New universal short-time scaling behaviour of critical relaxation processes

We study the critical relaxation properties of Model A (purely dissipative relaxation) starting from a macroscopically prepared initial state characterised by non-equilibrium values for order parameter and correlations. Using a renormalisation group approach we observe that even (macroscopically)early stages of the relaxation process display universal behaviour governed by a new, independent initial slip exponent. For large times, the system crosses over to the well-known long-time relaxation behaviour.The new exponent is calculated toO(²) in =4–d, whered is the spatial dimension of the system. The initial slip scaling form of general correlation and response functions as well as the order parameter is derived, exploiting a short-time operator expansion. The leading scaling behaviour is determined by initial states with sharp values of the order parameter. Non-vanishing correlations generate corrections to scaling.     

Characteristics of laminar lifted flames in coflow jets with initial temperature variation

Characteristics of laminar lifted flames of propane highly diluted with nitrogen have been investigated by varying the initial temperature in coflow jets. The result showed that the lifted flame maintained the tribrachial structure up to the initial temperature of 900 K and the liftoff height decreased with initial temperature and dilution ratio. The overall behavior of liftoff heights correlated well with the jet velocity scaled by the stoichiometric laminar burning velocity, emphasizing the importance of the stoichiometric laminar burning velocity on the propagation speed of tribrachial flame. The exponent of the liftoff height with jet velocity in the relation of increased with initial fuel mole fraction, which has been attributed to the differential diffusion between propane and diluent nitrogen. Consequently, nitrogen concentration varied along the stoichiometric contour, which affected the propagation speed. Also, the exponent increased with initial temperature due to the sensitiveness of the propagation speed variation with nitrogen dilution on initial temperature. The liftoff conditions have been observed for the jet velocity even smaller than the stoichiometric laminar burning velocity at relatively low initial temperatures. This can be attributed to the effect of the buoyancy. Liftoff velocities accounting for the relative buoyancy effect were found to have a satisfactory correlation with regardless of initial temperatures and nitrogen dilution.     

Exact analytical solution for the change of the photon statistics due tok-photon absorption

For unsaturatedk-photon absorption the exact solution of the master equation for the diagonal elements is presented. This solution is found by Laplace-transformation and recursion. It has the form of a double sum over the initial values. Commuting the order of summation we then show, that fork2 the photon distribution does not depend on the initial distribution if the initial mean photon number is sufficiently high and the square of the resulting photon number is small against the initial photon number.     

Time-dependent effective rates for molecular processes

The concept of time-dependent effective rates for molecular processes such as luminescence, introduced in our earlier work, is developed further by obtaining two new results. One is the explicit evaluation of those rates for four initial conditions corresponding to experimentally relevant methods of excitation of the molecule. The other is a proof that the limiting values of those rates for long times or for infinitely fast relaxation are independent of the initial condition. The latter result extends the validity of the rate depression effect (whereby the long time limit of the effective rate is different from its thermalized value) to arbitrary initial conditions.On leave of absence from the Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627 (permanent address)     

Barrierless formation and faceting of SiGe islands on Si(001)

The initial stages of the formation of SiGe islands on Si(001) pose a long-standing puzzle. We show that the behavior can be consistently explained by one simple assumption-that for strained SiGe, (001) is a stable orientation but not a facet orientation. Calculations of energy and morphology reproduce the key features of "prepyramid" and "pyramid" islands, and explain the initial formation and subsequent shape transition. Scanning tunneling microscopy measurements confirm the key assumptions and predictions of the model.     

In search of dark horses: Affinity maturation of phage-displayed ligands

Summary Most combinatorial libraries are sparse in that only a tiny fraction of the relevant class of compounds is represented. This sparseness can be compensated in some measure by alternating rounds of selection with rounds of mutagenesis. Thus, clones are selected from the initial library by some criterion of fitness, such as affinity for a particular receptor. The selected clones are then mutagenized to generate a mutant library, which serves as input to the next round of selection, and so on. If the first round of selection is too stringent, rejecting all but the very fittest clone in the initial library (the initial champion), we might miss dark horses; clones in the initial library that are inferior to the initial champion, yet can be mutated to even higher fitness than can that champion. A more thoughtful strategy is to alternate nonstringent selection with simultaneous mutagenesis of many selected clones en masse.     

内禀退相干下海森伯XY模型中的热纠缠性质及其相干调控

通过求解系统的Milburn方程,研究了内禀退相干下两比特海森伯XY模型中的热纠缠性质. 讨论了非均匀磁场、系统初始纠缠度、 两比特的相对相位对系统热纠缠的调控作用.结果表明:在系统一定的初始条件下, 磁场的引入能够大大提高两比特间的热纠缠 程度;在固有退相干存在的情况下,系统热纠缠强烈依赖于两个自旋比特的初始态, 通过控制两自旋比特的相对相位和振幅,可以 获得系统的稳定热纠缠.结果还表明:在没有外界磁场时,发现Bell正交态是系统的"暗态", 它的热纠缠度在演化过程中不受系 统内禀退相干的影响.     

