Fundamental natural frequencies of thin cylindrical shells: a comparative study

A comparative study of three approximate “explicit” formulae for estimating the fundamental natural frequency of a thin cylindrical shell, and its associated fundamental modenumber is presented. The objective is to identify the limits of the validity of each formula. The three approximate formulae considered in this study are based on: (a) the Weingarten-Soedel approximation of the Donnell-Mushtari-Vlasov equations, (b) the Calladine-Koga improved classical-beam-on-Winkler-foundation model, and (c) the Timoshenko-beam-on-Pasternak-foundation analogy of the shell. Results are compared against the analytical solutions of the equations of motion of Flügge, and results obtained by a commercial finite-element package. Tabulated results are given for length-to-radius ratios of 1, 2, 5, 10, and 20, and radius-to-thickness ratios of 20, 50, 100, 200, and 500.     

Sound radiation from inflow turbulence in axial flow fans

The sound radiated when inflow turbulence is present in axial flow fans has been investigated. Theoretically, two noise radiating mechanisms can be identified: (i) interaction of turbulence with the rotor potential field results in a quadrupole-type volume source distribution, producing “flow-interaction” noise; (ii) impingement of turbulence on the blades results in a dipole-type (fluctuating force) surface source distribution, producing “fluctuating lift” noise. A theoretical expression for the flow interaction sound power in the upstream radiation field has been developed, in terms of parameters that can be experimentally determined by near field flow measurements involving spatial cross-correlations of the fluctuating axial velocity, with respect to both radial and circumferential position. Both these measurements and radiated sound pressure measurements have been made for eight- and ten-bladed rotors of relatively low tip Mach number (< 0·3). The sound pressure measurements revealed the occurrence of band-spreading of discrete tones at the blade passing frequency and its harmonics, as would be theoretically predicted for quadrupole-type sources here. The theoretical predictions and the measurements, respectively, of the sound power radiated upstream were compared. The results indicated that, for the fans tested, the “fluctuating lift” noise strongly predominated over the “flow-interaction” noise. The observed sound power levels were consistent with levels estimated from the theory.     

Semiclassical dynamics of quasi-one-dimensional, attractive Bose-Einstein condensates

The strongly interacting regime for attractive Bose-Einstein condensates (BECs) tightly confined in an extended cylindrical trap is studied. For appropriately prepared, non-collapsing BECs, the ensuing dynamics are found to be governed by the one-dimensional focusing Nonlinear Schrödinger equation (NLS) in the semiclassical (small dispersion) regime. In spite of the modulational instability of this regime, some mathematically rigorous results on the strong asymptotics of the semiclassical limiting solutions were obtained recently. Using these results, “implosion-like” and “explosion-like” events are predicted whereby an initial hump focuses into a sharp spike which then expands into rapid oscillations. Seemingly related behavior has been observed in three-dimensional experiments and models, where a BEC with a sufficient number of atoms undergoes collapse. The dynamical regimes studied here, however, are not predicted to undergo collapse. Instead, distinct, ordered structures, appearing after the “implosion”, yield interesting new observables that may be experimentally accessible.     

Physics of strongly coupled quark-gluon plasma

This review covers our current understanding of strongly coupled Quark-Gluon Plasma (sQGP), especially theoretical progress in: (i) explaining the RHIC data by hydrodynamics; (ii) describing lattice data using electric-magnetic duality; (iii) understanding of gauge-string duality known as AdS/CFT and its application for “conformal” plasma. In view of the interdisciplinary nature of the subject, we include a brief introduction into several topics “for pedestrians”. Some fundamental questions addressed are: Why is sQGP such a good liquid? What is the nature of (de)confinement and what do we know about “magnetic” objects creating it? Do they play any important role in sQGP physics? Can we understand the AdS/CFT predictions, from the gauge theory side? Can they be tested experimentally? Can AdS/CFT duality help us understand rapid equilibration/entropy production? Can we work out a complete dynamical “gravity dual” to heavy ion collisions?     

