The Analyticity Breakdown for Frenkel-Kontorova Models in Quasi-periodic Media: Numerical Explorations

We study numerically the “analyticity breakdown” transition in 1-dimensional quasi-periodic media. This transition corresponds physically to the transition between pinned down and sliding ground states. Mathematically, it corresponds to the solutions of a functional equation losing their analyticity properties. We implemented some recent numerical algorithms that are efficient and backed up by rigorous results so that we can compute with confidence even close to the breakdown. We have uncovered several phenomena that we believe deserve a theoretical explanation: (A) The transition happens in a smooth surface. (B) There are scaling relations near breakdown. (C) The scaling near breakdown is very anisotropic. Derivatives in different directions blow up at different rates. Similar phenomena seem to happen in other KAM problems.     

Inherent mechanism of breakdown in laminar-turbulent transition of plane channel flows

We will first list some known facts of transition and turbulence, and then analyze results from direct numerical simulations done for the transition of plane channel flows, thus revealing the key mechanism of breakdown. 1 Arguments based on known facts A superficial reason for the fact that the change of mean flow profile plays the key role in transition is that the mean flow profiles for laminar and turbulent flow are drasti- cally different. But this does not provide the inherent mechanism o…     

On the definition of phase transition

It is shown that there exists a phase transition associated with a singularity of the free energy for a model such that for all temperatures the equilibrium state is unique and thus stable with respect to boundary perturbations. It is also shown on this model that there exist phase transitions without symmetry breakdown, which can be related to a phase transition with symmetry breakdown on an equivalent model.     

Temperature driven reversible breakdown of pseudomorphism in ultrathin Fe/Cu3Au films

We observe that ultrathin Fe/Cu(3)Au(001) films in the 6-13 A thickness range, beyond the thickness of pseudomorphism breakdown at room temperature, exhibit a temperature dependent structural phase transition in the range T(c) approximately 345-380 K. In the high temperature state the Fe film becomes pseudomorphic, while breakdown of pseudomorphism reversibly occurs as the system is cooled below the transition temperature. The difference between substrate and overlayer thermal expansion coefficient is highlighted as the driving force for the observed transition.     

The mechanism of breakdown in laminar-turbulent transition of a supersonic boundary layer on a flat plate-temporal mode

Recently, more and more attentions have been paid to the transition and turbulence of compressible flows, especially supersonic flows, but progress is very slow. In general, attentions were paid to the evolution of disturbances in laminar flow region, and the mechanism of breakdown process in laminar-turbulent transition remains unclear. The conventional idea of what leads to laminar-turbulent transition is that the transi-tion starts from the amplification of disturbances, and when the distur…     

Mechanisms of elementary events in the kinetics of electrical breakdown of polymer and ceramic dielectrics

The kinetics of electrical breakdown of thin (15–70 μm) layers of polymers and ceramics in a constant-sign field at 77–480 K has been investigated. The temperature dependences of the longevity (breakdown waiting time) of both dielectrics have been found to be similar to each other. At elevated temperatures, the longevity of the dielectrics varies exponentially with increasing temperature, and at reduced temperatures, it is temperature-independent (there is an athermal plateau). The mechanisms of elementary events controlling the process of preparation of the dielectrics for breakdown at elevated and reduced temperatures are the thermal-fluctuation over-barrier electron transition from trap to trap and the tunneling (under-barrier) transition, respectively. The hopping electron transport in the field direction gives rise to critical space charges causing breakdown of the dielectrics. The transition barrier heights (trap depths) have been determined. The low-temperature longevities of the polymer and the ceramic have been found to be similar, whereas the transition barrier for the ceramic is much higher than that for the polymer and the applied field in the former case is significantly (by a factor of tens) lower than that in the latter case. Electron traps in the polymer are adequately described by the Coulomb center model, whereas this is not the case for the ceramic.     

