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The theoretical background and historical development of the similarity theory during the past decades are reviewed. We demonstrate similar discharges in local and nonlocal kinetic regimes, taking the low-pressure capacitive radio frequency (rf) discharges and microdischarges as examples. By using fully kinetic particle-in-cell simulations, we verify the similarity law (SL) and show a violation of frequency scaling (f-scaling) in the low-pressure capacitive rf plasmas. The similarity relations for electron density and electron power absorption are confirmed in similar rf discharges. With only the driving frequency varied, the f-scaling for electron density is also validated, showing almost the same trend as the similarity scaling, across most of the frequency regime. However, violations of the f-scaling are observed at lower frequencies, which are found to be relevant to the electron heating mode transition from stochastic to Ohmic heating. The scaling characteristics have also been comprehensively studied for microdischarges with dimensions from hundreds to several microns, with transition from secondary electron dominated regime to field emission regime. Finally, practical applications of the similarity and scaling laws are summarized.

A homeostatic mechanism that keeps the brain highly susceptible to stimuli and optimizes many of its functions—although this is a compelling theoretical argument in favor of the brain criticality hypothesis, the experimental evidence accumulated during the last two decades is still not entirely convincing, causing the idea to be seemingly unknown in the more clinically-oriented neuroscience community. In this perspective review, we will briefly review the theoretical framework underlying such bold hypothesis, and point to where theory and experiments agree and disagree, highlighting potential ways to try and bridge the gap between them. Finally, we will discuss how the stand point of statistical physics could yield practical applications in neuroscience and help with the interpretation of what is a healthy or unhealthy brain, regardless of being able to validate the critical brain hypothesis.

An emerging paradigm for predicting the state evolution of chaotic systems is machine learning with reservoir computing, the core of which is a dynamical network of artificial neurons. Through training with measured time series, a reservoir machine can be harnessed to replicate the evolution of the target chaotic system for some amount of time, typically about half dozen Lyapunov times. Recently, we developed a reservoir computing framework with an additional parameter channel for predicting system collapse and chaotic transients associated with crisis. It was found that the crisis point after which transient chaos emerges can be accurately predicted. The idea of adding a parameter channel to reservoir computing has also been used by others to predict bifurcation points and distinct asymptotic behaviors. In this paper, we address three issues associated with machine-generated transient chaos. First, we report the results from a detailed study of the statistical behaviors of transient chaos generated by our parameter-aware reservoir computing machine. When multiple time series from a small number of distinct values of the bifurcation parameter, all in the regime of attracting chaos, are deployed to train the reservoir machine, it can generate the correct dynamical behavior in the regime of transient chaos of the target system in the sense that the basic statistical features of the machine generated transient chaos agree with those of the real system. Second, we demonstrate that our machine learning framework can reproduce intermittency of the target system. Third, we consider a system for which the known methods of sparse optimization fail to predict crisis and demonstrate that our reservoir computing scheme can solve this problem. These findings have potential applications in anticipating system collapse as induced by, e.g., a parameter drift that places the system in a transient regime.

The survival chance of a prey chased by a predator depends not only on their relative speeds but importantly also on the local environment they have to face. For example, a wolf chasing a deer might take a long time to cross a river which can quickly be crossed by the deer. Here, we propose a simple predator-prey model for a situation in which both the escaping prey and the chasing predator have to surmount an energetic barrier. Different barrier-assisted states of catching or final escaping are classified and suitable scaling laws separating these two states are derived. We discuss the effect of fluctuations on the catching times and determine states in which catching or escaping is more likely. We further identify trapping or escaping states which are determined by hydrodynamics and chemotactic interactions. Our results are of importance for both microbes and self-propelled unanimate microparticles following each other by non-reciprocal interactions in inhomogeneous landscapes.

Conductive particles greatly impair the insulation integrity of a gas insulated switchgear (GIS). Factors including applied voltage, frequency of the alternating current, size and coefficient of restitution of the metallic particle, pressurized gas, and sizes of the GIS dramatically influence the particle dynamics. Previous investigations basically focused on certain scenarios, seldom considered the effects from coefficient of restitution, and did not provide universal laws for the particle dynamics. This paper proposes a dimensionless number that considers all the above-mentioned factors, and presents the scaling law between dimensionless mean/maximum lifting height of a charged particle in GIS and the proposed dimensionless number. It is believed that the scaling law together with the dimensionless number can provide guidance and shrink the parameter window for relevant investigations on the GIS with sparsely distributed conductive particles.

