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The paper is concerned with the p-Laplacian minimizing problem with critical Stein–Weiss type term, and a nonlocal nonlinear equation involving fractional p-Laplacian operator and critical Stein–Weiss type term. Then main difficulty is hard to get the compactness of bounded minimizing sequence (and bounded Palais–Smale sequence). By the refined Sobolev inequality with Lorentz norm, we establish a abstract theorem, which is the relatively compactness result of bounded symmetric decreasing sequence. And then, as applications, we prove the existence, decay and regular results for the problems. [ABSTRACT FROM AUTHOR]

This paper is devoted to an initial-boundary value problem for a class of p -Kirchhoff type parabolic equations. Firstly, we consider this problem with a general nonlocal coefficient M (‖ ∇ u ‖ p p) and a general nonlinearity k (t) f (u). A new finite time blow-up criterion is established, also, the upper and lower bounds for the blow-up time are derived. Secondly, we deal with the case that M (‖ ∇ u ‖ p p) = a + b ‖ ∇ u ‖ p p , k (t) ≡ 1 and f (u) = | u | q − 1 u , which was considered by Li and Han [Math. Model. Anal. 2019; 24: 195-217] only for q > 2 p − 1. The threshold results for the existence of global and finite time blow-up solutions to this problem are obtained for the case 1 < q ≤ 2 p − 1 , which, together with the results given by Li and Han, shows that q = 2 p − 1 is critical for the existence of finite time blow-up solutions to this problem. These results partially generalize and extend some recent ones in previous literature. [ABSTRACT FROM AUTHOR]

I use critical phenomenological resources in Tetsurō Watsuji and Sarah Ahmed to explore the spatial origin of some social impairments in Autistic Spectrum Disorder (ASD). I argue that a critical phenomenological perspective puts pressure on the idea that social impairments in ASD are exclusively (or even primarily) neurocognitive deficits that can be addressed by focusing on cognitive factors internal to the autistic person - for example, training them to adopt a more neurotypical approach to social cognition. Instead, I argue that the structure and character of some neurotypical spaces may play a regulative role in shaping aspects of at least some of the social impairments autistic people exhibit when they inhabit these spaces. I also briefly consider some possible therapeutic applications of this critical phenomenological approach. [ABSTRACT FROM AUTHOR]

Abstract We consider a heat semigroup with an inverse square potential and prove critical dissipative estimates including the endpoint case. Some application to a nonlinear heat equation with an inverse square potential is also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of infinitely many solutions of the following degenerate magnetic fractional problem involving critical Sobolev‐Hardy nonlinearities: M([u]s,A2)(−△)Asu=λf(x,|u|)u+|u|2s∗(α)−2u|x|α,inRN,where s ∈ (0,1), N > 2s, 2s∗(α)=2(N−α)N−2s is the fractional Hardy‐Sobolev critical exponent with α ∈ [0,2s), λ is a positive real parameter, M:R0+→R0+ is a Kirchhoff function, A:RN→RN is a magnetic potential function, and (−△)As is the fractional magnetic operator. By using the new version of symmetric mountain pass theorem of Kajikiya, we prove that the problem admits infinitely many solutions for the suitable value of λ. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we investigate the following Choquard equation − Δ u + u = (I α ∗ | u | N + α N − 2 ) | u | N + α N − 2 − 2 u + g (u) in R N , where N ⩾ 3 , α ∈ (0 , N) , I α is the Riesz potential and g is a given function. If g satisfies the general subcritical growth conditions, we obtain the existence of a positive ground state solution. [ABSTRACT FROM AUTHOR]

This study investigates the behaviour of blow-up and global similarity solutions for the nonlinear dispersion equation (NDE), u t = ( | u | n u ) x x x ± ( | u | p − 1 u ) x x in R × R + , n > 0 and p > n + 1 , and attempts to give some aspects analytically and numerically. One can easily see that the proposed NDE is more complicated and hence more difficult than the corresponding semilinear equation. We will particularly pay attention to the first critical exponent p = p 0 = n + 2 , which helps us to simplify the rescaled nonlinear equation and compare with semilinear ones studied in the literature. [ABSTRACT FROM AUTHOR]

