Multipole expansion of the vibration transmission between a source and a receiver

The vibrational power transmitted by N forces applied, for example, by a machine upon isolators is regarded as the power transmitted by N independent poles of vibration: e.g., monopole, dipole, etc. The machine or source of vibration moves in a set of vibrational poles. The receiver is defined by a set of polar mobilities or impedances. The power transmission expressions were implemented on a practical structure, one using the source acceleration to measure the power transmitted by the isolators, the other using the receiving structure to estimate the magnitude of power by all sources of vibration, including the airborne noise.     

Magnetic excitations in neodymium,a sinusoidally modulated antiferromagnet

We report the first unambiguous observations of the magnetic excitations in neodymium metal, which exhibits complex antiferromagnetic structures below T_N = 20 K. The wavevector and temperature dependence of the excitations have been determined from neutron inelastic scattering measurements made at the Institut Laue-Langevin. Two district, low-energy, magnetic modes are observed for the [100] basal plane direction (TM) whilst there is only a single mode in the c-direction (TA) These modes are only observed clearly at low temperatures (T?8 K): they broaden and soften as the temperature is raised through T_N. Measurements were also made of the longitudinal and transverse acoustic phonon spectra in neodymium. The predictions of current theories of the excitations in sinusoidally modulated magnetic structures are discussed and compared with the results of our observations.     

Low-energy Ce spin excitations in CeFeAsO and CeFeAsO<Subscript>0.84</Subscript>F<Subscript>0.16</Subscript>

We use inelastic neutron scattering to study the low-energy spin excitations of polycrystalline samples of nonsuperconducting CeFeAsO and superconducting CeFeAsO_0.84F_0.16. Two sharp dispersionless modes are found at 0.85 and 1.16 meV in CeFeAsO below the Ce antiferromagnetic (AF) ordering temperature of T _N ^Ce ? 4 K. On warming to above T _N ^Ce ? 4 K, these two modes become one broad dispersionless mode that disappears just above the Fe ordering temperature T _N ^Fe ? 140 K. For superconducting CeFeAsO_0.84F_0.16, where Fe static AF order is suppressed, we find a weakly dispersive mode center at 0.4 meV that may arise from short-range Ce-Ce exchange interactions. Using a Heisenberg model, we simulate powder-averaged Ce spin wave excitations. Our results show that we need both Ce spin wave and crystal electric field excitations to account for the whole spectra of low-energy spin excitations.     

Analytic study of chaos of the tent map: Band structures,power spectra,and critical behaviors

Chaotic behaviors of the tent map (a piecewise-linear, continuous map with a unique maximum) are studied analytically throughout its chaotic region in terms of the invariant density and the power spectrum. As the height of the maximum is lowered, successive band-splitting transitions occur in the chaotic region and accumulate to the transition point into the nonchaotic region. The timecorrelation function of nonperiodic orbits and their power spectrum are calculated exactly at the band-splitting points and in the vicinity of these points. The method of eigenvalue problems of the Frobenius-Perron operator is used. 2 ^m?1 critical modes, wherem = 1,2, 3, ..., are found which exhibit the critical slowing-down near the 2 ^m?1-band to 2 ^m -band transition point. After the transition these modes become periodic modes which represent the cycling of nonperiodic orbits among 2 ^m bands together with the periodic modes generated by the preceding band splittings. Scaling laws near the transition point into the nonchaotic region are investigated and a new scaling law is found for the total intensity of the periodic part of the spectrum.     

Vacuum mass spectra for SU(N) self-dual Chern-Simons-Higgs systems

We study the SU(N) self-dual Chem-Simons-Higgs systems with adjoint matter coupling, and show that the sixth-order self-dual potential has p(N) gauge inequivalent degenerate minima, where p(N) is the number of partitions of N. We compute the masses of the gauge and scalar excitations in these different vacua, revealing an intricate mass structure which reflects the self-dual nature of the model.     

