Critical Behavior of Spatial Evolutionary Game with Altruistic to Spiteful Preferences on Two-Dimensional Lattices

Self-questioning mechanism which is similar to single spin-flip of Ising model in statistical physics is introduced into spatial evolutionary game model. We propose a game model with altruistic to spiteful preferences via weighted sums of own and opponent's payoffs. This game model can be transformed into Ising model with an external field. Both interaction between spins and the external field are determined by the elements of payoff matrix and the preference parameter. In the case of perfect rationality at zero social temperature, this game model has three different phases which are entirely cooperative phase, entirely non-cooperative phase and mixed phase. In the investigations of the game model with Monte Carlo simulation, two paths of payoff and preference parameters are taken. In one path, the system undergoes a discontinuous transition from cooperative phase to non-cooperative phase with the change of preference parameter. In another path, two continuous transitions appear one after another when system changes from cooperative phase to non-cooperative phase with the prefenrence parameter. The critical exponents ν, β, and γ of two continuous phase transitions are estimated by the finite-size scaling analysis. Both continuous phase transitions have the same critical exponents and they belong to the same universality class as the two-dimensional Ising model.     

Ab initio investigation of the CdTe (001) surface

Based on first-principles density functional pseudopotential calculations, the CdTe (001) surface has been studied. Atomic configurations of different reconstructions are obtained with good accuracy. This reveals the efficiency of the force calculation for the surface relaxations. The surface energies were calculated on relaxed surface slabs as a function of the chemical potentials. The main result is that the energy of the Te-terminated dimerized surface with a (2 × 1) reconstruction is larger than the Cd-terminated c(2×2) reconstructed surface. This is in agreement with what was suspected by the equilibrium model introduced by F. Tinjod et al., which explains the formation of the quantum dots in CdTe/ZnTe superstructures.     

Pohlmeyer reduction of superstring sigma model

Motivated by a desire to find a useful 2d Lorentz-invariant reformulation of the AdS₅×S⁵ superstring world-sheet theory in terms of physical degrees of freedom we construct the “Pohlmeyer-reduced” version of the corresponding sigma model. The Pohlmeyer reduction procedure involves several steps. Starting with a coset space string sigma model in the conformal gauge and writing the classical equations in terms of currents one can fix the residual conformal diffeomorphism symmetry and kappa-symmetry and introduce a new set of variables (related locally to currents but non-locally to the original string coordinate fields) so that the Virasoro constraints are automatically satisfied. The resulting equations can be obtained from a Lagrangian of a non-Abelian Toda type: a gauged WZW model with an integrable potential coupled also to a set of 2d fermionic fields. A gauge-fixed form of the Pohlmeyer-reduced theory can be found by integrating out the 2d gauge field of the gauged WZW model. The small-fluctuation spectrum near the trivial vacuum contains 8 bosonic and 8 fermionic degrees of freedom with equal mass. We conjecture that the reduced model has world-sheet supersymmetry and is ultraviolet-finite. We show that in the special case of the AdS₂×S² superstring model the reduced theory is indeed supersymmetric: it is equivalent to the N=2 supersymmetric extension of the sine-Gordon model.     

自我质疑机制下公共物品博弈模型的相变特性

公共物品博弈是研究群体相互作用的经典模型,广泛用于解释自私个体间合作的涌现和保持.本文从理论分析和蒙特卡罗模拟两个方面研究了二维正方格子上一个有偿惩罚机制下随自我质疑更新规则演化的公共物品博弈模型的相变特性.理论分析方面,将公共物品博弈模型转化为一个外场不为零的铁磁Ising模型.通过有效能量发现:不存在惩罚时,个体间的耦合强度为零,体系只有外场作用;存在惩罚时,个体间包含最近邻、次近邻和第三近邻相互作用且外场不为零.蒙特卡罗模拟方面,首先验证了理论分析的正确性,然后对公共物品博弈模型相关的一级相变和二级相变进行了有限尺度标度分析.研究发现:1)蒙特卡罗模拟所得结果与类Ising模型分析结果完全吻合;2)相比二维Ising模型,公共物品博弈的二级相变临界指数发生了变化;3)公共物品博弈的一级相变与二维Ising模型相同.     

Novel optic-fiber switches based on the wobble-type MEMS electromagnetic microactuator

Some novel optic-fiber switches based on an MEMS electromagnetic microactuator are developed in this paper and their design, fabrication and performance are described. A new kind of wobble-type MEMS electromagnetic microactuator is successfully developed, which can drive mirrors to enter or leave the optical path of a switch. It is layered, composed of two stators and one wobble disc, which improve the output torque of the actuator. Finally, 1×2, 2×2, 1×4 and 1×8 single mode optic-fiber switches, which have been fabricated, are measured. The operating voltage is less than 8 V, switching time is less than 5 ms, insertion loss is less than 0.8 dB, crosstalk is 60 dB, and extinction ratio is 60 dB. These optic-fiber switches show a promising future in optical fiber communication systems.     