A novel hybrid ES-FE-SEA for mid-frequency prediction of Transmission losses in complex acoustic systems

The widely-used numerical modeling approaches such as the finite element method (FEM) and statistical energy analysis (SEA) often have limited applicability to the transmission loss prediction in mid-frequency range. In this paper, a novel hybrid edge-based smoothed FEM coupled with statistical energy analysis (ES-FE-SEA) method is proposed to further improve the accuracy of “mid-frequency” transmission loss predictions. The application of ES-FEM will “soften” the well-known ‘‘overly-stiff’’ behavior in the standard FEM solution and reduce the inherent numerical dispersion error. While the SEA approach deals with the physical uncertainty in the relatively higher frequency range. The plate of interest is appropriately described by an ES-FEM model, due to its relative robustness to perturbations. Its adjacent reverberation cavities are modeled by employing the SEA approach, because of their high model density. The coupling and interaction between SEA subsystems and the FE subsystem is governed by the “reciprocity relationship” theorem. A standard numerical example for benchmarking is examined and excellent agreement was achieved between the prediction and reference results. The proposed ES-FE-SEA is also verified by various numerical examples. The method is finally applied to the modeling a complicated engineering problem–acoustic fields on both sides of the front windshield in a passenger car.     

Formation mechanism of “memory” phenomenon of microchannel plate image intensifier

A discrete resistance capacitance dynodes chain of channel multiplication model worked in a continuous variable dynode number described here is an attempt to explain the formation mechanism of “memory” phenomenon of microchannel plate image intensifier, wherein it was concluded conclusion that “memory” phenomenon of image intensifiers were the results of a silicon-rich layer, which existed between emission layer and conduction layer of channel inner wall of microchannel plate, having much higher resistance as compared with the conduction layer, and there are two distinct appearance ways of “negative memory” and “positive memory” only due to a difference in illumination and duration of the image intensifier suffered, and a strictly controlled MCP manufacture process would make considerable reduction of “memory” phenomenon occurrence ratio.     

Modeling cup-burner minimum extinguishing concentration of halogenated agents

The minimum extinguishing concentration (MEC) of a fire suppression agent is usually determined by the standard cup-burner tests. Recently, a simple model based on extinction of Perfectly Stirred Reactors (PSR) was developed and validated in the prediction of the MECs for inert fire suppressants. The results show good agreement between the model predictions and the experimental data. Furthermore, the results confirmed that the MECs of inert agents are directly correlated to agent integrated heat capacities. In this paper, the model is extended to halogenated agents by adding detailed chemical kinetics of the halogenated agents to a detailed chemical mechanism of n-heptane. The consideration of reactive halogenated species as fire suppression agents increases the complexity in computing the stoichiometry, yet the use of the PSR approach simplifies interpretations relative to 1-d and 2-d simulations. Using this approach, the MEC of halogenated agents are computed and compared against experimental data. Two methods of computation were employed. In the first, “inert PSR” case, only the heptane reaction chemistry was included; so the agent acts solely as an inert and the solution provides a reference point for expected behavior if the agent acted as an inert. In the second, or “reactive PSR” case, agent-related chemistry was included. Good agreement is achieved for Halon 1301 (CF₃Br) and R-32 (CH₂F₂). The computed “inert PSR” values agreed very well with the experimental MEC data for most fluorinated agents, suggesting that chemical inhibition by these fluorinated agents is counter-balanced by the exothermic HF formation and some competing chemical reactions; thus the “net” inhibition is small. In contrast, the “reactive PSR” results show good agreement with brominated agents and are consistent with the known strong catalytic effect of such compounds. The causes for differences between experiment and predicted values are explored and discussed while strengths and limitations are considered.     

Semiconductor nanocylindrical heterolayer in a radial electrostatic field: The electronic spectrum and optical properties

In the effective-mass approximation the single-electron states in a semiconductor cylindrical nanolayer under the presence of lateral-radial electrical field in the regime of strong quantization are considered. The explicit form of the energy spectrum and envelope wave functions of single-electron states is obtained in the cases of “large” and “moderate” radii of the system. The corresponding absorption characteristics of interband optical transitions in the layer under the presence of radial field are calculated.     