This paper is concerned with a semilinear elliptic inhomogeneous equation Δ u − u + ( 1 + a | x | q ) u p = 0 introduced in Chen and Kolokolnikov (2012) [2] as a simple prototype of self-replication in more complex reaction–diffusion systems. Under certain conditions on p , q , it was previously shown by Chen–Kolokolnikov that the equation has no radial ground state solution when the control parameter a is increased above some threshold. This property is important for the existence of a saddle-node bifurcation proposed in the Nishiura–Ueyema conditions, which is believed to be necessary for an initiation of a self-replication event. In this paper, we generalize Chen–Kolokolnikov's result to non-radial positive solutions by proving a Liouville-type nonexistence theorem. Furthermore we derive a local version of this nonexistence theorem for solutions defined on a bounded ball. Our result indicates that critical values of q derived in Ding and Ni (1986) [3] are also crucial for the existence and nonexistence problem of positive solutions when the space dimension N ≥ 3 . [ABSTRACT FROM AUTHOR]

In this paper, we consider positive solutions of a Cauchy problem for the following quasilinear degenerate parabolic equation with weighted non- local sources: ... where N ≥ 1, p > 2, q, r ≥ 1, s ≥ 0, and r + s > 1. We classify global and non-global solutions of the equation in the coexistence region by finding a new second critical exponent via the slow decay asymptotic behavior of an initial value at spatial infinity, and the life span of non-global solution is studied. [ABSTRACT FROM AUTHOR]

Asymptotic properties of the symmetric and asymmetric naming games have been studied under some restrictions in a community of agents. In one version, the vocabulary sizes of the agents are restricted to finite capacities. In this case, compared to the original naming games, the dynamics takes much longer time for achieving the consensus. In the second version, the symmetric game starts with a limited number of distinct names distributed among the agents. Three different quantities are measured for a quantitative comparison, namely, the maximum value of the total number of names in the community, the time at which the community attains the maximal number of names, and the global convergence time. Using an extensive numerical study, the entire set of three power law exponents characterizing these quantities are estimated for both the versions which are observed to be distinctly different from their counter parts of the original naming games. [ABSTRACT FROM AUTHOR]

The article talks about the importance of phase transitions and critical phenomena. It mentions its importance in femtometre scale in quantum chromodynamics to galaxy formation in the universe; and denaturation of bio-polymers to the magnetisation effects in storage media. It also discusses current research on phase transitions and critical phenomena in condensed-matter physics.

In this article, we find that µc ≡ 2N/(N(m - 1)+2) is the critical exponent for the asymptotic behavior of rescaled solutions tµ/²u(tβx, t) for the porous medium equation. [ABSTRACT FROM AUTHOR]

At the first time it was carried out the theoretical researches regarding pathways to get into a supercritical region at the ambient pressure with the main aim to avoid expensive and hazardous supercritical drying process and to make a silica aerogel production in whole more economical and commercial. These investigations based on fundamental knowledge about the critical phenomena in multicomponent systems. The representation of phase states in such systems by graphical images was used for the estimation ofLV(xL = xV) azeotrope influence onSLVandL˭Vequilibria. In the course of empiric selection of azeotropic mixtures the negative azeotropes advantage over positive ones was determined and grounded in theory. We report on the synthesis of hydrophobic silica aerogel by ambient pressure drying (APD) procedure, which involves two-step sol–gel process with tetraethyl orthosilicate (TEOS) as a silica precursor and isopropanol as the solvent and an elaborated flow chart using both types of azeotropes as the pore fluids. Guided by receiving our theoretical investigation, we obtained transparent crack-free silica aerogel samples with specific surface in the range of 711–913 m2/g, average pore diameter of ∼95–137 nm, and density of ca. 0.39–0.081 g/cm3. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the following fractional Schrödinger equations involving critical exponents: ( − Δ ) α u + V ( x ) u = k ( x ) f ( u ) + λ | u | 2 α ∗ − 2 u in R N , where ( − Δ ) α is the fractional Laplacian operator with α ∈ ( 0 , 1 ) , N ≥ 2 , λ is a positive real parameter and 2 α ∗ = 2 N / ( N − 2 α ) is the critical Sobolev exponent, V ( x ) and k ( x ) are positive and bounded functions satisfying some extra hypotheses. Based on the principle of concentration compactness in the fractional Sobolev space and the minimax arguments, we obtain the existence of a nontrivial radially symmetric weak solution for the above-mentioned equations without assuming the Ambrosetti–Rabinowitz condition on the subcritical nonlinearity. [ABSTRACT FROM AUTHOR]