Universal Rules of Transient Processes

We analyze the transients of a logistic map. The dependence of the transient duration on the initial conditions for different values of the control parameter is revealed. It is shown that as the control parameter increases, the dependence of the transient duration on the initial conditions becomes more complex, which can be explained by the appearance of unstable 2n-period cycles. It is also shown that several definite scaling laws exist for the discussed function.     

Anomalous fluctuation and relaxation in unstable systems

The essential ideas of the scaling theory of transient phenomena proposed by the author for a single macrovariable near the instability point are extended to multi-macrovariables in nonequilibrium systems. The time region is divided into three regimes according to the scaling behavior of the fluctuating parts of the macrovariables. In the first regime, the fluctuation is Gaussian and it is described by the linearized stochastic equation (or linear Fokker-Planck equation). In the second regime, the fluctuation is non-Gaussian, but it is probabilistic or stochastic (not dynamical) in the sense that the stochastic nature comes from the probability distribution in the initial regime and that each representative motion is deterministic, namely a random force can be neglected asymptotically in the second regime. In the final regime, the fluctuation is again Gaussian. A fluctuation-enhancement theorem for multi-macrovariables is given, which states that the fluctuation becomes enhanced by the order of the system size in the second regime, which is of order log , if the initial system is located just at the unstable point. An anomalous fluctuation theorem for multi-macrovariables is also proven, which states that the fluctuation is anomalously enhanced in proportion to ^–2 at times of order log if the initial system deviates by from the unstable point.This work is partially financed by the Scientific Research Fund of the Ministry of Education.     

Learning in synergetic systems for pattern recognition and associative action

Synergetic systems are in particular physical systems which can produce spatial or temporal patterns by means of the interaction of their individual parts. We show how such a system can be devised or even learn by itself to reproduce given patterns described by their probability distribution function. If an initial state close to one of the learned patterns is presented to such a system, it will pull the initial state into an attractor belonging to the learned state (pattern recognition via associative memory). Furthermore we show how such a system can be devised or can learn to perform any prescribed stationary continous Markov process. If a set of incomplete or partly incorrect initial data is offered to such a system, it may correct it and perform associative action.     

Dense Coding in a Two-Spin Squeezing Model with Intrinsic Decoherence

Quantum dense coding in a two-spin squeezing model under intrinsic decoherence with different initial states (Werner state and Bell state) is investigated. It shows that dense coding capacity χ oscillates with time and finally reaches different stable values. χ can be enhanced by decreasing the magnetic field Ω and the intrinsic decoherence γ or increasing the squeezing interaction μ, moreover, one can obtain a valid dense coding capacity (χ satisfies χ > 1) by modulating these parameters. The stable value of χ reveals that the decoherence cannot entirely destroy the dense coding capacity. In addition, decreasing Ω or increasing μ can not only enhance the stable value of χ but also impair the effects of decoherence. As the initial state is the Werner state, the purity r of initial state plays a key role in adjusting the value of dense coding capacity, χ can be significantly increased by improving the purity of initial state. For the initial state is Bell state, the large spin squeezing interaction compared with the magnetic field guarantees the optimal dense coding. One cannot always achieve a valid dense coding capacity for the Werner state, while for the Bell state, the dense coding capacity χ remains stuck at the range of greater than 1.     

The Gravitating Perfect Fluid-Scalar Field Equations: Quintessence and Tachyonic Matter

The system consisting of a self gravitating perfect fluid and scalar field is considered in detail. The scalar fields considered are the quintessence and tachyonic forms which have important application in cosmology. Mathematical properties of the general system of equations are studied including the algebraic and differential identities as well as the eigenvalue structure. The Cauchy problem for both quintessence and the tachyon is presented. We discuss the initial constraint equations which must be satisfied by the initial data. A Cauchy evolution scheme is presented in the form of a Taylor series about the Cauchy surface. Finally, a simple numerical example is provided to illustrate this scheme.     

Classical solution of the nonlinear Boltzmann equation in allR 3: Asymptotic behavior of solutions

Proof is given of the existence of a classical solution to the nonlinear Boltzmann equation in allR ³. The solution, which is global in time, exists if the initial data go to zero fast enough at infinity and the mean free path is sufficiently large. The solution is smooth in the space variable if the initial value is smooth. The asymptotic behavior of solutions is also given. It is shown that ast the solution to the Boltzmann equation can be approximated by the solution to the free motion problem.     

Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion

The asymptotic stability of traveling wave solutions with shock profile is investigated for several systems in gas dynamics. 1) The solution of a scalar conservation law with viscosity approaches the traveling wave solution at the ratet ^– (for some>0) ast, provided that the initial disturbance is small and of integral zero, and in addition decays at an algebraic rate for |x|. 2) The traveling wave solution with Nishida and Smoller's condition of the system of a viscous heat-conductive ideal gas is asymptotically stable, provided the initial disturbance is small and of integral zero. 3) The traveling wave solution with weak shock profile of the Broadwell model system of the Boltzmann equation is asymptotically stable, provided the initial disturbance is small and its hydrodynamical moments are of integral zero. Each proof is given by applying an elementary energy method to the integrated system of the conservation form of the original one. The property of integral zero of the initial disturbance plays a crucial role in this procedure.     