High-order angular response beamformer for vector sensors

A linear processing scheme for computing higher-order angular response modes of a vector sensor is described. Examples of modal response beampatterns are presented. The response modes form (in principle) a complete, orthonormal set that can be transformed into steerable sets of one or more directive beams. The linear processing scheme facilitates calibration of vector sensor measurement systems. The angular resolution that can be achieved with the new processing scheme is predicted to be (155/N_m) degrees, where N_m is the highest order of computed response mode, for the higher orders. The number of higher-order response modes appears to be limited only by the computational power available.     

Excitation of coherent correlated states in the Jaynes-Cummings model by external deterministic forces: II

In terms of excitation creation and annihilation operators of the Jaynes-Cummings model, acting in the representation of dressed states, the Hamiltonian is written which describes the character of the spectrum of excitations of two modes, representing a quantum analog of the classical behavior of two interacting one-dimensional anharmonic oscillators, namely, the field and atomic oscillators. The anharmonicity is caused by the nonlinearity of the oscillator interaction and manifests itself in the dependence of the frequencies of both modes on the number of excitations, i.e., on the energy. It is shown that an external deterministic force, acting on the system during a certain time t ₀, transfers it from a vacuum state to a coherent state or from one of the coherent states to another coherent state. The probability of the transition from the vacuum state to the coherent state with a given number of excitations represents the Poissonian distribution for the number of excitations formed in the (atom + field) system by the end of action of the external force. It was found to be proportional to the excitation time t ₀.     

Spin Excitations in the Field-Induced Phase of the Quasi-One-Dimensional S = 1 Heisenberg Antiferromagnet NDMAP

The S = 1 quasi-one-dimensional Heisenberg antiferromagnet [Ni(C₅H₁₄N₂)₂N₃](PF₆), abbreviated as NDMAP, has been studied by electron spin resonance in a magnetic field above the critical field (H _c). We studied angular and frequency dependences of spin excitations. The angular dependence of the spin excitations in the vicinity of H _c is explained well by a phenomenological field theory, but the agreement between the experiment and the calculation is not satisfactory above 10 T. In high magnetic fields above 15 T, we obtained some characteristic spin excitations which are well explained by conventional antiferromagnetic resonance modes. These results suggest that the spin excitations change from a quantum state to a classical one due to the suppression of quantum fluctuations by high magnetic fields.     

Vibrational power flow from machines into built-up structures,part II: Wave propagation and power flow in beam-stiffened plates

Wave propagation and power flow due to force and torque (moment) excitation has been studied at the driving point and in the far field of an infinite plate with a single line-stiffener. Such a structure excited by forces or torques applied to the beam behaves like an uncoupled beam at the driving point. In the far field, power transmitted by flexural waves in the beam is radiated into the plate whilst power transmitted by torsional waves in the beam is not radiated. The plate carries a cylindrical wave with a strong directivity.     

Z(N) topological excitations in Yang-Mills theories: duality and confinement

We investigate the properties of Z(N) topological excitations in Wilson's lattice formulation of SU(N) Yang-Mills theories. We exhibit the Z(N) topological excitations as exact classical solutions on the lattice. After giving detailed qualitative discussions about the Z(N) excitations and their relevance to confinement, we investigate the Z(N) lattice gauge theories with the Wilson action and show that Z(2), Z(3) and Z(4) models are self-dual systems. (The self-duality of the Z(2) case has been known previously.) This property enables us to locate the critical points exactly in those systems under the assumption that the phase transition occurs at only one point in the coupling constant space. We then derive the effective action for the Z(N) topological excitations in the lattice SU(N) Yang-Mills theories in the steepest descent approximation. The critical coupling constants in the SU(N) models corresponding to the phase transition caused by the Z(N) excitations are estimated by using the information on the Z(N) models with the Wilson action. It is quite probable that the estimated value $\text{g}{}_{\mathrm{<mtext>r</mtext>}}{}^2\text{/4π}{}^2\text{～}\text{1}\text{31}$ (for SU(3)) is an upper bound. This indicates that the Wilson model of the SU(3) gauge field can be effective action of the QCD gluons which exhibit permanent quark confinement and, at the same time, freedom up to the distance characterized by the energy, at least, ～1 TeV.     