Stable Degeneracies for Ising Models

We introduce and consider the notion of stable degeneracies of translation invariant energy functions, taken at spin configurations of a finite Ising model. By this term we mean the lack of injectivity that cannot be lifted by changing the interaction.     

Single-mode fibre optic Bragg grating sensing on the base of birefringence in surface-mounting and embedding applications

Birefringence effects in the two typical installation techniques of fibre Bragg grating(FBG) sensor are investigated: surface-mounting and embedding configurations. When the FBG is bonded on a host material, the sensitivity loss in ultrasonic measurement caused by glue-induced low-birefringence is first reported. Next, the transverse stress-induced high birefringence when the FBG is embedded into a fabric composite laminate is measured as 3.6×10⁻⁴. Such induced-birefringence effects are experimentally analysed in mechanical applications. Simple and effective solutions with respect to the respective installation configurations for removing the birefringence effect are proposed and the obtained zero-birefringence cases are compared with the birefringent cases.     

Rigorous solution of the spin-1 quantum Ising model with single-ion anisotropy

We solve the spin-1 quantum Ising model with single-ion anisotropy by mapping it onto a series of segmented spin-1/2 transverse Ising chains, separated by the S(z)=0 states called holes. A recursion formula is derived for the partition function to simplify the summation of hole configurations. This allows the thermodynamic quantities of this model to be rigorously determined in the thermodynamic limit. The low temperature behavior is governed by the interplay between the hole excitations and the fermionic excitations within each spin-1/2 Ising segment. The quantum critical fluctuations around the Ising critical point of the transverse Ising model are strongly suppressed by the hole excitations.     

Slab CO2 lasers excited by switching power

In this paper we present a new discharge technique to excite slab CO₂ lasers. A uniform stable glow discharge has been obtained in a volume of 3 × 30 × 446 mm³. Output power is 10 W, and a gain of 0.26% cm⁻¹ has been obtained.     

Semi-local cosmic strings and the cosmological constant problem

We study the cosmological constant problem in a three-dimensional N = 2 supergravity theory with gauge groupSU (2)_global × U(1)_local. The model we consider is known to admit string-like configurations, the so-called semi-local cosmic strings. We show that the stability of these solitonic solutions is provided by supersymmetry through the existence of a lower bound for the energy, even though the manifold of the Higgs vacuum does not contain non-contractible loops. Charged Killing spinors do exist over configurations that saturate the Bogomol'nyi bound, as a consequence of an Aharonov-Bohm-like effect. Nevertheless, there are no physical fermionic zero modes on these backgrounds. The exact vanishing of the cosmological constant does not imply, then, Bose-Fermi degeneracy. This provides a non-trivial example of the recent claim made by Witten on the vanishing of the cosmological constant in three dimensions without unphysical degeneracies.     

Theoretical investigations of spin splittings in asymmetric AlSb/InAs/GaSb heterostructures and the possibility of electric field induced magnetization

We use the effective bond orbital model method to examine the spin splitting due to the Rashba effect in AlSb/InAs/GaSb asymmetric heterostructures. We find for the resulting two-dimensional electron gas (2DEG) under study that large theoretical values of the Bychkov–Rashba coefficients in the range of 30 × 10 ^{− 10}to 50 × 10 ^{− 10}eV · cm can be achieved. Finally, we present a phenomenon that might lead to a direct observation of the Rashba effect. We derive an expression, valid in the diffusive limit, for the spin polarization of the current resulting from a bias parallel to the plane of the quantum well.     

Two series of triple- and single-domain reconstructions induced by europium on vicinal Si(1 1 1) [ ]-miscut surface

The growth and properties of Eu-induced one-dimensional reconstructions on vicinal Si(1 1 1) surface miscut in the [ ] direction have been studied by low energy electron diffraction and scanning tunneling microscope in the submonolayer range. The focus has been attended to the formation of single-domain structures and the influence of preparation parameters on the domain orientation. We have found the critical conditions for the preparation of a variety of Eu-induced single-domain (n×2) and (n×1) structures. In addition, a new intermediate phase showing the 9×1 periodicity between 3×2 and 2×1 phases is detected.     

Random telegraph signal noise simulation of decanano MOSFETs subject to atomic scale structure variation

As MOSFETs shrink into the decanano regime it is predicted that random telegraph signals (RTS), resulting from trapping events in defect states near the Si/SiO₂ interface, will significantly affect analogue and digital circuit performance. At these same scales, intrinsic parameter fluctuations introduced by atomic differences between devices will also be significant. In this work, a methodology based on 3D simulation is developed which can correctly model RTS noise in the time and frequency domain in the presence of random discrete dopants. The approach is illustrated with results obtained for 30×30  nm devices. We find that atomicity can significantly increase RTS magnitude in devices with particular doping configurations, and ensemble average RTS effects vary markedly from those predicted on an assumption of continuous doping.     

