One-loop scalar field contributions to graviton-graviton scattering and helicity non-conservation in quantum gravity

We present and discuss the helicity amplitudes for graviton-graviton scattering via a loop of massless scalars. The amplitudes have the expected analytic structure but do not conserve helicity. We prove that as a consequence helicity is not conserved in pure quantum gravity either and the helicity flip amplitudes are given by two times the scalar loop contributions. Implications for the higher-loop renormalizability of quantum gravity are discussed.     

The effects of ultrasonication power and time on the dispersion stability of few-layer graphene nanofluids under the constant ultrasonic energy consumption condition

Few-layer graphene (FLG) nanofluids have received widespread interest in recent years due to their excellent thermal and optical properties. However, the low dispersion stability is one of the main bottlenecks for their commercialization. Ultrasonication is an effective method and almost an essential step to improve the stability of nanofluids. This work aimed to determine the optimal ultrasonication process for preparing stable FLG nanofluids, particularly under the constant ultrasonic energy consumption condition. For this purpose, FLG nanofluids were prepared under various amplitudes (20%–80%) and times (33.75–135 min) and evaluated by both sedimentation and optical spectrum analysis techniques. It was found that ultrasonication treatment at 30% amplitude for 90 min was sufficient for proper dispersion of FLG, and a further increase in the ultrasonication power would not benefit the stability enhancement much. However, for FLG nanofluids prepared at amplitudes higher than 30% under the constant ultrasonic energy consumption condition, their stability deteriorated seriously due to the reduced ultrasonication time, while for FLG nanofluids prepared at 20% amplitude for 135 min, they showed the higher stability, which indicates that the stability of FLG nanofluids is more sensitive to ultrasonication time than power. Therefore, a relatively longer ultrasonication time rather than a higher amplitude is recommended to prepare stable FLG nanofluids for practical applications at given ultrasonic energy consumption.     

Calculation of the optimal imaging parameters for frequency modulation atomic force microscopy

True atomic resolution of conductors and insulators is now routinely obtained in vacuum by frequency modulation atomic force microscopy. So far, the imaging parameters (i.e., eigenfrequency, stiffness and oscillation amplitude of the cantilever, frequency shift) which result in optimal spatial resolution for a given cantilever and sample have been found empirically. Here, we calculate the optimal set of parameters from first principles as a function of the tip–sample system. The result shows that the either the acquisition rate or the signal-to-noise ratio could be increased by up to two orders of magnitude by using stiffer cantilevers and smaller amplitudes than are in use today.     

Symmetry constraints in optimal polarization formalisms with an application to p−p scattering

The paper contains results (a) for the general optimal polarization formalism with constraints from time reversal invariance, identical particles, and parity conservation, (b) for the specific reaction involving four $\text{spin}\text{-}\text{1}\text{2}$ particles, (c) for the application of the formalism to elastic p?p scattering at 6 GeV/c and at 800 MeV. The choice of the orientation axes under various symmetry constraints is discussed for the general optimal formalism, showing the narrowing of the choices which nevertheless retains an infinite continuum of possibilities. The transformation properties of amplitudes among these various optimal frames are specified. The transformation of observables among these frames is also discussed for the reaction with four $\text{spin}\text{-}\text{1}\text{2}$ particles. Then the relationship between the observables and the bilinear combination of amplitudes is given for the reaction with four $\text{spin}\text{-}\text{1}\text{2}$ particles, for the constraints of identical particles, identical particles and time reversal invariance, and identical particles and time reversal invariance and parity conservation. The results are applied to the analysis of the Argonne data at 6 GeV/c, t = ?0.6 GeV²/c², for elastic p?p scattering. The amplitudes are easily determined when the proper optimal frame is used, and the display of the amplitudes in other optimal frames suggest some features that may be significant in searching for dynamics. Another application is presented to 800 MeV elastic p?p scattering at several angles, showing that in the proper optimal frame very accurate results can be obtained about a subset of amplitude parameters on the basis of an incomplete set of data. Such an analysis is shown to be helpful in the design of future experiments.     