Entropy, a term used in Physics to quantify the degree of randomness in a complex system, is shown to be relevant for portfolio diversification. The link between entropy and diversification lies in the notion of uncertainty. We introduce the concept of available diversification in an investment universe and of diversification curves. We build a framework for assembling a fully diversified risk parity-like portfolio with a fundamental-based high-conviction strategy, through a constrained entropy-maximisation process by which a portion of potential portfolio return is swapped for extra diversification. The main results of this study are:• mean-variance optimised portfolios are highly concentrated and scarcely related to the asset return assumptions;• few basis points of expected returns can be converted into a huge amount of extra diversification that making the portfolio allocation more robust to parameter uncertainty;• on a more conceptual ground, we investigate the relationship between portfolio risk and diversification concluding that they should be managed distinctly.The empirical analysis presented in this work shows that entropy is a useful means to alleviate the lack of diversification of portfolios on the efficient frontier. [ABSTRACT FROM AUTHOR]

We have studied the magnetic and magnetocaloric properties of the La 0.65 Eu 0.05 Sr 0.3 Mn 0.95 Cr 0.05 O 3 manganite prepared by using a soft chemical method (Pechini method). This compound presents a single magnetic transition from ferromagnetic (FM) to paramagnetic (PM) phase at T C = 338 K. To investigate the nature of the magnetic phase transition, found to be of second-order, a detailed critical exponent study has been performed by dc-magnetization M (H,T) measurements around the Curie temperature T C . Modified Arrott plot method has been adopted to study the critical behavior of the compound around its transition region. The values deduced for the critical exponents β , γ and δ are close to the theoretical prediction of the mean-field model, indicating that the magnetic interactions are long-range. Moreover, we have investigated the validity and usefulness of the theoretical modeling in our compound La 0.65 Eu 0.05 Sr 0.3 Mn 0.95 Cr 0.05 O 3 based on the mean-field analysis of the magnetic entropy change (−Δ S M ) versus the magnetization data. Results obtained through this approach are compared to those obtained from extrapolation of the Arrott curves. An excellent agreement is found between the experimental (−Δ S M ) and the one estimated by Landau theory. [ABSTRACT FROM AUTHOR]

In this article, we study a class of semilinear elliptic equations involving Hardy-Sobolev critical exponents and Hardy-Sobolev-Maz'ya poten-tial in a bounded domain. We obtain the existence of positive solutions using the Mountain Pass Lemma. [ABSTRACT FROM AUTHOR]

In this paper we consider a class of elliptic problems of p-Kirchhoff type with critical exponent in bounded domains and new results as regards the existence and multiplicity of solutions are obtained by using the concentration-compactness principle and variational method. [ABSTRACT FROM AUTHOR]

Anisotropic magnetoresistance measurements show that the magnetization state in epitaxial Ni80Fe20/Fe50Mn50 bilayers exhibits aging over a wide range of temperatures and magnetic fields. The observed power-law time dependence indicates that aging is characterized by a wide range of activation time scales. Aging characteristics are also inconsistent with a superposition of independent activation barriers expected for Arrhenius-type relaxation. The observed effects indicate a fundamental connection with the critical phenomena in complex condensed matter systems. [ABSTRACT FROM AUTHOR]

The critical phenomena around the Curie temperature ( TC ) of a polycrystalline La0.7Sr0.3Mn0.9Ti0.1O3 were studied based on magnetic field and temperature dependence of magnetization. Using the modified Arrott plot method, we determined the critical parameters TC \approx 234 K, \beta =0.372 \pm 0.012 , \gamma =1.171 \pm 0.112 , and \delta = 4.15 \pm 0.01 . With these critical values, the M(H) data of the sample fall onto two universal branches of the scaling function , where \varepsilon = (T-T_{C})/T_{C} , and f_{+} for T > TC and f- for T < TC . This pointed to the existence of a short-range ferromagnetic (FM) order in La0.7Sr0.3Mn0.9Ti0.1O3, which is attributed to FM clusters persisting in a wide temperature range, even above T_C . Electron-spin-resonance spectra affirmed the presence of the FM clusters at temperatures as high as T = T\mathrm {min}(\approx 1.3 ~TC) , above which the sample is completely paramagnetic. Based on the M(H) data, we also calculated the magnetic-entropy change ( \Delta Sm) , which reached a maximum ( \vert \Delta S\mathrm {max}\vert ) \approx 4.3 J/kg \cdot K) around the {\rm T}_{C} , corresponding to the relative cooling power of \sim 200 J/kg for a field change \Delta H = 50 ~\textrm kOe . A linear relationship \vert \Delta S\mathrm {max}\vert \propto H^{n} is achieved with a local exponent $n = 0.59$ determined from $n = 1+ (\beta - 1)/(\beta + \gamma)$ , indicative of a short-range FM system. [ABSTRACT FROM AUTHOR]