Enhanced critical current densities in Cu-sheathed MgB2

Micron-scale mixing of magnesium and boron powders by mechanical alloying allows the MgB₂ formation reaction to proceed as low as 450 °C, with high-quality material formed in an hour at 600 °C. At these low reaction temperatures the reaction can be performed in situ in a copper sheath, and it is found that the presence of copper enhances the superconducting properties of the MgB₂. Self-field critical current densities, calculated from full critical-state simulation of magnetization hysteresis, are up to 7 × 10⁵ A/cm² at 13.6 K and 1 × 10⁵ A/cm² at 30 K.     

The Baxter model and scale invariant field theory

We investigate the Baxter model and its special case, the two-dimensional Ising model, within the hypothesis of an underlying scale invariant field theory. The translation of the Euclidean lattice expressions for physical operators (spinors, etc.) and pairs of the spin (order), disorder variables of the Ising model to corresponding expressions in terms of relativistic Majorana fields is carried out. All order, disorder correlation functions can be easily computed from the relativistic formulas. The generalization of such correlation functions to the Baxter model is obtained by switching on an energy-energy interaction between two Ising models. The energy-energy coupling turns out to be the Thirring coupling when linear combinations Ψ = Ψ_I + iΨ_II of Majorana fields are introduced. The critical indices α, ν, , γ and β are determined from the correlation functions and are seen to be consistent with the scaling picture.     

New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain

In this paper we show how an infinite system of coupled Toda-type nonlinear differential equations derived by one of us can be used efficiently to calculate the time-dependent pair-correlations in the Ising chain in a transverse field. The results are seen to match extremely well long large-time asymptotic expansions newly derived here. For our initial conditions we use new long asymptotic expansions for the equal-time pair correlation functions of the transverse Ising chain, extending an old result of T.T. Wu for the 2d Ising model. Using this one can also study the equal-time wavevector-dependent correlation function of the quantum chain, a.k.a. the q-dependent diagonal susceptibility in the 2d Ising model, in great detail with very little computational effort. Supported in part by the National Science Foundation under grant PHY 07-58139 and by the Australian Research Council under Project ID: LX0989627.     

Measurement of thickness of a thin film by means of laser interference at many incident angles

An optical method for directly measuring the thickness of a thin transparent film has been proposed by means of multi-wave laser interference at many incident angles, and confirmed experimentally by means of equipment made on an experimental basis. Two methods are available: one can be used when an index of refraction of the film, a wavelength λ, and two successive angles of incidence at which the sinusoidal light intensity has minimum values, are known (Method I), and another can be used without an index of film refraction when three successive angles of incidence and a wavelength are known (Method II). The smallest measurable thickness is 1.43λ for Method I, and 2.5λ for Method II. The largest measurable thickness is about 100λ for both methods. The measurement error by means of numerical calculation is Δh/h−1.01×10⁻², and that obtained experimentally with an angular resolution of incident light of 0.3° is Δh/h7×10⁻² for Method I. The refractive index can also be measured by means of Method II.     

Magnetization of a Gapped Spin 1/2 Antiferromagnetic Ising Chain near the Critical External Field

We study the magnetization of gapped spin 1/2 XXZ Heisenberg Ising chains and calculate the scattering length among massive spinons. We obtain the magnetization close to the critical external magnetic field. The leading correction term determined by the scattering length among massive spinons is given. Our results are in agreement with exact results and with experimental results. We show that the deviation from the massive free hard core boson picture can be accounted very well by the leading correction term due to the spinon-spinon interaction. We show that the deviation increases along with the increasing of the Ising term.     

Anomalous Universality in the Anisotropic Ashkin–Teller Model

The Ashkin–Teller (AT) model is a generalization of Ising 2–d to a four states spin model; it can be written in the form of two Ising layers (in general with different couplings) interacting via a four–spin interaction. It was conjectured long ago (by Kadanoff and Wegner, Wu and Lin, Baxter and others) that AT has in general two critical points, and that universality holds, in the sense that the critical exponents are the same as in the Ising model, except when the couplings of the two Ising layers are equal (isotropic case). We obtain an explicit expression for the specific heat from which we prove this conjecture in the weakly interacting case and we locate precisely the critical points. We find the somewhat unexpected feature that, despite universality, holds for the specific heat, nevertheless nonuniversal critical indexes appear: for instance the distance between the critical points rescale with an anomalous exponent as we let the couplings of the two Ising layers coincide (isotropic limit); and so does the constant in front of the logarithm in the specific heat. Our result also explains how the crossover from universal to nonuniversal behaviour is realized.Partially supported by NSF Grant DMR 01–279–26     

Magnetization of a Gapped Spin 1/2 Antiferromagnetic Ising Chain near the Critical External Field

We study the magnetization of gapped spin 1/2 XXZ Heisenberg Ising chains and calculate the scattering length among massive spinons. We obtain the magnetization close to the critical external magnetic field. The leading correction term determined by the scattering length among massive spinons is given. Our results are in agreement with exact results and with experimental results. We show that the deviation from the massive free hard core boson picture can be accounted very well by the leading correction term due to the spinon-spinon interaction. We show that the deviation increases along with the increasing of the Ising term.