We develop a deep neural network (DNN) that accounts for the phase behaviors of polymer-containing liquid mixtures. The key component in the DNN consists of a theory-embedded layer that captures the characteristic features of the phase behavior via coarse-grained mean-field theory and scaling laws and substantially enhances the accuracy of the DNN. Moreover, this layer enables us to reduce the size of the DNN for the phase diagrams of the mixtures. This study also presents the predictive power of the DNN for the phase behaviors of polymer solutions and salt-free and salt-doped diblock copolymer melts.

Synopsis We discuss the accuracy of various published ab initio calculations of highly excited Born-Oppenheimer bound and doubly excited states in diatomic molecules. We show that some of these results appear questionable and in a few cases even clearly unreliable, a fact which may also affect the prediction of collision cross sections based on such data. Our analysis uses Quantum Defect Theory scaling laws and is supported by variational R-matrix calculations. Some simple recipes are discussed, which may help users of ab initio quantum chemistry packages to assess the quality of their results.

The total photoionization cross section of planar helium has been calculated up to the single ionization threshold I22 of triple P states. The cross section shows chaotic fluctuations as the energy E approaches the double ionization threshold E=0. By analyzing the fluctuating part of the cross section, we show that its amplitude decreases as ?E? mu for E-> 0- as predicted in Byunet al(2007 Phys. Rev. Lett., 98, 113001). The Fourier transform of the fluctuating part reveals peaks at the classical actions of closed triple collision orbits. Furthermore, the relative height of the peaks is consistent with the semiclassical predictions. Our findings underline that the fluctuating part of the photoionization cross section can be described by classical triple collision orbits in the semiclassical limit. These orbits all lie in the collinear eZe subspace, demonstrating that the fluctuations are dominated by the dynamics of this low dimensional phase space.

We draw an analogy between droplet formation in dilute particle and polymer systems. Our arguments are based on finite-size scaling results from studies of a two-dimensional lattice gas to three-dimensional bead-spring polymers. To set the results in perspective, we compare with in part rigorous theoretical scaling laws for canonical condensation in a supersaturated gas at fixed temperature, and derive corresponding scaling predictions for an undercooled gas at fixed density. The latter allows one to efficiently employ parallel multicanonical simulations and to reach previously not accessible scaling regimes. While the asymptotic scaling can not be observed for the comparably small polymer system sizes, they demonstrate an intermediate scaling regime also observable for particle condensation. Altogether, our extensive results from computer simulations provide clear evidence for the close analogy between particle condensation and polymer aggregation in dilute systems., 10 pages, 6 figures

Experiments on NSTX and MAST have shown the thermal energy confinement time in spherical tokmaks (STs), , to have a stronger toroidal field and weaker plasma current dependence than in conventional large aspect ratio tokamaks. These scalings were derived for single machines both of which are similarly sized, consequently the NSTX and MAST scaling laws do not include a size dependence, and so cannot be used to extrapolate the performance of future STs. Using physics-based dimensional arguments we extend the NSTX scaling to include a size scaling. We also resolve a colinearity problem specific to NSTX data by assuming core transport is gyro-Bohm like. The resulting scaling has approximately zero beta dependence, a typical collisionality dependence, and a relatively weak safety factor dependence: . With the exception of the safety factor, all exponents are consistent with recent experiments in large aspect ratio tokamaks. This apparent difference between STs and large aspect ratio tokamaks is consistent with MAST and NSTX results. We have considered the implications of the scaling for pilot plants and reactors and find it may be possible to develop more compact reactors based on the ST approach.

The multiplicity distribution of projectile protons and multiplicity correlations between black particles, grey particles, shower particles, compound particles, heavily ionized track particles, projectile helium fragments and projectile spectator protons in 84Kr-emulsion collisions at 1.7 A GeV are investigated. It is found that the projectile spectator proton multiplicity distribution becomes broader with increasing target mass. The average multiplicity of shower particles and compound particles strongly depends on the number of projectile spectator protons, but the average multiplicity of black particles, grey particles and heavily ionized track particles weakly depends on the number of projectile spectator protons. The average multiplicity of projectile helium fragments increases linearly with increasing numbers of projectile spectator protons. Finally, the multiplicity distribution of projectile spectator protons obeys a KNO type of scaling law.

The characteristics of compound particle multiplicity distribution and multiplicity correlations between the compound particle and the grey particle, black particle, shower particle and heavily ionized track particle are investigated in this paper. It is found that the average multiplicities of the grey particle, black particle, shower particle and heavily ionized track particle increase with an increase in the number of compound particles, which can be explained by the impact geometrical model. The compound multiplicity distribution is observed to obey a Koba-Nielson-Olesen (KNO) type of scaling law.