Locking bandwidth and birefringence effects for polarized optical injection in vertical-cavity surface-emitting lasers

The aim of this paper is to investigate the effects of external optical injection taking account of polarization and electron spin properties in vertical-cavity surface-emitting lasers (VCSELs). Using external polarized injection we seek the locked phases and amplitudes of specific polarized fields in terms of injection level and frequency detuning, taking account of two kinds of distinguishable carrier density (spin-up and spin-down). For the conventional form of optical injection without taking account of spin-polarized fields there are three fundamental equations describing the carrier density, field amplitude and phase. However, by using the spin flip model (SFM), the combined effect of polarized fields along two perpendicular crystal axes and electron spin properties results in six equations. We analyse the conditions for stable locking and also the influence of birefringence effects on the stability map of detuning versus optical injection for both cases of injection polarized parallel and perpendicular to the lasing mode of the solitary VCSEL. For given values of pumping and spin relaxation rate there is a minimum birefringence rate for orthogonal injection. Above this value three regions of elliptical polarization are found in the stability map, namely “quasi-stability” (QS), “coupled limit cycle” (CLC) and “coupled chaos” (CC). The three regions of linear polarization, namely chaos, limit cycle and stability, are reduced in area compared to the case of parallel injection. For orthogonal injection it is found that increased birefringence or reduced spin relaxation rate causes the stable locking region to begin at higher injected power and frequency detuning.     

Three-dimensional vibrations of cylindrical elastic solids with V-notches and sharp radial cracks

This paper provides free vibration data for cylindrical elastic solids, specifically thick circular plates and cylinders with V-notches and sharp radial cracks, for which no extensive previously published database is known to exist. Bending moment and shear force singularities are known to exist at the sharp reentrant corner of a thick V-notched plate under transverse vibratory motion, and three-dimensional (3-D) normal and transverse shear stresses are known to exist at the sharp reentrant terminus edge of a V-notched cylindrical elastic solid under 3-D free vibration. A theoretical analysis is done in this work utilizing a variational Ritz procedure including these essential singularity effects. The procedure incorporates a complete set of admissible algebraic-trigonometric polynomials in conjunction with an admissible set of “edge functions” that explicitly model the 3-D stress singularities which exist along a reentrant terminus edge (i.e., α>180°) of the V-notch. The first set of polynomials guarantees convergence to exact frequencies, as sufficient terms are retained. The second set of edge functions—in addition to representing the corner stress singularities—substantially accelerates the convergence of frequency solutions. This is demonstrated through extensive convergence studies that have been carried out by the investigators. Numerical analysis has been carried out and the results have been given for cylindrical elastic solids with various V-notch angles and depths. The relative depth of the V-notch is defined as (1−c/a), and the notch angle is defined as (360°−α). For a very small notch angle (1° or less), the notch may be regarded as a “sharp radial crack.” Accurate (four significant figure) frequencies are presented for a wide spectrum of notch angles (360°−α), depths (1−c/a), and thickness ratios (a/h for plates and h/a for cylinders). An extended database of frequencies for completely free thick sectorial, semi-circular, and segmented plates and cylinders are also reported herein as interesting special cases. A generalization of the elasticity-based Ritz analysis and findings applicable here is an arbitrarily shaped V-notched cylindrical solid, being a surface traced out by a family of generatrix, which pass through the circumference of an arbitrarily shaped V-notched directrix curve, r(θ), several of which are described for future investigations and close extensions of this work.     

Self-organization of five species in a cyclic competition game

Cyclic competition game models, particularly the “rock–paper–scissors” model, play important roles in exploring the problem of multi-species coexistence in spatially ecological systems. We propose an extended “rock–paper–scissors” game to model cyclic interactions among five species, and find that two of the five can coexistent when biodiversity disappears, which is different from the “rock–paper–scissors” game. As the number of fingers is five, we named the new model the “fingers” game, where the thumb, forefinger, middle finger, ring finger, and little finger cyclically dominate their subsequent species and are dominated by their former species. We investigate the “fingers” model in two ways: direct simulations and nonlinear partial differential equations. An important finding is that the number of species in a cyclic competition game has an influence on the emergence of biodiversity. To be specific, the “rock–paper–scissors” model is in favor of maintaining biodiversity in comparison with the “fingers” model when the variables (population size, reproduction rate, selection rate, and migration rate) are the same. It is also shown that the mobility and reproduction rate can promote or jeopardize biodiversity.     

