Criticality of Parasitic Disease Transmission in a Diffusive Population

Through using the methods of finite-size effect and short time dynamic scaling, we study the critical behavior of parasitic disease spreading process in a diffusive population mediated by a static vector environment. Through comprehensive analysis of parasitic disease spreading we find that this model presents a dynamical phase transition from disease-free state to endemic state with a finite population density. We determine the critical population density, above which the system reaches an epidemic spreading stationary state. We also perform a scaling analysis to determine the order parameter and critical relaxation exponents. The results show that the model does not belong to the usual directed percolation universality class and is compatible with the class of directed percolation with diffusive and conserved fields.     

Multi-physics analysis of the RFQ for Injector Scheme II of C-ADS driver linac

A 162.5 MHz, 2.1 MeV radio frequency quadruples （RFQ） structure is being designed for the Injector Scheme Ⅱ of the China Accelerator Driven Sub-critical System （C-ADS） linac. The RFQ will operate in continuous wave （CW） mode as required. For the CW normal conducting machine, the heat management will be one of the most important issues, since the temperature fluctuation may cause cavity deformation and lead to the resonant frequency shift. Therefore a detailed multi-physics analysis is necessary to ensure that the cavity can stably work at the required power level. The multi-physics analysis process includes RF electromagnetic analysis, thermal analysis, mechanical analysis, and this process will be iterated for several cycles until a satisfactory solution can be found. As one of the widely accepted measures, the cooling water system is used for frequency fine tunning, so the tunning capability of the cooling water system is also studied under different conditions. The results indicate that with the cooling water system, both the temperature rise and the frequency shift can be controlled at an acceptable level.     

Impact of symmetrized and Burt—Foreman Hamiltonians on spurious solutions and energy levels of InAs/GaAs quantum dots

<正>We present a systematic investigation of calculating quantum dots(QDs) energy levels using the finite element method in the frame of the eight-band k·p method.Numerical results including piezoelectricity,electron and hole levels,as well as wave functions are achieved.In the calculation of energy levels,we do observe spurious solutions(SSs) no matter Burt-Foreman or symmetrized Hamiltonians are used.Different theories are used to analyse the SSs,we find that the ellipticity theory can give a better explanation for the origin of SSs and symmetrized Hamiltonian is easier to lead to SSs.The energy levels simulated with the two Hamiltonians are compared to each other after eliminating SSs,different Hamiltonians cause a larger difference on electron energy levels than that on hole energy levels and this difference decreases with the increase of QD size.     

Mechanical properties an undercut evaluated resonance test and of silicon nanobeams with by combining the dynamic finite element analysis

Mechanical properties of silicon nanobeams are of prime importance in nanoelectromechanical system applications. A numerical experimental method of determining resonant frequencies and Young＇s modulus of nanobeams by combining finite element analysis and frequency response tests based on an electrostatic excitation and visual detection by using a laser Doppler vibrometer is presented in this paper. Silicon nanobeam test structures are fabricated from silicon-oninsulator wafers by using a standard lithography and anisotropic wet etching release process, which inevitably generates the undercut of the nanobeam clamping. In conjunction with three-dimensional finite element numerical simulations incorporating the geometric undercut, dynamic resonance tests reveal that the undercut significantly reduces resonant frequencies of nanobeams due to the fact that it effectively increases the nanobeam length by a correct value △L, which is a key parameter that is correlated with deviations in the resonant frequencies predicted from the ideal Euler-Bernoulli beam theory and experimentally measured data. By using a least-square fit expression including △L, we finally extract Young＇s modulus from the measured resonance frequency versus effective length dependency and find that Young＇s modulus of a silicon nanobeam with 200-nm thickness is close to that of bulk silicon. This result supports that the finite size effect due to the surface effect does not play a role in the mechanical elastic behaviour of silicon nanobeams with thickness larger than 200 nm.     

Strategies for h-Adaptive Refinement for a Finite Element Treatment of Harmonic Oscillator Schrodinger Eigenproblem

A Schrodinger eigenvalue problem is solved for the 219 quantum simple harmonic oscillator using a finite element discretization of real space within which elements are adaptively spatially refined. We compare two competing methods of adaptively discretizing the real-space grid on which computations are performed without modifying the standard polynomial basis-set traditionally used in finite element interpolations; namely, （i） an application of the Kelly error estimator, and （ii） a refinement based on the local potential level. When the performance of these methods are compared to standard uniform global refinement, we find that they significantly improve the total time spent in the eigensolver.     

Finite element analysis of Rayleigh wave interaction with finite-size,surface-breaking cracks

The interaction of surface acoustic waves with finite-size, surface-breaking, semi-circular cracks is studied numerically, and experimentally. We focus on the behavior of the reflection coefficient of the Rayleigh wave from such cracks in the far field of the crack, when the depth of the crack is comparable to the wavelength of the interrogating surface wave. The cases in which the depth of the crack is much smaller or much larger compared to the wavelength have been extensively investigated by many authors and are not considered here except for validating the numerical and experimental results in these regimes. The theoretical, finite element, and experimental results presented are in very good agreement over the range were the crack depth is much smaller or much larger compared to the wavelength of the incident Rayleigh wave. In the transition regime, between these two limiting cases, only the finite element and experimental data show good agreement since the theoretical predictions are no longer applicable. In the high crack depth to wavelength ratio (a/lambda(R)) regime, the finite element and experimental results close to the crack approach the limiting value of the reflection coefficient from a 90 degrees corner.     