In his Two New Sciences Galileo Galilei deals with the strength of objects, discussing how it changes with size. Our daily life offers many examples of effects due to change of dimensions and sometimes the consequences are unintuitive. This subject is really interesting for secondary school students and it can be presented through simple demonstrations.

With the experimental binding energies and configurations, the root-mean-square radii of p-wave valence neutron distributions for nuclei up to the second p-shell have been calculated in the framework of the single-particle potential model. By analyzing the relations between the radii and the binding energies, the scaling laws of p-wave valence neutron distributions are obtained. The quantitative conditions for the formation of p-wave neutron halos are deduced from these scaling laws. Based on the investigation on the probability of finding the valence nucleon outside the range of the interaction potential, a 2p3/2 halo state in 47S is anticipated for the first time. These obtained results might provide reference for searching for p-wave neutron halos in nuclei up to the second p-shell.

We study the time of equipartition, T eq , of energy in the one-dimensional Discrete Nonlinear Klein-Gordon (DNKG) equation in the framework of the Wave Turbulence (WT) theory. We discuss the applicability of the WT theory and show how this approach can explain qualitatively the route to thermalization and the scaling of the equipartition time as a function of the nonlinear parameter ϵ , defined as the ratio between the nonlinear and linear part of the Hamiltonian. Two scaling laws, and , for different degrees of nonlinearity are explained in terms of four-wave or six-wave processes in the WT theory. The predictions are verified with extensive numerical simulations varying the system size and the degree of nonlinearity.

Large systems of statistical physics often display properties that are independent of particulars that characterize their microscopic components. Universal dynamical patterns are manifested by the presence of scaling laws, which provides a common insight into governing physics of processes as vastly diverse as, e.g., growth of geological formations and processes underlying social patterns. Here, the author provides highlights from this vibrant arena of interdisciplinary research and suggests that times call for augmenting undergraduate physics curriculum.

We propose a conceptual analysis of stationary reaction–diffusion patterns with geometric spatial scaling laws as observed in Liesegang patterns. We give necessary and sufficient conditions for such patterns to occur in a robust fashion. The main ingredients are a skew-product structure in the kinetics, caused by irreversible chemical reactions, the existence of localized spikes and slowly decaying boundary layers. The proofs invoke the analysis of homoclinic orbits in orbit-flip position for spatial dynamics. In particular, we show that there exists a manifold of initial conditions that do not converge to the equilibrium but to the homoclinic orbit as a set.

In this paper the coherent-state approximation (CA) method is used to deal with the problem of the decoherence of the entangled states of two two-state systems. As the base of the discussion, the dissipation of one two-state system has been investigated at first. The improved results calculated by CA are given in the paper. It is shown that the right approaching behavior and scaling law have been obtained when CA is applied to the problem of dissipation of two two-state systems coupled with environment. The whole evolution process and calculated results of the decoherence of the entangled states show also the scaling law, right approaching behavior, and rich phenomenon.

Certain atomic transport and surface properties of liquid alkaline earth metals are reported. The diffusion and viscosity coefficient of liquid Mg, Ca, Sr and Ba metals are calculated using scaling laws which express the possible relationship between the excess entropy and transport properties of liquids. The excess entropies are computed by the two body approximation. As the input pseudopotential, the individual version of the electron–ion potential proposed by Fioalhais and coworkers which was originally developed for the solid state is used. Static structure factors are derived from the solution of the Ornstein-Zernike integral equation with Rogers–Young closure. From present investigations, it is shown that these scaling laws lead to a good estimation for the diffusion and viscosity coefficients of liquid alkaline earth metals.

Two catalyzed-birth models of n-species (n≥2) aggregates with exchange-driven growth processes are proposed and compared. In the first one, the exchange reaction occurs between any two aggregates Amk and Amj of the same species with the rate kernels Km(k,j) = Kmkj (m = 1,2,...,n, n≥2), and aggregates of An species catalyze a monomer-birth of Al species (l = 1,2,...,n−1) with the catalysis rate kernel Jl(k,j) = Jlkjυ. The kinetic behaviors are investigated by means of the mean-field theory. We find that the evolution behavior of aggregate-size distribution alk(t) of Al species depends crucially on the value of the catalysis rate parameter υ: (i) alk(t) obeys the conventional scaling law in the case of υ≤0, (ii) alk(t) satisfies a modified scaling form in the case of υ>0. In the second model, the mechanism of monomer-birth of An-species catalyzed by Al species is added on the basis of the first model, that is, the aggregates of Al and An species catalyze each other to cause monomer-birth. The kinetic behaviors of Al and An species are found to fall into two categories for the different υ: (i) growth obeying conventional scaling form with υ≤0, (ii) gelling at finite time with υ>0.