We report a study of the critical phenomena of perovskite-manganite compound La 0.6 Pr 0.1 Sr 0.3 MnO 3 around the Curie temperature. Experimental results based on magnetic measurements using Banerjee criterion reveals that the sample exhibits a second-order paramagnetic–ferromagnetic transition. The critical behavior analysis and the Kouvel–Fisher method suggests that the critical phenomena around the critical point can be correctly described by the 3D-Heisenberg model. Critical exponents were estimated and found β =0.354±0.009 and γ =1.264±0.035 at T C =325.5±0.443 K. The critical exponent δ is determined separately from the isothermal magnetization at T C and evaluated to δ =4.934±0.0004. These critical exponents obey the Widom scaling relation δ =1 ‏ + γ / β . Based on the critical exponents, the magnetization–field–temperature ( M–H–T ) data around T C collapses into two curves obeying the single scaling equation M ( H , ε ) = | ε | β f ± ( H / | ε | β + γ ) where ε =( T−T C )/ T C is the reduced temperature. [ABSTRACT FROM AUTHOR]

We consider the linear stochastic recursion $$x_{i+1} = a_{i}x_{i}+b_{i}$$ where the multipliers $$a_i$$ are random and have Markovian dependence given by the exponential of a standard Brownian motion and $$b_{i}$$ are i.i.d. positive random noise independent of $$a_{i}$$ . Using large deviations theory we study the growth rates (Lyapunov exponents) of the positive integer moments $$\lambda _q = \lim _{n\rightarrow \infty } \frac{1}{n} \log \mathbb {E}[(x_n)^q]$$ with $$q\in \mathbb {Z}_+$$ . We show that the Lyapunov exponents $$\lambda _q$$ exist, under appropriate scaling of the model parameters, and have non-analytic behavior manifested as a phase transition. We study the properties of the phase transition and the critical exponents using both analytic and numerical methods. [ABSTRACT FROM AUTHOR]

Distribution functions for systems in nonequilibrium steady states are usually determined through detailed experiments, both in numerical and real-life settings in the laboratory. However, for a protocol-driven distribution function, it is usually prohibitive to perform such detailed experiments for the entire range of the protocol. In this article we show that distribution functions of nonequilibrium steady states (NESS) evolving under a slowly varying protocol can be accurately obtained from limited data and the closest known detailed state of the system. In this manner, one needs to perform only a few detailed experiments to obtain the nonequilibrium distribution function for the entire gamut of nonlinearity. We achieve this by maximizing the relative entropy functional (MaxRent) subject to constraints supplied by the problem definition and new measurements. MaxRent is found to be superior to the principle of maximum entropy (MaxEnt), which maximizes Shannon's informational entropy for estimating distributions but lacks the ability to incorporate additional prior information. The MaxRent principle is illustrated using a toy model of ϕ4 thermal conduction consisting of a single lattice point. An external protocol controlled position-dependent temperature field drives the system out of equilibrium. Two different thermostatting schemes are employed: the Hoover-Holian deterministic thermostat (which produces multifractal dynamics under strong nonlinearity) and the Langevin stochastic thermostat (which produces phase-space-filling dynamics). Out of the 80 possible states produced by the protocol, we assume that four states are known to us in detail, one of which is used as input into MaxRent at a time. We find that MaxRent approximates the phase-space density functions for every value of the protocol, even when they are far from the known distribution. MaxEnt, however, is unable to capture the fine details of the phase-space distribution functions. We expect this method to be useful in other external protocol-driven nonequilibrium cases as well, making it unnecessary to perform detailed experiments for all values of the protocol when one wishes to obtain approximate distributions. [ABSTRACT FROM AUTHOR]