An increase in the sensitivity of the saturated absorption method in the multimode regime

A possibility for an increase in the signal-to-noise ratio in the laser spectroscopy that is free of Doppler broadening and is based on the saturated absorption is considered. The application of the counter-propagating laser beams in the multimode regime is proposed. The number of atoms that effectively interact with the field, and, hence, the intensity of a narrow resonance in the line shape can be increased due to the interaction of the counterpropagating modes with different frequencies. It is demonstrated that, for the intrinsic photon noise, the signal-to-noise ratio can be increased by a factor of √N, where N is the number of modes. For the remaining noises (fluctuations of the radiation power, noise of photodetector, etc.), the signal-to-noise ratio can be increased by a factor of N.     

Resonant Bragg reflection from quantum-well structures

The resonant spectra of light reflected and transmitted by a heterostructure with a finite system of equidistant quantum wells have been calculated. Recurrence relations have been derived connecting the amplitude reflection coefficients from N and N - 2 quantum wells, and analytical properties of the reflection coefficient as a function of the complex frequency ω have been established. A method has been proposed which allows one to find complex frequencies of coupled exciton-photon nonstationary modes, or exciton-polaritons. It has been shown that the resonant Bragg structures represent a particular case where among N eigenmodes only one is radiative.     

Non-trivial saddle points and band structure of bound states of the two-dimensional O(N) vector model

We discuss O(N) invariant scalar field theories in 0 + 1 space-time dimensions (quantum mechanics) and in 1 + 1 space-time dimensions (field theory). Combining ordinary “Large N” saddle point techniques and simple properties of the diagonal resolvent of one-dimensional Schrödinger operators we find non-trivial (non-constant) solutions to the saddle point equations of these models in addition to the saddle point describing the ground state of the theory. In the “Large N” limit these saddle points are exact for the quantum mechanical case, but only approximate in the two-dimensional theory. In the latter case they are the leading contributions to the time evolution kernel at short times, or equivalently, the leading contribution to the high temperature expansion of partition function stemming from space dependent static configurations in case of the Euclidean theory. We interpret these novel saddle points as collective O(N) singlet excitations of the field theory, each embracing a host of finer quantum states arranged in O(N) multiplets, in an analogous manner to the band structure of molecular spectra.     

Low-energy Ce spin excitations in CeFeAsO and CeFeAsO0.84F0.16

We use inelastic neutron scattering to study the low-energy spin excitations of polycrystalline samples of nonsuperconducting CeFeAsO and superconducting CeFeAsO_0.84F_0.16. Two sharp dispersionless modes are found at 0.85 and 1.16 meV in CeFeAsO below the Ce antiferromagnetic (AF) ordering temperature of T _N ^Ce ˜ 4 K. On warming to above T _N ^Ce ˜ 4 K, these two modes become one broad dispersionless mode that disappears just above the Fe ordering temperature T _N ^Fe ˜ 140 K. For superconducting CeFeAsO_0.84F_0.16, where Fe static AF order is suppressed, we find a weakly dispersive mode center at 0.4 meV that may arise from short-range Ce-Ce exchange interactions. Using a Heisenberg model, we simulate powder-averaged Ce spin wave excitations. Our results show that we need both Ce spin wave and crystal electric field excitations to account for the whole spectra of low-energy spin excitations.     