稍不均匀电场中低气压击穿的起始路径研究

稍不均匀电场间隙的起始击穿路径问题对于气体放电触发以及电极表面削蚀有重要意义.为研究低气压击穿工况中起始路径的位置规律,本文建立了一种基于蒙特卡罗碰撞模型与电子运动轨迹假设相结合的路径判断模型(determination of the critical path模型, DCP模型),并以2种电极装置的击穿试验来验证DCP模型的正确性.通过负电极表面的痕迹捕捉和击穿电压的测量可以分别验证DCP模型对起始击穿路径和击穿电压的计算能力.根据试验结果,起始击穿路径在不同压强或流率下会发生转移,且转移趋势与计算结果相符;同时, DCP模型对击穿电压的计算误差不超过7.9%,可初步验证DCP模型的计算精度.在此基础上,利用DCP模型对其他4种典型的电极装置进行数值计算,发现全部击穿案例都存在一些共性:随着间隙压强或流率的升高,最小电压区域((pd) min过渡区)的起始路径转移频繁,并伴随击穿电压上下波动,近似持平,且起始路径几乎都服从较长路径向较短路径的转移规律.最后,通过DCP模型的数值分析,揭示了上述起始路径相关规律的内在机理.     

Study of breakdown in yttrium aluminum garnet at subnanosecond times of increasing voltage

Crystallographically oriented channels with bottlenecks in the regions of reflection of the pulses have been obtained in aluminum yttrium garnet during multipulsed nanosecond breakdown from the anode under voltages of 100–140 kV, and the propagation rate of the fronts of the phase transition in this voltage range has been determined. It has been shown that the character of the observed pattern of the sequential formation of separate chains of the complete breakdown structure indicates that the channel is formed only locally and immediately at the point of time of passing the breakdown front since the maximal field strength, the magnitude of which determines the diameter of the breakdown channel, is observed in the vicinity of the breakdown front.     

On the theory of plasma streamer development

The temporal dynamics of initial stage of breakdown development in high-pressure gases, i.e., ionization avalanche initiation and development, its transition to plasma avalanche and then to plasma streamer, is discussed. Simple formulas for times of transitions between various breakdown stages and ionization front propagation velocities at individual stages are derived.     

Single bubble of an electronegative gas in transformer oil in the presence of an electric field

The influence of the electric field on a single air bubble in transformer oil has been studied. It has been shown that, depending on its size, the bubble may initiate breakdown. The sizes of air and sulfur hexafluoride bubbles at which breakdown will not be observed have been estimated based on the condition for the avalanche-to-streamer transition.     

Breakdown of chaos symmetry and intermittency in the double-well potential system

The chaos-chaos transition in a one-particle system in the symmetric double-well potential under an external periodic field is studied from the viewpoint of the breakdown of the chaos symmetry and the development of the intermittency characteristics. It is found that the similarity exponent introduced to analyze the intermittency characteristics satisfies a scaling law near the transition point.     

Winterberg’s Conjectured Breaking of the Superluminal Quantum Correlations over Large Distances

We elaborate further on a hypothesis by Winterberg that turbulent fluctuations of the zero point field may lead to a breakdown of the superluminal quantum correlations over very large distances. A phenomenological model that was proposed by Winterberg to estimate the transition scale of the conjectured breakdown, does not lead to a distance that is large enough to be agreeable with recent experiments. We consider, but rule out, the possibility of a steeper slope in the energy spectrum of the turbulent fluctuations, due to compressibility, as a possible mechanism that may lead to an increased lower-bound for the transition scale. Instead, we argue that Winterberg overestimated the intensity of the ZPF turbulent fluctuations. We calculate a very generous corrected lower bound for the transition distance which is consistent with current experiments.     

Combined effects of particle interaction and nonlinear sweep on Landau-Zener transition

We investigate the Landau-Zener transition (LZT) of a two-level system with two types of nonlinearity: particle interaction and nonlinear time-dependent energy sweep, both numerically and analytically. Due to the interplay between these two types of nonlinearity, many interesting phenomena in different parameter regions occur, including breakdown of adiabaticity, fade-out of interference phenomenon, and asymmetry of transition probability. The potential experimental observation of transition dynamics in this system is suggested.     

