Robustness of critical points in a complex adaptive system: Effects of hedge behavior

In our recent papers, we have identified a class of phase transitions in the market-directed resource-allocation game, and found that there exists a critical point at which the phase transitions occur. The critical point is given by a certain resource ratio. Here, by performing computer simulations and theoretical analysis, we report that the critical point is robust against various kinds of human hedge behavior where the numbers of herds and contrarians can be varied widely. This means that the critical point can be independent of the total number of participants composed of normal agents, herds and contrarians, under some conditions. This finding means that the critical points we identified in this complex adaptive system (with adaptive agents) may also be an intensive quantity, similar to those revealed in traditional physical systems (with non-adaptive units).     

Renormalization for golden circles

We prove that twist maps of the cylinder that are attracted by any fixed point of MacKay's renormalization operator have a transitive invariant golden circle, provided the fixed point satisfies a few simple, purely topological conditions. These conditions can be verified by finite-precision arithmetics; they are fulfilled for the simple fixed point and seem to be fulfilled for the critical fixed point. Taking existence and hyperbolicity of the critical fixed point for granted, we conclude that the standard map has a critical invariant golden circle; the induced map on the circle is topologically conjugate to a rigid rotation; we can show that the conjugator is Hölder continuous; moreover, it is not differentiable on a dense set of points.This paper is part of a PhD thesis that is in preparation under the supervision of Oscar E. Lanford III at the ETH. I thank Oscar Lanford for having asked me precisely the right questions.     

The critical point of quantum chromodynamics through lattice and experiment

This talk discusses methods of extending lattice computations at finite temperature into regions of finite chemical potential, and the conditions under which such results from the lattice may be compared to experiments. Such comparisons away from a critical point are absolutely essential for quantitative use of lattice QCD in heavy-ion physics. An outline of various arguments which can then be used to locate the critical point is also presented.     

An evaluation of surface properties and frictional forces generated from Al–Mo–Ni coating on piston ring

Surface properties of the Al–Mo–Ni coating plasma sprayed on the piston ring material and the frictional forces obtained by testing carried out under different loads, temperatures and frictional conditions were evaluated.

Al–Mo–Ni composite material was deposited on the AISI 440C test steel using plasma spraying method. The coated and uncoated samples were tested by being exposed to frictional testing under dry and lubricated conditions. Test temperatures of 25, 100, 200, and 300 °C and loads of 83, 100, 200, and 300 N were applied during the tests in order to obtain the frictional response of the coating under conditions similar to real piston ring/cylinder friction conditions. Gray cast iron was used as a counterface material. All the tests were carried out with a constant sliding speed of 1 m/s.

The properties of the coating were determined by using EDX and SEM analyses. Hardness distribution on the cross-section of the coating was also determined. In addition, the variations of the surface roughness after testing with test temperatures and loads under dry and lubricated conditions were recorded versus sliding distance.

It was determined that the surface roughness increased with increasing loads. It increased with temperature up to 200 °C and then decreased at 300 °C under dry test conditions.

Under lubricated conditions, the roughness decreased under the loads of 100 N and then increased. The roughness decreased at 200 °C but below and above this point it increased with the test temperature.

Frictional forces observed under dry and lubricated test conditions increased with load at running-in period of the sliding. The steady-state period was then established with the sliding distance as a normal situation. However, the frictional forces were generally lower at a higher test temperature than those at a lower test temperature. Surprisingly, the test temperature of 200 °C was a critical point for frictional forces and surface roughness.     

Diffusion cooling in a magnetic field

Diffusion cooling of electrons in a weakly ionized plasma in the presence of a magnetic field is studied using the balance equations of momentum transfer theory, well known in "swarm" or test particle analysis. It is shown that for a cylindrical, axially symmetric system, the electron temperature profile can be "hollow" (i.e., T(e)相似文献   

等离子体尺寸对放电极紫外光源影响

计算了放电等离子体极紫外光刻光源中,不同等离子体长度条件下的收集效率,实验上研究了等离子体长度对Xe气放电极紫外辐射的影响。结合本系统光学收集系统设计参数和理论计算结果,给出了不同等离子体长度条件下中间焦点处13.5 nm（2%带宽）光功率。结果表明等离子体长度为3~6 mm时毛细管光源中间焦点光功率和尺寸最优。     

Second to tenth order susceptibilities of conserved charges within a modified Nambu-Jona-Lasinio model

We discuss the sign and energy dependence of second to tenth order susceptibilities of the baryon number,charge number, and strangeness for the analysis of critical conditions in heavy ion collisions in the LHC and RHIC by applying a modified Nambu-Jona-Lasinio model. This model is fitted to the quark condensate of the lattice QCD result at finite temperature and zero baryon chemical potential. The presence of a critical point made these susceptibilities deviate considerably from a Hadron-Resonance-Gas model that shows no criticality. The sign, magnitude, and energy dependence of these higher order fluctuations hint towards the existence and location of a critical point that could be discovered in future heavy ion collision experiments.     