两种不同尺度的颗粒在水平振动容器内分离规律的模拟

用分子动力学方法模拟二维颗粒系统在水平振动下的分离现象.通过数值模拟发现,在固定的振幅下,存在使得分离效率最佳的振动频率,在固定的振动频率下,也存在一个使得分离效率最佳的振幅.根据模拟结果,给出了最佳振幅对振动频率的经验公式.同时,还指出了存在两种不同的分离机制,当振动的加速度过大时,处于垂直边界附近的大粒子会通过容器的边界直接被抛到最顶部.     

Response of a two-level system to a sequence of N radiation pulses

A general expression has been obtained for the polarisation of an assembly of two-level systems irradiated by a sequence of N radiation pulses. The times and amplitudes of the echo-polarisation have been obtained. The method is an extension of the T-matrix method for the exact solution of the problem of interaction of radiation with two-level systems. The number of polarisation echoes is 3 ^N?1?N. The echo times are given by $$t' = (1 + a)t_N + (b - a)t_{N - 1} + (c - b)t_{N - 2} + \cdots + (q - p)t_1 $$ wheret _k are the pulse times anda, b, c take on values 1, 0, ? 1. From the general expression the amplitudes of echoes due to sequences of 2, 3 and 4 pulses are obtained as special cases. Distinct echo sequences determined by time relations among the incident pulses are discussed. The echo sequences exhibit interesting features which are of significance in the application of the phenomenon in holophony, etc.     

Implications of heterogeneous inputs and connectivity on the synchronization in excitable networks

We study the combined implications of connectivity and heterogeneous inputs on the synchronization features of a one-dimensional chain of diffusively coupled FitzHugh Nagumo (FHN) systems. The uncoupled systems are triggered into a regime of chaotic firing by periodic parametric forces modeling external stimuli. Due to the parameter dispersion involved in randomly distributed amplitudes and/or phases of the forces the units are nonidentical and the firing events on the chain of uncoupled units will be asynchronous leading to a distribution of the spiking times. Interest is focused on mutually synchronized spikings arising through the coupling where the connectivity of the network may range from nearest-neighbor interaction to global interactions. From our studies we conclude that increasing the interaction radius does not necessarily entail better spike synchrony and the coupling strength plays a more important role than connectivity. It is found that for driving with random amplitudes together with random phases a critical interaction radius exists beyond which firing becomes suppressed if the coupling between the units is too strong. In such cases of ‘firing death’ the units perform only small-amplitude oscillations which are mutually synchronous. The optimal coupling for spike synchrony is of intermediate strength and altering the connectivity does not really matter for the degree of spike synchrony. Distinct to that, when all the phases are equal and only the amplitudes of the forces are randomly distributed enhanced spike synchrony is achieved for sufficiently strong coupling regardless of the interaction radius.     

Application of the out-of-phase absorption mode to separating overlapping EPR signals with different T1 values

The use of 90 degrees-out-of-phase first-harmonic absorption (V1'-) EPR to resolve the spectra from nitroxide spin labels with differing T1-relaxation times is described. Non-linear V1'-EPR spectra recorded under moderate saturation have sharper lines compared with the in-phase V1-EPR spectra, and amplitudes that preferentially enhance components with longer T1-relaxation. Discrimination between V1'-spectral components can be increased further by means of selective paramagnetic relaxation enhancement agents. Examples are given of biophysical applications to double labelling in single-component membranes and phase separation in two-component membranes, to lipid-peptide complexes, and to binding of spin-labelled reagents. It is concluded that optimal resolution in V1'-EPR spectroscopy is obtained at relatively low Zeeman modulation frequencies (20-30 kHz) and moderate saturation (H1 approximately 0.2-0.3 G).     

Planar Symmetrical XY3 and Boron Trihalides: Mean-Square Amplitudes and Keating Coordinates

The E' block of the mean-square amplitude matrix (Σ) for the planar symmetrical XY₃ molecular model is treated theoretically in terms of the Keating coordinates. A numerical example for ¹¹BF₃ is given. Also the mean amplitudes of vibration (ι) and Bastiansen-Morino shrinkage effect (Δ) are considered. New relations which connect the mean-square amplitudes and force constants are given. Previous works on mean amplitudes and related quantities for boron trihalides from vibrational spectroscopy and gas electron diffraction are reviewed, and some new calculations are reported.     