Vibratile Coherence and Squeezing in Two Trapped Ions

It is shown that two trapped ions interacting with laser beams resonant to the first red side-band of center-of-mass mode,in Lamb-Dicke regime and under rotating wave approximation,is described by a Jaynes-Cummings model.For the initial condition that the motional state of center-of-mass mode is in vacuum state and the internal state is prepared in a coherent superposition of states,coherence and squeezing for the vibratile motion of center-of-mass mode are discussed,particularly,a“weak” coherent state and a “weak” squeezed vacuum state are obtained.Collapse and revival are also observed in this type of initial condition.     

CFBR-Ⅱ堆脉冲状态反应性温度系数测量

反应性温度系数是脉冲堆重要参数之一, 采用一种特殊的方法测量了脉冲状态反应性温度系数。 把脉冲的全过程分为峰和坪两个过程, 根据Fuchs-Hansen模型知道脉冲峰过程的反应性减小量为系统初始超瞬发反应性的2倍, 采用脉冲波形去坪的方法分离出峰过程贡献的温升, 由此得到CFBR-Ⅱ堆的脉冲反应性温度系数αT=-0.00202 $/K。 Reactivity temperature coefficient is one of important parameters of burst reactor. The methods of measuring the coefficient were introduced and analyzed. The whole process of burst is split into “peak” process and “tail” process. Reactivity reduction is twice as large as initial excess reactivity in “peak” process from Fuchs Hansen model. Increment of temperature induced by “peak” process was got through removing “tail”. So we deduced reactivity temperature coefficient of CFBR-Ⅱ αT=-0.00202 $/K.     

Renormalization Group Flow of the Two-Dimensional O(N) Spin Model

We develop a new block spin transformation and apply it to the 2D O(N) spin model. The transformation does not yield complicated non-local terms and then the transformation recursion formula seems to be controllable for any initial inverse temperature > 0. The main part of the block spin transformation of the model with large N converges to a massive state, no matter how low the initial temperature 1/ is, and is close to the flow of the hierarchical model advocated by Dyson and Wilson several decades ago.     

On “hyperboloidal” Cauchy data for vacuum einstein equations and obstructions to smoothness of Scri

The relationship between the geometric properties of hyperboloidal Cauchy data for vacuum Einstein equations at the conformal boundary of the initial data surface and between the space-time geometry is analyzed in detail. We prove that a necessary condition for existence of a smooth or a polyhomogeneous Scri (i.e., a Scri around which the metric is expandable in terms ofr ^–j log ⁱ r rather than in terms ofr ^–j ) is the vanishing of the shear of the conformal boundary of the initial data surface. We derive the boundary constraints which have to be satisfied by an initial data set for compatibility with Friedrich's conformal framework. We show that a sufficient condition for existence of a smooth Scri (not necessarily complete) is the vanishing of the shear of the conformal boundary of the initial data surface and smoothness up to boundary of the conformally rescaled initial data. We also show that the occurrence of some log terms in an asymptotic expansion at the conformal boundary of solutions of the constraint equations is related to the non-vanishing of the Weyl tensor at the conformal boundary.Supported in part by KBN grant #2 1047 91 01     

Hydrodynamic correlation functions of hard-sphere fluids at short times

The short-time behavior of the coherent intermediate scattering function for a fluid of hard-sphere particles is calculated exactly through ordert ⁴, and the other hydrodynamic correlation functions are calculated exactly through ordert ². It is shown that for all of the correlation functions considered the Enskog theory gives a fair approximation. Also, the initial time behavior of various Green-Kubo integrands is studied. For the shear-viscosity integrand it is found that at densityn³=0.837 the prediction of the Enskog theory is 32% too low. The initial value of the bulk viscosity integrand is nonzero, in contrast to the Enskog result. The initial value of the thermal conductivity integrand at high densities is predicted well by Enskog theory.     

An Approach for Extracting Small-Signal Equivalent Circuit of Double Heterojunction δ-Doped PHEMTs for Millimeter Wave Applications

Pseudomorphic high electron mobility transistors (PHEMTs) are very important in millimeterwave application. A simple and accurate method for extracting small-signal equivalent curcuit for Double Heterojunction -doped PHEMT valid up to 40GHz is presented. First, the parasitic parameters of the equivalent circuit are determined using pinch off PHEMT except for PAD capacitances. The initial intrinsic elements are then determined by conventional analytical method. Advanced Design System is then used to optimize the whole model parameters with very small dispersion of initial values. Good agreement is obtained between simulation results and measured results for a 0.25um DH PHEMT.