A complete eigenvalue spectrum of the parameters is given wherein some higher peak numbers of multipeak electromagnetic solitons in plasma are included. Moreover some interesting scaling laws are obtained for field energy via numerical approaches.

We consider a class of continuum models of epitaxial growth of thin films with two competing mechanisms: (1) the surface relaxation described by high-order gradients of the surface profile and (2) the Ehrlich–Schwoebel (ES) effect which is the asymmetry in the adatom attachment and detachment to and from atomic steps. Mathematically, these models are gradient-flows of some effective free-energy functionals for which large slopes are preferred for surfaces with low energy.We characterize the large-system asymptotics of the minimum energy and the magnitude of gradients of energy-minimizing surfaces. We also show that, in the large-system limit, the renormalized energy with an infinite ES barrier is the Γ-limit of those with a finite one, indicating the enhancement of the ES effect in a large system. Introducing λ-minimizers as energy minimizers among all candidates that are spatially λ-periodical, we show the existence of a sequence of such λ-minimizers that are in fact equilibriums. For the case of a finite ES effect, we prove the well-posedness of the initial-boundary-value problem of the continuum model and obtain bounds for the scaling laws of interface width, surface slope and energy, all of which characterize the surface coarsening during the film growth. We conclude with a discussion on the implications of our rigorous analysis.

The microworld inspires and fascinates many people. The behaviour of small animals in that miniature world differs from that of 'large' ones in the macroworld. For some people, the capacities of small animals are nearly miraculous. If we could imitate these small beings, our capabilities would increase many times over. Unfortunately, this is not reality. The behaviour of small animals is not miraculous. It is the aim of this paper to show why this is the case by taking into account so-called scaling laws, which allow us to deal with some science-fiction stories. These same scaling laws are used to study the morphology of the giant fictional animal King Kong.

Electrothermal devices exhibit increasing secondary effects upon downscaling. These effects alter their temperature profiles and thermal energy distributions. Based on scaling laws, we show that the Thomson effect is increased over Joule heating as the structures are sized down. Thermal models are upgraded to take into account this secondary effect, and finite element simulations together with experimental runs validate them.

Condensation-induced water drop growth was studied on a super-hydrophobic spike surface. The dynamics are described by three main stages depending on the size of the drop with respect to the different spike pattern length scales. The initial stage is characterized by nucleation of the drops at the bottom (cavities) of the spikes. During the intermediate stage, large drops are surrounded by smaller drops within the neighboring cavities in what is described as a "bright ring". This ring persists until coalescence occurs with the central drop. The last stage is characterized by Wenzel-type drops growing with scaling laws similar to that on a planar surface but with contact angle θ* ≈ 111°, lower than for deposited drops (θ = 164°). Condensation on spike surfaces does not retain anything of super-hydrophobicity, in contrast to super-hydrophobic square and strip patterns.

Investigation of the energy confinement in ohmic and lower hybrid current drive (LHCD) plasmas in HT-7 has been performed. In ohmic discharges at low densities the global energy confinement time τE increases almost linearly with the density, saturates at a critical density (2.5 × 1013/cm3 for HT-7) and is nearly constant at higher densities. The energy confinement time is in good agreement with the Neo-Alcator scaling law at different densities and currents. In the LHCD plasmas the global energy confinement time similar to that of the L-mode discharges has been observed to be in good agreement with the low confinement mode (L mode) scaling law of ITER89-P in higher electron density and plasma current.

Small tokamaks have an important role in fusion research. More than 40 small tokamaks are operational. Research on small tokamaks has created a scientific basis for the scaling-up to larger tokamaks. Well-known scientific and engineering schools, which are now determining the main directions of fusion science and technology, have been established through research on small tokamaks. Combined efforts within a network of small and medium size tokamaks will further enhance the contribution of small tokamaks. A new concept of interactive coordinated research using small tokamaks in the mainstream fusion science areas, in testing of new diagnostics, materials and technologies as well as in education, training and broadening of the geography of fusion research in the scope of the IAEA Coordinated Research Project, is presented.