Zero-temperature nonequilibrium dynamics of the spherical Scherrington-Kirkpatrick model of a spin glass in an external field

The decay of the nonequilibrium spin-spin autocorrelation function is calculated analytically and numerically based on the Langevin dynamics for the spherical Scherrington-Kirkpatrick model (p = 2) of a spin glass in a constant magnetic field at zero temperature. The behavior of the spin system is analyzed for different amplitudes of the external constant magnetic field and different waiting times. In the mean-field approximation, the critical value of the external magnetic field is found. The occurrence of the spin-glass phase in weak magnetic fields is demonstrated. For stronger fields, the stationary behavior of the correlation function is revealed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 10–16, April, 2007.     

High-energy collisions of intrinsically deformed particles

The Chou-Yang model of the elastic profile function for high-energy collisions is modified to take into account the possibility that the projectile, the target, or both, are deformed from sphericity. Simple expressions for the elastic amplitudes and total cross sections are derived under the assumption that the collision times are much shorter than the rotation periods of the projectile and target (adiabatic approximation). A simplified, purely geometric interpretation of the results on total cross sections is given and justified in terms of the quantum-mechanical treatment.     

Time-optimal coherence-order-selective transfer of in-phase coherence in heteronuclear IS spin systems

Based on principles of geometric optimal control theory, coherence transfer building blocks can be derived which achieve optimal sensitivity. Here, experimental pulse sequences are presented that achieve the best possible coherence-order-selective in-phase transfer (S(-)-->I(-)) for a heteronuclear 2-spin system for any given mixing time in the absence of relaxation. For short mixing times, the optimal experiment improves the sensitivity of isotropic mixing by up to 12.5%.     

Optimal sum-rule inequalities for spin-12 compton scattering

A formalism appropriate for model-independent dispersion theoretical investigations of the (not necessarily forward) Compton scattering off $\text{spin}\text{-}\text{1}\text{2}$ hadronic targets, which fully exploits the analyticity properties of the amplitudes (to lowest order in electromagnetism) in ν² at fixed t ($\text{ν =}\text{1}\text{4}\text{(s ? u); s, t}$, u = Mandelstam variables), is developed. It relies on methods which are specific to boundary-value problems for analytic matrix-valued functions. An analytic factorization of the positive definite hermitian matrix associated with the bilinear expression of the unpolarized differential cross section (u.d.c.s.) in terms of the Bardeen-Tung (B.T.) invariant amplitudes is explicitly obtained. For t in a specified portion of the physical region, six new amplitudes describing the process are thereby constructed which have the same good analyticity structure in ν² as the (crossing symmetrized) B.T. amplitudes, while their connection with the usual helicity amplitudes is given by a matrix which is unitary on the unitarity cut. A bound on a certain integral over the u.d.c.s. above the first inelastic threshold, established in terms of the target's charge and anomalous magnetic moment, improves a previous weaker result, being now optimal under the information accepted as known.     

Simulation of a Radio-Frequency Photogun for the Generation of Ultrashort Beams

A radio-frequency photogun for the generation of ultrashort electron beams to be used in fast electron diffractoscopy, wakefield acceleration experiments, and the design of accelerating structures of the millimeter range is modeled. The beam parameters at the photogun output needed for each type of experiment are determined. The general outline of the photogun is given, its electrodynamic parameters are calculated, and the accelerating field distribution is obtained. The particle dynamics is analyzed in the context of the required output beam parameters. The optimal initial beam characteristics and field amplitudes are chosen. A conclusion is made regarding the obtained beam parameters.     

Algorithm for optimal filtering of random Markov signals with pulse-disturbance-amplitude estimation

Optimal filtering problem of random Markov signals with simultaneous estimation of pulse disturbance amplitudes is considered. Linear models of stochastic difference equations in discrete time are used to describe signals, observed processes, and pulse disturbances. Pulse disturbances occur at random times with random amplitudes. A real-time calculation procedure is obtained for the joint a posteriori probability density function of random signals and pulse disturbance amplitudes. A quasioptimal filtering algorithm is derived in the case of scalar signals and scalar observed processes by a partition method. Computer simulation results are presented.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 4, pp. 496–513, April, 1996.     