Scaling analysis, in which one infers scaling exponents and a scaling function in a scaling law from given data, is a powerful tool for determining universal properties of critical phenomena in many fields of science. However, there are corrections to scaling in many cases, and then the inference problem becomes ill-posed by an uncontrollable irrelevant scaling variable. We propose a new kernel method based on Gaussian process regression to fix this problem generally. We test the performance of the new kernel method for some example eases. In all cases, when the precision of the example data increases, inference results of the new kernel method correctly converge. Because there is no limitation in the new kernel method for the scaling function even with corrections to scaling, unlike in the conventional method, the new kernel method can be widely applied to real data in critical phenomena. [ABSTRACT FROM AUTHOR]

The tasks posed for renormalization group theory (RGT) within statistical physics by critical phenomena theory in the 1960's are set out briefly in contradistinction to quantum field theory (QFT), which was the origin for Ken Wilson's concerns. Kadanoff's 1966 block spin scaling picture and its difficulties are presented; Wilson's early vision of flows is described from the author's perspective. How Wilson's subsequent breakthrough ideas, published in 1971, led to the epsilon expansion and the resulting clarity is related. Concluding sections complete the general picture of flows in a space of Hamiltonians, universality and scaling. The article represents a 40% condensation (but with added items) of an earlier account: Rev. Mod. Phys. 70, 653-681 (1998). [ABSTRACT FROM AUTHOR]

We investigate time-independent disorder on several two-dimensional discrete-time quantum walks. We find numerically that, contrary to claims in the literature, random onsite phase disorder, spin-dependent or otherwise, cannot localize the Hadamard quantum walk; rather, it induces diffusive spreading of the walker. In contrast, split-step quantum walks are generically localized by phase disorder. We explain this difference by showing that the Hadamard walk is a special case of the split-step quantum walk, with parameters tuned to a critical point at a topological phase transition. We show that the topological phase transition can also be reached by introducing strong disorder in the rotation angles. We determine the critical exponent for the divergence of the localization length at the topological phase transition, and find v = 2.6, in both cases. This places the two-dimensional split-step quantum walk in the universality class of the quantum Hall effect. [ABSTRACT FROM AUTHOR]

The coastal erosion along the world's coastlines is a natural process that occurs through the actions of marine and subaerial physico-chemical phenomena, waves, tides, and currents. The development of cliff erosion predictive models is limited due to the complex interactions between environmental processes and material properties over a wide range of temporal and spatial scales. As a result of this erosive action, gravity driven mass movements occur and the coastline moves inland. Like other studied earth natural and synthetically modelled phenomena characterized as self-organized critical (SOC), the recession of the cliff has a seemingly random, sporadic behavior, with a wide range of yearly recession rate values probabilistically distributed by a power-law. Usually, SOC systems are defined by a number of scaling features in the size distribution of its parameters and on its spatial and/or temporal pattern. Particularly, some previous studies of derived parameters from slope movements catalogues, have allowed detecting certain SOC features in this phenomenon, which also shares the recession of cliffs. Due to the complexity of the phenomenon and, as for other natural processes, there is no definitive model of recession of coastal cliffs. In this work, various analysis techniques have been applied to identify SOC features in the distribution and pattern to a particular case: the Holderness shoreline. This coast is a great case study to use when examining coastal processes and the structures associated with them. It is one of World's fastest eroding coastlines (2 m/yr in average, max observed 22 m/yr). Cliffs, ranging from 2 m up to 35 m in height, and made up of glacial tills, mainly compose this coast. It is this soft boulder clay that is being rapidly eroded and where coastline recession measurements have been recorded by the Cliff Erosion Monitoring Program (East Riding of Yorkshire Council, UK). The original database has been filtered by grouping contiguous sections, with similar geomorphological and dynamic features, to configure a complete and suitable catalogue of yearly recession rates (in m/yr) to analyze. Results show SOC fingerprint characteristics in the limited range scaling of the probability distribution function, in the variographic analysis and in the zero-mean Gaussian distribution of the Fourier coefficients. Therefore it cannot be neglected the possibility that Holderness cliffs behave as a SOC system. According to the discussed results, predictability possibilities of sea-cliff recession phenomena have been concluded. [ABSTRACT FROM AUTHOR]