Regeneration of surface roughness by the Langevin equation using stochastic analysis on AFM image of a carbon fiber

A new method was developed using AFM images of a fiber surface to regenerate the surface roughness in 3D geometry, such as the cylindrical shape of a “model” fiber. The Langevin equation was used to derive the fluctuations of a carbon fiber surface image. The equation contains two quantities, D⁽¹⁾ (h) and D⁽²⁾ (h) which in physics represent drift and diffusion coefficients. Knowing this coefficient and adding a proper noise function, a similar surface of larger dimension with the same statistical properties of the initial data was created. The generated surface was mapped into cylindrical coordinates, then a mesh generated. The resulting reconstructed surface, input over the geometry of a cylindrical shape, can be implemented for finite element analysis of a single fiber surrounded by matrix and generalized to a many fiber model.     

Theoretical studies of argon adsorption in MCM-41 mesoporous systems

Adsorption isotherms are predicted for spherical adsorbates in cylindrical channels of MCM-41 mesoporous materials over a wide range of temperatures by using the “fragment method”. This prediction shows that an equilibrium capillary condensation is impossible for pores with diameters smaller than 2.5 nm. The adsorbate distribution in relatively large pore channels was described by the quasi-chemical approximation (QCA) that takes into account direct pair correlations between interacting molecules. In order to improve the lattice-gas model in the vicinity of the critical point, a calibration function that takes into account information from the fragment method, was introduced into the QCA equations. The influence of the size factor of pores on argon adsorption isotherms was demonstrated.     

Fractional motions

Brownian motion is the archetypal model for random transport processes in science and engineering. Brownian motion displays neither wild fluctuations (the “Noah effect”), nor long-range correlations (the “Joseph effect”). The quintessential model for processes displaying the Noah effect is Lévy motion, the quintessential model for processes displaying the Joseph effect is fractional Brownian motion, and the prototypical model for processes displaying both the Noah and Joseph effects is fractional Lévy motion. In this paper we review these four random-motion models–henceforth termed “fractional motions” –via a unified physical setting that is based on Langevin’s equation, the Einstein–Smoluchowski paradigm, and stochastic scaling limits. The unified setting explains the universal macroscopic emergence of fractional motions, and predicts–according to microscopic-level details–which of the four fractional motions will emerge on the macroscopic level. The statistical properties of fractional motions are classified and parametrized by two exponents—a “Noah exponent” governing their fluctuations, and a “Joseph exponent” governing their dispersions and correlations. This self-contained review provides a concise and cohesive introduction to fractional motions.     

Chemical modification of silica-gel with diethylenetriamine via an end-group protection approach for adsorption to Hg(II)

Four kinds of silica-gel supported diethylenetriamine adsorbents with different structures, were prepared by so-called “heterogeneous-direct-amination” (hetero-DA), “homogeneous-direct-amination” (homo-DA), “heterogeneous end-group protection” (hetero-EGP), and “homogeneous end-group protection” (homo-EGP) methods, respectively. The obtained products were named SG-HE-dD, SG-HO-dD, SG-HE-pD and SG-HO-pD, respectively (where SG means silica-gel; HE means heterogeneous, HO means homogeneous, d means direct, p means protected and D means diethylenetriamine). Their structures were characterized by FT-IR, elemental analysis, porous structure analysis and thermogravimetric analysis. The adsorption capabilities of such adsorbents towards Hg(II) were studied and evaluated by static method. SG-HE-pD and SG-HO-pD showed higher performance towards Hg(II) adsorption than corresponding counterparts SG-HE-dD and SG-HO-dD, even though the former two possessed lower contents of diethylenetriamine (DETA). The kinetics data indicated that the adsorption process was governed by the film diffusion and followed pseudo-first-order rate model for SG-HE-dD, SG-HO-dD and SG-HE-pD and pseudo-second-order model for SG-HO-pD. The Langmuir model was applied to fit the experimental equilibrium data for all adsorbents. The end-group protection method exhibited its advantage in preparation of effective adsorbent for metal ions uptake compared to the direct-amination method.     