Construction of Covariant Bases for Two-Particle Reactions

A method for the construction of the Lorentz-covariant bases occurring in the decomposition of spinor amplitudes (M-functions) of four massive particle processes is given. Each particle of spin- is described by a spinor state of the type-(s, 0) and/or (0, s), but the essential parts of our method apply whatever the type of spinor state used, and the necessary relations between the hitherto familiar types of spinor states are given, by means of which the relationship between the resulting sets of invariant amplitudes can be made explicit. By way of illustration four worked examples are presented.     

Effect of noise and occupancy on optimal reverberation times for speech intelligibility in classrooms

The question of what is the optimal reverberation time for speech intelligibility in an occupied classroom has been studied recently in two different ways, with contradictory results. Experiments have been performed under various conditions of speech-signal to background-noise level difference and reverberation time, finding an optimal reverberation time of zero. Theoretical predictions of appropriate speech-intelligibility metrics, based on diffuse-field theory, found nonzero optimal reverberation times. These two contradictory results are explained by the different ways in which the two methods account for background noise, both of which are unrealistic. To obtain more realistic and accurate predictions, noise sources inside the classroom are considered. A more realistic treatment of noise is incorporated into diffuse-field theory by considering both speech and noise sources and the effects of reverberation on their steady-state levels. The model shows that the optimal reverberation time is zero when the speech source is closer to the listener than the noise source, and nonzero when the noise source is closer than the speech source. Diffuse-field theory is used to determine optimal reverberation times in unoccupied classrooms given optimal values for the occupied classroom. Resulting times can be as high as several seconds in large classrooms; in some cases, optimal values are unachievable, because the occupants contribute too much absorption.     

Elastic scattering of 1.17 and 1.33 MeV gamma rays by molybdenum,tantalum and lead

Elastic scattering cross-sections of lead, tantalum and molybdenum were determined with the help of a Ge (Li) detector for 1.17 and 1.33 MeV rays between 30° and 115°. Theoretical evaluations of the cross-sections are based on a coherent addition of the well-known nuclear Thomson scattering amplitudes, the Rayleigh amplitudes calculated by Kissel and Pratt and the Delbrück amplitudes given by Papatzacos and Mork. The fairly good agreement between experiment and theory reveals the importance of the real Delbrück amplitudes. However, the experimental results in the 30–60° range tend to lie slightly but systematically below the calculated cross-sections. Work supported in part by a grant from the National Bureau of Standards, Washington, DC under the SFCP programme.     

Invariant Amplitudes for Coherent Electromagnetic Pseudoscalar Production from a Spin-One Target, II: Crossing, Multipoles, and Observables

 The formal properties of the recently derived set of linearly independent invariant amplitudes for the electromagnetic production of a pseudoscalar particle from a spin-one particle have been further exploited. The crossing properties are discussed in detail. Since not all of the amplitudes have simple crossing behaviour, we introduce an alternative set of basic amplitudes which are either symmetric or antisymmetric under crossing. The multipole decomposition is given, and the representation of the multipoles as integrals over the invariant functions weighted with Legendre polynomials is derived. Furthermore, differential cross section and polarization observables are expressed in terms of the corresponding invariant functions. Received July 5, 1999; accepted for publication September 19, 1999     

Stimulated emission of relativistic particles by external sources in spacetime

Explicit solutions are derived for transition amplitudes associated with stimulated emission of relativistic particles by external sources inspacetime. More precisely, exact expressions are obtained for transition amplitudes for any process where there are initially, at a given time, an arbitrary number of particles localized in various regions of space, prior to the switching on of an intervening source, and then, finally, at a later time when the intervening source ceases to operate, a given number of particles are found to be localized in various regions of space. The analysis is given for massive particles ofarbitrary integer and half-integer spins. The solutions are obtained by carrying out a unitarity expansion inconfiguration space, where particles travel between emitters and detectors in the presence of an intervening source. Considered as an application is the process: particlearbitrary number of particles, where the latter particles emerge spatially with a cone.