We study the following elliptic equation with two Sobolev-Hardy critical exponents {... x ∈ Ω, u = 0, x ∈ ∂Ω, where Ω ⊂ ℝN (N ≥ 3) is a bounded smooth domain, 0 ∈ ∂Ω, 0 ≤ s2 < s1 ≤ 2 and 2* (s) := 2(N-s) / N-2. In this paper, by means of variational methods, we obtain the existence of sign-changing solutions if H(0) < 0, where H(0) denote the mean curvature of ∂Ω at 0. [ABSTRACT FROM AUTHOR]

Representing the fluid flow as a collection of coherent structures of various size, the statistical temperature of the flow state is determined as a function of the Reynolds number. It is shown that at small Reynolds numbers, associated with laminar states, the temperature is positive, while at large Reynolds numbers, associated with turbulent states, it is negative. At intermediate Reynolds numbers, the temperature changes from positive to negative as the size of the coherent structures increases, similar to what was predicted by Onsager for a system of parallel point-vortices in an inviscid fluid. It is also shown that in the range of intermediate Reynolds numbers the temperature exhibits a critical divergence. [ABSTRACT FROM AUTHOR]

We use the conformal bootstrap to perform a precision study of the operator spectrum of the critical 3d Ising model. We conjecture that the 3d Ising spectrum minimizes the central charge $$c$$ in the space of unitary solutions to crossing symmetry. Because extremal solutions to crossing symmetry are uniquely determined, we are able to precisely reconstruct the first several $$\mathbb {Z}_2$$ -even operator dimensions and their OPE coefficients. We observe that a sharp transition in the operator spectrum occurs at the 3d Ising dimension $$\Delta _\sigma = 0.518154(15)$$ , and find strong numerical evidence that operators decouple from the spectrum as one approaches the 3d Ising point. We compare this behavior to the analogous situation in 2d, where the disappearance of operators can be understood in terms of degenerate Virasoro representations. [ABSTRACT FROM AUTHOR]

We consider the $$n$$ -component $$|\varphi |^4$$ spin model on $${\mathbb {Z}}^4$$ , for all $$n \ge 1$$ , with small coupling constant. We prove that the susceptibility has a logarithmic correction to mean field scaling, with exponent $$\frac{n+2}{n+8}$$ for the logarithm. We also analyse the asymptotic behaviour of the pressure as the critical point is approached, and prove that the specific heat has fractional logarithmic scaling for $$n =1,2,3$$ ; double logarithmic scaling for $$n=4$$ ; and is bounded when $$n>4$$ . In addition, for the model defined on the $$4$$ -dimensional discrete torus, we prove that the scaling limit as the critical point is approached is a multiple of a Gaussian free field on the continuum torus, whereas, in the subcritical regime, the scaling limit is Gaussian white noise with intensity given by the susceptibility. The proofs are based on a rigorous renormalisation group method in the spirit of Wilson, developed in a companion series of papers to study the 4-dimensional weakly self-avoiding walk, and adapted here to the $$|\varphi |^4$$ model. [ABSTRACT FROM AUTHOR]

It is well know that systems with an interaction decaying as a power of the distance may have critical exponents that are different from those of short-range systems. The boundary between long-range and short-range is known, however the behavior in the crossover region is not well understood. In this paper we propose a general form for the crossover function and we compute it in a particular limit. We compare our predictions with the results of numerical simulations for two-dimensional long-range percolation. [ABSTRACT FROM AUTHOR]

The study of the statistical properties of random matrices of large size has a long history, dating back to Wigner, who suggested using Gaussian ensembles to give a statistical description of the spectrum of complex Hamiltonians and derived the famous semi-circle law, the work of Dyson and many others. Later, 't Hooft noticed that, in $$SU(N)$$ non-Abelian gauge theories, tessalated surfaces can be associated to Feynman diagrams and that the large $$N$$ expansion corresponds to an expansion in successive topologies. Following this observation, some times later, it was realized that some ensembles of random matrices in the large N expansion and the so-called double scaling limit could be used as toy models for quantum gravity: 2D quantum gravity coupled to conformal matter. This has resulted in a tremendous expansion of random matrix theory, tackled with increasingly sophisticated mathematical methods and number of matrix models have been solved exactly. However, the somewhat paradoxical situation is that either models can be solved exactly or little can be said. Since the solved models display critical points and universal properties, it is tempting to use renormalization group ideas to determine universal properties, without solving models explicitly. Initiated by Brézin and Zinn-Justin, the approach has led to encouraging results, first for matrix integrals and then quantum mechanics with matrices, but has not yet become a universal tool as initially hoped. In particular, general quantum field theories with matrix fields require more detailed investigations. To better understand some of the encountered difficulties, we first apply analogous ideas to the simpler $$O(N)$$ symmetric vector models, models that can be solved quite generally in the large $$N$$ limit. Unlike other attempts, our method is a close extension of Brézin and Zinn-Justin. Discussing vector and matrix models with similar approximation scheme, we notice that in all cases (vector and matrix integrals, vector and matrix path integrals in the local approximation), at leading order, non-trivial fixed points satisfy the same universal algebraic equation, and this is the main result of this work. However, its precise meaning and role have still to be better understood. [ABSTRACT FROM AUTHOR]