Dynamic characteristics of composite laminates

An exact solution for the vibration of elastic composite laminates in cylindrical bending is presented. Dispersion curves for multi-layer symmetrical and unsymmetrical laminates with materials possessing high and low degrees of anisotropy at various fiber orientations are compared with those obtained from an approximate shear deformation theory. Mode shapes are also drawn for different wavelengths and their variation with fiber orientation is studied. Equations are developed for the wave propagation in an infinite medium consisting of a repeated pair of anisotropic layers by extending the “continuum” theory of Sun, Achenbach and Herrmann. Dispersion characteristics for 0–90° fiber orientations obtained by the “continuum” approach are also compared with those obtained by the exact method. The range of validity of each approximate theory is then assessed.     

Research on adaptive temperature control in sound field induced by self-focused concave spherical transducer

Temperature control of hyperthermia treatments is generally implemented with multipoint feedback system comprised of phased-array transducer, which is complicated and high cost. Our simulations to the acoustic field induced by a self-focused concave spherical transducer (0.5 MHz, 9 cm aperture width, 8.0 cm focal length) show that the distribution of temperature can keep the same “cigar shape” in the focal region during ultrasound insonation. Based on the characteristic of the temperature change, a two-dimensional model of a “cigar shape” tumor is designed and tested through numerical simulation. One single-point on the border of the “cigar shape” tumor is selected as the control target and is controlled at the temperature of 43 °C by using a self-tuning regulator (STR). Considering the nonlinear effects of biological medium, an accurate state-space model obtained via the finite Fourier integral transformation to the bioheat equation is presented and used for calculating temperature. Computer simulations were performed with the perfusion rates of 2.0 kg/(m³ s) and 4.5 kg/(m³ s) to the different targets, it was found that the temperatures on the border of the “cigar shape” tumor can achieve the desired temperature of 43 °C by control of one single-point. A larger perfusion rate requires a higher power output to obtain the same temperature elevation under the same insonation time and needs a higher cost for compensating the energy loss carried away by blood flow after steady state. The power output increases with the controlled region while achieving the same temperature at the same time. Especially, there is no overshoot during temperature elevation and no oscillation after steady state. The simulation results demonstrate that the proposed approach may offers a way for obtaining a single-point, low-cost hyperthermia system.     

Families of spatial solitons in a two-channel waveguide with the cubic-quintic nonlinearity

We present eight types of spatial optical solitons which are possible in a model of a planar waveguide that includes a dual-channel trapping structure and competing (cubic-quintic) nonlinearity. The families of trapped beams include “broad” and “narrow” symmetric and antisymmetric solitons, composite states, built as combinations of broad and narrow beams with identical or opposite signs (“unipolar” and “bipolar” states, respectively), and “single-sided” broad and narrow beams trapped, essentially, in a single channel. The stability of the families is investigated via the computation of eigenvalues of small perturbations, and is verified in direct simulations. Three species-narrow symmetric, broad antisymmetric, and unipolar composite states-are unstable to perturbations with real eigenvalues, while the other five families are stable. The unstable states do not decay, but, instead, spontaneously transform themselves into persistent breathers, which, in some cases, demonstrate dynamical symmetry breaking and chaotic internal oscillations. A noteworthy feature is a stability exchange between the broad and narrow antisymmetric states: in the limit when the two channels merge into one, the former species becomes stable, while the latter one loses its stability. Different branches of the stationary states are linked by four bifurcations, which take different forms in the model with the strong and weak coupling between the channels.     

五通道Z箍缩等离子体K壳层线谱成像

采用5个针孔配接5块对数螺线晶体单色器方案,研制了一台五通道靶室内置式X射线单色成像器,并利用该成像器在阳加速器上成功获取了铝丝阵负载Z箍缩内爆等离子体的K壳层自辐射五通道单色线谱图像。该成像器结构紧凑,安装调节简便精准,能谱分辨力高（小于1.3 eV）,能够清楚分辨Al的类氦主共振线（1 598.4 eV）和互组合线（1 588.3 eV）,以及类氢主共振线（1729 eV）及其伴线（1 727.7 eV）光谱图像。由于阳加速器驱动能力有限,这些图像均由若干的离散热斑组成,并且大都集中在柱状等离子体轴线上,说明这些热斑附近的电子温度和密度较周围要高;类氦主共振线较类氢主共振线图像强度高、热斑区域大,反映了Z箍缩等离子体温度不够高,原子被激发到类氢离子的数量远少于类氦离子。