Optimal transport in a ratchet coupled to a modulated environment: The role of Levy walks

We consider a Brownian particle in a ratchet potential coupled to a modulated environment and subjected to an external oscillating force. The modulated environment is modelled by a finite number N of uncoupled harmonic oscillators. Superdiffusive motion and Levy walks (anomalous random walks) are observed for any N and for low values of the external amplitude F. The coexistence of left and right running states enhances the power α from the time dependence of the mean square displacement (MSD). It is shown that α is twice the average of the power of the separated left and right MSDs. Normal random walks are obtained by increasing F. We show that the maximal mobility of particles along the periodic structure occurs just before superdiffusive motion disappears and Levy walks are transformed into normal random walks.     

The Use of a hierarchy scheme for the evaluation of normal modes of vibration

In vibrational analysis it is the common practice to initially approximate a set of force constants rather than to initially approximate a set of normal modes. This does not allow a flexible and easily analyzed computational system. A hierarchy scheme of approximation has been developed. Systematic testing of alternative hierarchies and geometries is essential since a force field may always be evaluated to match exactly observed and calculated frequencies for any set of approximate normal modes. Other physical requirements must therefore be considered to establish the correctness of an answer. A set of N linearly independent internal coordinates of a particular symmetry type are placed in a hierarchy and a set of N orthormal modes are developed in such a way that the nth normal mode does not change the internal coordinates of the n + 1 to Nth members of the hierarchy. Constraints on the form of the force field require iteration from these well-defined initial approximations. The hierarchy scheme offers a much more satisfying physical picture of characteristic group frequencies and lends itself readily to the use of perturbation theory.     

Exploring the Origin of Maximum Entropy States Relevant to Resonant Modes in Modern Chladni Plates

The resonant modes generated from the modern Chladni experiment are systematically confirmed to intimately correspond to the maximum entropy states obtained from the inhomogeneous Helmholtz equation for the square and equilateral triangle plates. To investigate the origin of maximum entropy states, the inhomogeneous Helmholtz equation is modified to consider the point interaction coming from the driving oscillator. The coupling strength associated with the point interaction is characterized by a dimensionless factor α. The δ potential of the point interaction is numerically modelled by a truncated basis with an upper index N. The asymptotic behavior for the upper index N is thoroughly explored to verify that the coupling strength of α = 1.0 can make the theoretical resonant modes agree excellently with the maximum entropy states as N→∞. It is further authenticated that nearly the same resonant modes can be obtained by using a larger coupling strength α when a smaller upper index N is exploited in the calculation.     

一种T形高功率微波功率合成器

提出了一种新型功率合成器,其工作原理为:通过在两个相互垂直的过模矩形波导中放置两组相互垂直的金属插板,对具有不同极化方向的矩形波导TE10模进行隔离传输,实现高功率微波的双路通道功率合成。基于这一原理初步设计了一个中心频率为9.55 GHz的功率合成器,并进行了数值模拟。模拟结果表明:这种功率合成器可以承受高功率,单通道工作时的功率容量分别大于7.31 GW和6.83 GW,中心频率上两个通道的单模功率传输效率分别达到了98%和99%,反射损耗分别小于-36 dB和-21 dB,通道之间的耦合损耗分别小于-30 dB和-45 dB。     

Light scattering observations of spin reversal excitations in the fractional quantum Hall regime

Resonant inelastic light scattering experiments access the low lying excitations of electron liquids in the fractional quantum Hall regime in the range 2/5≥ν≥1/3. Modes associated with changes in the charge and spin degrees of freedom are measured. Spectra of spin reversed excitations at filling factor ν?1/3 and at ν?2/5 identify a structure of lowest spin-split Landau levels of composite fermions (CFs) that is similar to that of electrons. Observations of spin wave excitations enable determinations of energies required to reverse spin. The spin reversal energies obtained from the spectra illustrate the significant residual interactions of composite fermions. At ν=1/3 energies of spin reversal modes are larger but relatively close to spin conserving excitations that are linked to activated transport. Predictions of composite fermion theory are in good quantitative agreement with experimental results.