A personal and subjective recollection, concerning mainly Wilson's lectures delivered over the spring of 1972 at Princeton University (summary of a talk at Cornell University on November 16, 2013 at the occasion of the memorial Kenneth G. Wilson conference). [ABSTRACT FROM AUTHOR]

Kenneth Wilson had an enormous impact on the renormalization group and field theories in general. I had the great pleasure to work in three fields to which he contributed essentially: Critical phenomena, gauge-invariance in duality and confinement, and flow equations and similarity renormalization. [ABSTRACT FROM AUTHOR]

Charge, spin, and lattice degrees of orderings are of great interest in the layered quantum material RFe2O4 (R 5 Y, Er, Yb, Tm, and Lu) system. Recently many unique properties have been found using various experimental methods. However so far the nature of the two-dimensional (2D) charge ordering (CO) state is not clear and no observation of its fine structure in energy has been reported. Here we report unambiguous observation of double 2D CO states at relatively high temperature in a polycrystalline Er0.1Yb0.9Fe2O4 using Raman scattering. The energy gaps between the 3D and the double 2D states are 170 meV (41.2 THz) and 193 meV (46.6 THz), respectively. We also observed a spin ordering (SO) state at below 210 K with characteristic energy of 45 meV (10.7 THz). Our investigation experimentally identified new fine structures of quantum orders in the system, which also extends the capability of optical methods in investigating other layered quantum materials. [ABSTRACT FROM AUTHOR]

Abstract: The stationary state solutions of the Ising-typed thin films with different layers in the presence of an external oscillatory field are examined within the effective-field theory. The study focuses on the effects of external field frequency and amplitude on the overall behavior. Particular attention is paid on evolution of the special point with dynamic field frequency corresponding to critical temperature of the three-dimensional infinite bulk system where the surface and modified exchange parameters are of no importance. Some findings such as surface enhancement phenomenon and effect of thickness on the dynamic process are introduced together with some other well known characteristics. An attempt is made to explain the relations between the competing time scales (intrinsic microscopic relaxation time of the system and the time period of the external oscillatory field) and frequency dispersion of the critical temperature coordinate of the special point. [Copyright &y& Elsevier]

Self-consistent dynamical approximations for strongly correlated fermion systems are particularly successful in capturing the dynamical competition of local correlations. In these, the effect of spatially extended degrees of freedom is usually only taken into account in a mean field fashion or as a secondary effect. As a result, critical exponents associated with phase transitions have a mean field character. Here we demonstrate that diagrammatic multiscale methods anchored around local approximations are indeed capable of capturing the non-mean-field nature of the critical point of the lattice model encoded in a nonvanishing anomalous dimension and of correctly describing the transition to mean-field-like behavior as the number of spatial dimensions increases. [ABSTRACT FROM AUTHOR]

The critical behavior of the three-dimensional random-bond Potts models with many states (and) is studied by the finite-time dynamic method. We evaluate the static and dynamic critical exponents as well as the critical temperatures. The asymptotic critical behavior foris identified with, andbut the exponents obtained forwithare the only effective ones. Our results support thatis positive and the intrinsiccan escape the boundsuggested by previous work. By comparing with the results for various, we infer that the asymptotic critical behavior of the three-dimensional random-bond Potts model with many states is-dependent. [ABSTRACT FROM AUTHOR]

Utilizing a modified embedded atom method potential, we performed large-scale classical molecular dynamics simulations (with up to 50 million atoms) to investigate the response of Ga single crystals to shock compression along the three major orientations of the orthorhombic A11 ground state, i.e., [001], [010], and [100]. For weak shocks with particle velocity up<300 m/s, these defect-free single crystals respond elastically, but for stronger shocks, they undergo a structural phase transformation and then (for even stronger shocks) melt. For intermediate shock strengths (300m/s