Rapid thermal relaxation in near-critical fluids and critical speeding up: discrepancies caused by boundary effects

We present one-dimensional numerical simulations reporting the temperature evolution of a pure fluid subjected to heating near its liquid-vapor critical point under weightlessness. In this model, thermal boundary conditions are imposed at the outer edges of the solids in contact with the fluid. Our investigations concern the thermal conditions at the edges of the fluid and their consequences on the fluid's global response. The results for piston effect heating are shown to be significantly affected by the simulation of the solid boundaries. Concerning critical speeding up, it is even found that taking conductive solids into account can make the bulk fluid temperature change in a way opposed to that predicted in their absence.     

Thermodynamic Derivation of Scaling at the Liquid–Vapor Critical Point

With the use of thermodynamics and general equilibrium conditions only, we study the entropy of a fluid in the vicinity of the critical point of the liquid–vapor phase transition. By assuming a general form for the coexistence curve in the vicinity of the critical point, we show that the functional dependence of the entropy as a function of energy and particle densities necessarily obeys the scaling form hypothesized by Widom. Our analysis allows for a discussion of the properties of the corresponding scaling function, with the interesting prediction that the critical isotherm has the same functional dependence, between the energy and the number of particles densities, as the coexistence curve. In addition to the derivation of the expected equalities of the critical exponents, the conditions that lead to scaling also imply that, while the specific heat at constant volume can diverge at the critical point, the isothermal compressibility must do so.     

Properties of then-body correlation functions near the liquid-gas critical point. Correlation inequalities

We investigate the behavior of the many-body correlation functions in the vicinity of the gas-liquid critical point. We use the framework of the liquid state theory and, accordingly, no reference to an effective Landau-Ginzburg Hamiltonian is made. The critical condition is introduced by means of the equation of state. From the Baxter equation relating the many-body correlation functionsh(n) andh(n+1), we find that the integrals of all theh(n) diverge at the critical point. Then we present strong arguments and this leads to GKS-like inequalities, under some limiting conditions: the interparticle distances must be large and the thermodynamic state of the system must be close to the critical point. In order to get these inequalities, an upper bound forh(n) is obtained. Particular attention must be paid to the fact that the usual asymptotic approximations of the liquid state theory are no longer valid.     

Hyperscaling above the upper critical dimension

Above the upper critical dimension, the breakdown of hyperscaling is associated with dangerous irrelevant variables in the renormalization group formalism at least for systems with periodic boundary conditions. While these have been extensively studied, there have been only a few analyses of finite-size scaling with free boundary conditions. The conventional expectation there is that, in contrast to periodic geometries, finite-size scaling is Gaussian, governed by a correlation length commensurate with the lattice extent. Here, detailed numerical studies of the five-dimensional Ising model indicate that this expectation is unsupported, both at the infinite-volume critical point and at the pseudocritical point where the finite-size susceptibility peaks. Instead the evidence indicates that finite-size scaling at the pseudocritical point is similar to that in the periodic case. An analytic explanation is offered which allows hyperscaling to be extended beyond the upper critical dimension.     

Accretion of Phantom Energy by Bardeen Black Hole

In this paper we deal with the accretion of phantom energy onto static spherically symmetric Bardeen black hole. It is shown that the mass of black hole reduces with the accretion of phantom energy. We compute accretion rate onto Bardeen black hole at critical point. Furthermore, we obtain the conditions at critical point, under which accretion is possible and also discuss certain relevant cases. Finally, we discuss the validity of generalized second law of thermodynamics at the event horizon of Bardeen black hole.     

A theory of Reflectivity Oscillations in High-Power Laser Interaction with Inhomogeneous Expanding Plasmas for the Case of Strong Anomalous Absorption Near Critical Plasma Density I

It is shown at first that the ponderomotive laser force appreciably may enhance the values of the dielectric function ?(x) near the critical plasma density. If in some spatial region near ? = 0 a large anomalous collision frequency is assumed, sharply rising at some point, pump field depletion may also lead to strong changes in the density scale length. As a first approach we have calculated the laser reflectivity in the case when the anomalous collision frequency and the density scale length jump at some point near the critical one. We obtain temporal oscillations of the reflectivity if due to thermal plasma expansion the density scale length increases with time. The calculated frequency and amplitude of the reflectivity oscillations are shown to be in good agreement with measured values in the case of Nd-laser heating of solid targets.     

On the possibility of realizing a periodic low-density spatial distribution of excitons

The solutions of a system of coupled integro-differential Bogolyubov equations for distribution functions have been used to determine conditions, both in temperature and in concentration, under which a spatially uniform distribution of excitons transforms spontaneously into a periodic state with a small amplitude. The analysis rests on the concept assuming the existence of a biexciton interaction potential. The criterion for the appearance of a weak periodic component in the exciton distribution is derived from the condition of branching of solutions of Hammerstein-type equations at the point where the parameters of this equation reach critical values.     

