subcritical and critical cases.The exponent range of the decay estimates is extended to 0〈γ≤4 and γ〈d with Hartree potential V（x） =｜x｜-γ.

A SIMPLE METHOD FOR PREDICTION OF THE REDUCED SCATTERING COEFFICIENT IN TISSUE-SIMULATING PHANTOMS

This paper proposes a method for predicting the reduced scattering coefficients of tissuesimulating phantoms or the desired amount of scatters for producing phantoms according to Mie scattering theory without measurements with other instruments.The concentration of the scatters TiO2 particles is determined according to Mie theory calculation and added to transparent host epoxy resin to produce phantoms with different reduced scattering coefficients.Black India Ink is added to alter the absorption coefficients of the phantoms.The reduced scattering coefficients of phantoms are measured with single integrating sphere system.The results show that the measurements are in direct proportion to the concentration of TiO2 and have identical with Mie theory calculation at multiple wavelengths.The method proposed can accurately determine the concentration of scatters in the phantoms to ensure the phantoms are qualified with desired reduced scattering coefficients at specified wavelength.This investigation should be possible to manufacture the phantom simply in reasonably accurate for evaluation of biomedical optical imaging systems.

Quantum Mechanical Approach for Rutherford Scattering and Nuclear Scattering with Born Approximation

Rutherford classical scattering theory, as its quantum mechanical analogue, is modified for scattering cross-section and the impact parameter by using quantum mechanical momentum, (de Broglie hypothesis), energy relationship for matter oscillator (Einstein’s oscillator) and quantum mechanical wave vectors, and , respectively. It is observed that the quantum mechanical scattering cross-section and the impact parameter depended on inverse square law of quantum action (Planck’s constant). Born approximation is revisited for quantum mechanical scattering. Using Bessel and Neumann asymptotic functions and response of nuclear surface potential barrier, born approximations were modified. The coulombic fields inside the nucleus of the atom are studied for reflection and transmission with corresponding wave vectors, phase shifts and eigenfunctions Bulk quantum mechanical tunneling and reflection scattering, both for ruptured and unruptured nucleus of the atom, are deciphered with corresponding wave vectors, phase shifts and eigenfunction. Similar calculation ware accomplished for quantum surface tunneling and reflection scattering with corresponding wave vectors, phase shifts and eigenfunctions. Such diverse quantum mechanical scattering cross-section with corresponding wave vectors for tunneling and reflection, phase shifts and eigenfunctions will pave a new dimension to understanding the behavior of exchange fields in the nucleus of the atom with insides layers both ruptured and unruptured. Phase shifts, δl for each of the energy profile (partial) will be different and indeed their corresponding wave vectors for exchange energy eigenvalues.

Design of Four-Channel Demultiplexer Based on Whispering-Gallery Mode Resonators

A new four-channel demultiplexer of single photons is proposed, in which four microresonators are utilized to link the four drop waveguides and the bus waveguide. By adjusting the system parameters, the crosstalk effect of the multiple channel frequencies is suppressed, and multiple peak frequencies with high drop efficiencies in these output ports are achieved. As the 2 × 2 model is scalable, the proposed structure can provide potential applications in designing scalable optical devices.

Highly Efficient Two-Channel Drop Filter of Single Photons with One Drop Waveguide

A novel double-channel drop filter of single photons with only a drop waveguide is proposed. In the structure, two microresonators with a qubit are used to connect the drop waveguide and the bus waveguide with a reflector. By tuning the system parameters, multiple wavelengths with high drop efficiencies in two output channels of the drop waveguide are obtained. As the reflector is independent on its exact location, and one drop waveguide with two drop channels saves the integrated space, this may suggest a potential filtering device which functions in photonic integrated circuits and dense wavelength division multiplexing communication.