Materials undergoing reversible solid-to-solid martensitic phase transformations are desirable for applications in medical sensors and actuators, eco-friendly refrigerators and energy conversion devices. The ability to pass back and forth through the phase transformation many times without degradation of properties (termed 'reversibility') is critical for these applications. Materials tuned to satisfy a certain geometric compatibility condition have been shown to exhibit high reversibility, measured by low hysteresis and small migration of transformation temperature under cycling. Recently, stronger compatibility conditions called the 'cofactor conditions' have been proposed theoretically to achieve even better reversibility. Here we report the enhanced reversibility and unusual microstructure of the first martensitic material, Zn45Au30Cu25, that closely satisfies the cofactor conditions. We observe four striking properties of this material. (1) Despite a transformation strain of 8%, the transformation temperature shifts less than 0.5 °C after more than 16,000 thermal cycles. For comparison, the transformation temperature of the ubiquitous NiTi alloy shifts up to 20 °C in the first 20 cycles. (2) The hysteresis remains approximately 2 °C during this cycling. For comparison, the hysteresis of the NiTi alloy is up to 70 °C (refs 9, 12). (3) The alloy exhibits an unusual riverine microstructure of martensite not seen in other martensites. (4) Unlike that of typical polycrystal martensites, its microstructure changes drastically in consecutive transformation cycles, whereas macroscopic properties such as transformation temperature and latent heat are nearly reproducible. These results promise a concrete strategy for seeking ultra-reliable martensitic materials. [ABSTRACT FROM AUTHOR]

DNA sequencing is the basic workhorse of modern day biology and medicine. Shotgun sequencing is the dominant technique used: many randomly located short fragments called reads are extracted from the DNA sequence, and these reads are assembled to reconstruct the original sequence. A basic question is: given a sequencing technology and the statistics of the DNA sequence, what is the minimum number of reads required for reliable reconstruction? This number provides a fundamental limit to the performance of any assembly algorithm. For a simple statistical model of the DNA sequence and the read process, we show that the answer admits a critical phenomenon in the asymptotic limit of long DNA sequences: if the read length is below a threshold, reconstruction is impossible no matter how many reads are observed, and if the read length is above the threshold, having enough reads to cover the DNA sequence is sufficient to reconstruct. The threshold is computed in terms of the Renyi entropy rate of the DNA sequence. We also study the impact of noise in the read process on the performance. [ABSTRACT FROM AUTHOR]

In this paper we present an approach that permits to study the behavior of the nematic phase's order parameter exponent (β) for all temperatures of the phase; our method makes an independent calculation ofβfor each temperature valueT. Here use hypothetical data to analyze the consistence of the results, the limitation of the experimental data usability and the influences of the experimental errors on theβ(T) curves. After that, we use experimental data to show that the order parameter critical-like exponent presents a constant behavior along the entire domain of the nematic phase. [ABSTRACT FROM AUTHOR]

Accurate prediction of local properties of transition-metal nanoalloys from the electronic structure is a challenge for building new materials with novel properties in a controlled way. To this aim, developing unified descriptions of local electronic states as a function of a minimal set of parameters is the way to disentangle structural and chemical effects. This is achieved here within sp-d tight-binding calculations using a self-consistent procedure taking into account both the changes in the structural environment (coordination effect) and in the chemical one (alloying effect). From these calculations, trends in the distributions of energy electronic states are obtained through band shifts and widths allowing one to study in a systematic way ordering tendency and local properties in nanoalloys in a wide range of sizes and structural complexity. [ABSTRACT FROM AUTHOR]

Abstract: We obtain the uniqueness and blow-up profile of positive least energy solution of a critical exponent problem with Hardy potential in a ball. [Copyright &y& Elsevier]

We apply simulated tempering and magnetizing (STM) Monte Carlo simulations to the two-dimensional threestate Potts model in an external magnetic field in order to investigate the crossover scaling behaviour in the temperature-field plane at the Potts critical point and towards the Ising universality class for negative magnetic fields. Our data set has been generated by STM simulations of several square lattices with sizes up to 160×160 spins, supplemented by conventional canonical simulations of larger lattices at selected simulation points. We present careful scaling and finite-size scaling analyses of the crossover behaviour with respect to temperature, magnetic field and lattice size. [ABSTRACT FROM AUTHOR]