Boundary entropy of one-dimensional quantum systems at low temperature

The boundary beta function generates the renormalization group acting on the universality classes of one-dimensional quantum systems with boundary which are critical in the bulk but not critical at the boundary. We prove a gradient formula for the boundary beta function, expressing it as the gradient of the boundary entropy s at fixed nonzero temperature. The gradient formula implies that s decreases under renormalization, except at critical points (where it stays constant). At a critical point, the number exp((s) is the "ground-state degeneracy," g, of Affleck and Ludwig, so we have proved their long-standing conjecture that g decreases under renormalization, from critical point to critical point. The gradient formula also implies that s decreases with temperature, except at critical points, where it is independent of temperature. It remains open whether the boundary entropy is always bounded below.     

The influence of external boundary conditions on the spherical model of a ferromagnet. I. Magnetization profiles

The spherical model of a ferromagnet is investigated for various (external) boundary conditions. It is shown that, besides the well-known critical point, a second one can be produced by the boundary conditions. Although the main asymptotic of the free energy is analytic at the new critical point, theO(N^1–2/d) asymptotic possesses a singularity here. A natural order parameter of the model has singularities at both critical points. The magnetization profile is studied for the whole range of the model's parameters and at different scales. It is shown that (in an appropriate regime) below the second critical temperature the magnetization profile freezes, that is, becomes temperature independent. Distributions of the single spin variables and some macroscopic observables (including normalized total spin) are studied for the whole temperature range including the critical points.     

空气中飞秒激光自聚焦等离子体通道的电导特性

 通过电学探测法，采用不同焦距的聚焦透镜，在不同激光能量、不同极性外加电压的条件下，对大气中的飞秒激光自聚焦等离子体电离通道特性进行了实验研究。发现激光脉冲经不同焦距的聚焦透镜作用后均存在较长的电离通道，通道的等效电阻率有所变化，通常电阻率的最大值出现在透镜的几何焦点附近，并且焦距越长，此电阻率的局部峰值点离几何焦点位置越近。在外加不同极性电压时，自由电子受到所加静电场作用力、洛仑兹力以及有质动力的共同作用。焦点前，通道电流变化不明显，加正向电压产生的电流略微大于加负向电压时的电流；焦点后则是加负向电压产生的电流大于加正向电压时的电流。     

侧风条件下短舱流动分离等离子体流动控制研究

利用数值仿真开展了侧风条件下短舱流动分离等离子体流动控制研究,首先研究了不同侧风条件下短舱流动分离特性,揭示了侧风角度以及速度大小对流动分离的影响规律.随着侧风角度的增加,进气唇口处分离区域不断扩大且进气截面的总压损失更加严重;随着侧风速度的变大,分离区域变化并不明显,进气截面总压损失系数降低.进一步将等离子体激励布置...     

Contribution to the statistical theory of solutions of polymers in a critical solvent

The thermodynamics of high polymers in equilibrium with a low-molecular solvent with a large correlation radius (super-and near-critical solvent) is studied. Special attention is devoted to the analysis of typical phase diagrams describing the conditions of solubility of a polymer in such a solvent. The nature of these diagrams is determined by the existence of long-range multiparticle attraction between the monomers, which increases as the critical point of the solvent is approached. At the critical point the contribution of this attraction to the free energy of the system is nonanalytic with respect to the polymer concentration. It is shown that the nontrivial dependences of the polymer-polymer and polymer-solvent coupling constants, which appear in the phenomenological analysis, on the pressure and temperature of the solvent play an important role in the quantitative analysis of the phase diagrams of the solubility of the polymer. These dependences are found in explicit form under the assumption that in the absence of intermonomer bonds the system can be described as a compressible two-component lattice alloy. The partition function of the system under study is represented as a functional integral over two coupled, strongly fluctuating fields, one of which, describing the fluctuations of the polymer density, is the 0 component. By virtue of the specific nature of the problem, the effective temperature corresponding to the 0-component of the field cannot be specified independently, but can be determined by minimizing the total free energy of the system. Zh. éksp. Teor. Fiz. 114, 910–929 (September 1998)     

A One‐Dimensional Particle‐in‐Cell Model of Plasma Build‐Up in Vacuum Arcs

Understanding the mechanism of plasma build‐up in vacuum arcs is essential in many fields of physics. A one‐dimensional particle‐in‐cell computer simulation model is presented, which models the plasma developing from a field emitter tip under electrical breakdown conditions, taking into account the relevant physical phenomena. As a starting point, only an external electric field and an initial enhancement factor of the tip are assumed. General requirements for plasma formation have been identified and formulated in terms of the initial local field and a critical neutral density. The dependence of plasma build‐up on tip melting current, the evaporation rate of neutrals and external circuit time constant has been investigated for copper and simulations imply that arcing involves melting currents around 0.5–1 A/μm², evaporation of neutrals to electron field emission ratios in the regime 0.01 – 0.05, plasma build‐up timescales in the order of ～ 1 – 10 ns and two different regimes depending on initial conditions, one producing an arc plasma, the other one not. Also the influence of the initial field enhancement factor and the external electric field required for ignition has been explored, and results are consistent with the experimentally measured local field value of ～ 10 GV/m for copper (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)