Anti-plane problem analysis for icosahedral quasicrystals under shear loadings

The present paper is concerned with the longitudinal shear elasticity of three-dimensional icosahedral quasicrystals. By virtue of the Dugdale hypothesis along with the method of complex potential theory, it involves two defect problems of the icosahedral quasicrystals. The first one is the calculation of stress intensity factors and the size of the cohesive force zone in a half-infinite crack. Meanwhile, the crack tip tearing displacements can be exactly derived. The other is the demonstration of the generalized stress intensity factors induced by a sharp V-notch as an extension of a crack. The generalized E-integral around the notch tip gives the energy release rate when the V-notch degenerates into a crack. Apart from their own usefulness in carrying out some simplified crack analyses, the results obtained in this work can particularly serve as a basis for fracture mechanics of anti-plane defect problems of icosahedral quasicrystals.     

Elastic behaviour of a wedge sharp crack emanating from a disclination dipole near a semi-elliptical blunt crack

The interaction between a wedge disclination dipole and a crack emanating from a semi-elliptic hole is investigated. Utilising the complex variable method, the closed form solutions are derived for complex potentials and stress fields. The stress intensity factor at the tip of the crack and the image force acting on the disclination dipole center are also calculated. The influence of the morphology of the blunt crack and the position of the disclination dipole on the shielding effect to the crack and the image force is examined in detail. The results indicate that the shielding or anti-shielding effect to the stress intensity factor increases when the wedge disclination dipole approaches the tip of the crack. The effects of the morphology of the blunt crack on the stress intensity factor of the crack and the image force are very significant.     

Shielding Effect and Emission Criterion of a Screw Dislocation Near an Interfacial

Shielding effect and emission criterion of a screw dislocation near an interracial crisscross crack are dealt with in this paper. Utilizing the conformal mapping technique, the closed-form solutions are derived for complex potentials and stress fields due to a screw dislocation located near the interracial crisscross crack. The stress intensity factor on the crack tips and the critical stress intensity factor for dislocation emission are also calculated. The influence of the orientation of the dislocation and the morphology of the crisscross crack as well as the material elastic dissimilarity on the shielding effect and the emission criterion is discussed in detail. The results show that positive screw dislocations can reduce the stress intensity factor of the interracial crisscross crack tip （shielding effect）. The shielding effect increases with the increase of the shear modulus of the lower half-plane, but it decreases with the increase of the dislocation azimuth angle and the distance between the dislocation and the crack tip. The critical loads at infinity for dislocation emission increases with the increase of emission angle and the vertical length of the crisscross crack, and the most probable angle for screw dislocation emission is zero. The present solutions contain previous results as special cases.     

Critical Behaviors in a Stochastic Local Limited One-Dimensional Rice-Pile Model

A stochastic local limited one-dimensional rice-pile model is numerically investigated. The distributions for avalanche sizes have a clear power-law behavior and it displays a simple finite size scaling. We obtain the avalanche exponents Ts= 1.54±0.10,βs = 2.17±0.10 and TT = 1.80±0.10, βT =1.46 ± 0.10. This self-organized critical model belongs to the same universality class with the Oslo rice-pile model studied by K. Christensen et al. [Phys. Rev. Lett. 77 （1996） 107], a rice-pile model studied by L.A.N. Amaral et al. [Phys. Rev. E 54 （1996） 4512], and a simple deterministic self-organized critical model studied by M.S. Vieira [Phys. Rev. E 61 （2000） 6056].     

Dynamic investigation of the finite dissolution of silicon particles in aluminum melt with a lower dissolution limit

The finite dissolution model of silicon particles in the aluminum melt is built and calculated by the finite difference method, and the lower dissolution limit of silicon particles in the aluminum melt is proposed and verified by experiments, which could be the origin of microinhomogeneity in aluminum-silicon melts. When the effects of curvature and interface reaction on dissolution are not considered; the dissolution rate first decreases and later increases with time. When the effects of curvature and interface reaction on dissolution are considered, the dissolution rate first decreases and later increases when the interface reaction coefficient （k） is larger than 10 1, and the dissolution rate first decreases and later tends to be constant when k is smaller than 10-3. The dissolution is controlled by both diffusion and interface reaction when k is larger than 10-3, while the dissolution is controlled only by the interface reaction when k is smaller than 10-4.     

Design on a highly birefringent and nonlinear photonic crystal fiber in the C waveband

In this paper, a novel photonic crystal fiber （PCF） with high birefringence and nonlinearity is designed. The charac- teristics of birefringence, dispersion and nonlinearity are studied by using the full-vector finite element method （FVFEM）. The numerical results show that the phase birefringence and nonlinear coefficient of PCF can be up to 4.51× 10-3 and 32.8972 w-l.km-1 at 1.55 μm, respectively. The proposed PCF could be found to have important applications in the polarization-dependent nonlinear optics such as the pulse compress and reshaping in the C waveband.     