Electrical breakdown as an insulator-to-metal transition

The effect of dielectric strengthening under electrical breakdown in thin oxide films and other materials is discussed. The breakdown phenomenon is considered as an insulator-to-metal phase transition. The effect of strengthening is thus associated with the fact that no phase transition seems to be possible when the system size is decreased below a certain characteristic length d _c (it is a so-called ‘tachyon instability’). This dimension is estimated to be d _c?～?ξ, where ξ is the correlation length for metal–insulator transition.     

Statistical study of nanosecond electric breakdowns in n-hexane

Methods for analyzing statistical distributions of the breakdown delay time are generalized. A statistical approach is used to study electric breakdown in n-hexane in a 2.1-MV/cm quasi-uniform electric field at a pulse duration of ∼5×10⁻⁸ s. Two different mechanisms for the anode breakdown are shown to coexist and compete with each other. One of them incorporates the “bubble” stage, whereas the other one is related to ionization in the liquid itself. It is found that the weaker influence of the external pressure on the pulsed electric strength of liquids in the nanosecond range is caused by a transition to the ionization mechanism for the anode breakdown at elevated pressures.     

Investigation of the electrical breakdown mechanism in neon at 13.3 mbar pressure using the time delay method

The results of the investigation of electrical breakdown in neon filled diode at 13.3 mbar pressure in function of distances between electrodes (0.1 < d < 20 mm), using electrical breakdown time delay method, are presented in this paper. The Paschen curve, as well as the electrical breakdown time delay mean values, and discharge formative time dependence of distance between electrodes are analyzed. The electrical breakdown time delay distributions and Laue diagrams, both as the functions of the distances between electrodes, were used in consideration. The shapes of the established distributions indicate the complex nature of the discharge formation mechanism. The results also indicate that on the right hand side of the Paschen curve (pd > 15 mbar · cm) the transition regime between Townsend and streamer mechanism of electrical breakdown is dominant.     

Coherent Structures in Transition of a Flat-Plate Boundary Layer at Ma = 0.7

Direct numerical simulation （DNS） of a spatially evolving fiat-plate boundary layer transition process at free stream Mach number 0. 7 is performed. Tollmien-Schlichting （T-S） waves are added on the inlet boundary as the disturbances before transition. Typical coherent structures in the transition process are investigated based on the second invariant of velocity gradient tensor. The instantaneous shear stress and the mean velocity profile in the transition region are studied. In our view, the fact that the peak value of shear stress in the stress concentration area increases and exceeds a threshold value during the later stage of the trallsition process plays an important role in the laminar breakdown process.     

A Quenched Study for QCD Phase-Transition on Anisotropic Lattices

The QCD deconfinement phase transition in pure SU(3) gauge theory is studied on an anisotropic lattice. The critical temperature is determined to be T_c ≈ 285 MeV. The relation between the deconfinement phase transition and the breakdown of Z(3) center symmetry is also discussed.     

On the plasma mechanism of developing the early stages of breakdown in gases

The time evolution of the initial stages of breakdown in high-pressure gases is theoretically investigated. The following three stages are considered: initial: the origination and development of an ionization avalanche, the change of this avalanche to a plasma avalanche, and the change of the plasma avalanche to a plasma streamer. The streamer ionizes the gas via its radiation, causes new avalanches propagating in an enhanced discharge field, and bridges the discharge gap. Simple formulas are derived for the times of transition between various breakdown stages and for the ionization front velocity at separate stages.     

Gas-liquid instability in the many-fermion system and the breakdown of perturbation theory based on the plane-wave Hartree-Fock hamiltonian

The unambiguous breakdown of a perturbation series for the ground state properties of a quantum liquid of interacting fermions, based on an unperturbed single-particle hamiltonian defined self-consistently in terms of plane-wave orbitals, is discussed and related to the gas-liquid phase transition.