A Two-Dimensional Brans-Dicke Star Model with Exotic Matter and Dark Energy

A two-dimensional Brans-Dicke star model with exotic matter and dark energy is studied in this paper, the field equation and balance equation are derived at finite temperature, the analytic solutions of these equations can be used to calculate the mass of star. In addition, we find that star＇s mass has a minimum when matter state parameter γ→0.     

Finite Size Effect in Path Integral Monte Carlo Simulations of ^4He Systems

Path integral Monte Carlo （PIMC） simulations are a powerful computational method to study interacting quantum systems at finite temperatures. In this work, PIMC has been applied to study the finite size effect of the simulated systems of ^4He. We determine the energy as a function of temperature at saturated-vapor-pressure （SVP） conditions in the temperature range of T ∈ [1.0 K,4.0 K], and the equation of state （EOS） in the grmmd state For systems consisted of 32, 64 and 128 ^4He atoms, respectively, We find that the energy at SVP is influenced significantly by the size of the simulated system in the temperature range of T ∈ [2.1 K, 3.0 K] and the larger the system is, the better results are obtained in comparison with the experimental values; while the EOS appeared to be unrelated to it.     

Casimir Force at a Finite Cut-Off

We calculate the Casimir force at a finite cut-off A by summing the forces induced by the all fluctuation modes. We show that the Casimir force is independent of the cut-off function in the limit L∧ → ∞. There is a correction in the order of （L∧）^-2, when L∧ is finite and large. This correction becomes remarkable when L is comparable with the microscopic length scale ∧^-1. It has been demonstrated that the Casimir force at a finite cut-off should be defined by summing forces of all fluctuation modes, instead of the derivative of Casimir energy with respect to L where an additional derivative of the cut-off function has been introduced.     

Dynamical Symmetry Breaking of Maximally Generalized Yang-Mills Model and Its Restoration at Finite Temperatures

In terms of the Nambu-Jona-Lasinio mechanism, dynamical breaking of gauge symmetry for the maximally generalized Vang-Mills model is investigated. The gauge symmetry behavior at finite temperature is also investigated and it is shown that the gauge symmetry broken dynamically at zero temperature can be restored at finite temperatures.     

Object Picture of Electromagnetic Quasinormal Ringing for a Stringy Black Hole

We investigate the evolution of an electromagnetic field in the spacetime of a stringy black hole. The object picture of the quasinormal ringing has been obtained by the finite difference method. Compared with a Schwarzschild black hole, the results show that the electromagnetic field damps more slowly for a stringy black hole.     

From Rosochatius System to KdV Equation

The Rosochatius system on the sphere, an integrable mechanical system discovered in the nineteenth century, is investigated in a suitably chosen framework with the sphere as an invariant set, to avoid the complicated constraint presentations. Higher order Rosochatius flows are defined and straightened out in the Jacobi variety of the associated hyperelliptic curve. A relation is found between these flows and the KdV equation, whose finite genus solution is calculated in the context of the Rosoehatius hierarchy.     

A new magneto-cardiogram study using a vector model with a virtual heart and the boundary element method

A cardiac vector model is presented and verified, and then the forward problem for cardiac magnetic fields and electric potential are discussed based on this model and the realistic human torso volume conductor model, including lungs. A torso-cardiac vector model is used for a 12-lead electrocardiographic (ECG) and magneto-cardiogram (MCG) simulation study by using the boundary element method (BEM). Also, we obtain the MCG wave picture using a compound four-channel HTc ·SQUID system in a magnetically shielded room. By comparing the simulated results and experimental results, we verify the cardiac vector model and then do a preliminary study of the forward problem of MCG and ECG. Therefore, the results show that the vector model is reasonable in cardiac electrophysiology.     

△-Resonances in Ground State Properties of ^40 20Ca Spherical Cold Finite Nucleus at Equilibrium and under Compression

The ground state properties of the spherical nucleus ^40Ca have been investigated by using constrained spherical Hartree Fock （CSHF） approximation at equilibrium and under high radial compression in a six major shells. The effective baryon-baryon interaction that includes the △（1236） resonance freedom degrees to calculate nuclear properties is used. The nucleon-nucleon （N-N） interaction is based on Reid soft core （RSC） potential. The results of calculations show that much of increase in the nuclear energy generated under compression is used to create the massive △ particles. The number of △ ＇s can be increased to about 2.1% of constituents of nucleus when nuclear density reaches about 1.34 times of normal density. The single particle energy levels are calculated and their behavior under compression is also examined. △ good agreement has been found between current calculations and phenomenological shell model for low lying single-particle spectra. The gap between shells is very clear and L-S coupling become stronger as increasing the static load on the nucleus. The results show a considerable reduction in compressibility when freedom degrees of △＇s are taken into account. It has been found that the total nuclear radial density becomes denser in the interior and less dense in the exterior region of nucleus. The surface of nucleus becomes more and more responsive to compression than outer region.