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Quantum Chromodynamics predicts that the strong coupling strength α s decreases with increasing energy or momentum transfer, and vanishes at asymptotically high energies. The history and the status of experimental tests of asymptotic freedom are summarised in this review. [ABSTRACT FROM AUTHOR]

Recently, Ai, Bender and Sarkar gave a prescription on how to obtain -symmetric field theory results from an analytic continuation of Hermitian field theories. We perform this analytic continuation for the massless (critical) O (N) model with quartic interaction in (3+1) dimensions. In the large- N limit, this theory is exactly solvable, and has negative β -function in the ultraviolet, and a stable bound state in the infrared. The coupling diverges at a scale Λ c , but can be continued into the far infrared. At finite temperature, the theory exhibits two phases separated by a second-order phase transition near T c ≃ Λ c / e . [ABSTRACT FROM AUTHOR]

In this paper, we study the Kelvinons, which are monopole ring solutions to the Euler equations, regularized as the Burgers vortex in the viscous core. There is finite anomalous dissipation in the inviscid limit. However, in the anomalous Hamiltonian, some terms are growing as logarithms of Reynolds number; these terms come from the core of the Burgers vortex. In our theory, the turbulent multifractal phenomenon is similar to asymptotic freedom in QCD, with these logarithmic terms summed up by an RG equation. The small effective coupling does not imply small velocity; on the contrary, velocity is large compared to its fluctuations, which opens the way for a quantitative theory. In the leading order in the perturbation theory in this effective coupling constant, we compute running multifractal dimensions for high moments of velocity circulation, which is in good agreement with the data for quantum Turbulence and available data for classical Turbulence. The logarithmic dependence of fractal dimensions on the loop size comes from the running coupling in anomalous dimensions. This slow logarithmic drift of fractal dimensions would be barely observable at Reynolds numbers achievable at modern DNS. [ABSTRACT FROM AUTHOR]

The partition function of four-dimensional Euclidean, non-supersymmetric SU (2) Yang–Mills theory is calculated in the perturbative and weak coupling regime, i.e., in a small open ball about the flat connection and when the gauge coupling constant acquires a small but finite value. The computation is based on various known inequalities, valid only in four dimensions, providing two-sided estimates for the exponentiated Yang–Mills action in terms of the L 2 -norm of the derivative of the gauge potential only; these estimates then give rise to Gaußian-like infinite- dimensional formal integrals involving the Laplacian and hence can be computed via zeta-function and heat kernel techniques. It then turns out that these formal integrals give a sharp value for the partition function in the aforementioned perturbative and weak coupling regime of the theory. In the resulting expression for the partition function, the original classical value of the coupling constant is shifted to a smaller one which can be interpreted as the manifestation, in this approach, of a non-trivial β -function and asymptotic freedom in pure non-Abelian gauge theories. [ABSTRACT FROM AUTHOR]

A recently developed variational resummation technique incorporating renormalization group properties has been shown to solve the scale dependence problem that plagues the evaluation of physical observables. This method is used in the present work to evaluate thermodynamical quantities within the two‐dimensional nonlinear sigma model, which shares some features with Yang‐Mills theories like asymptotic freedom, trace anomaly, and the nonperturbative generation of a mass gap. Besides the fact that nonperturbative results can be readily generated solely by considering lowest‐order contributions, we also show that its next‐to‐leading correction indicates convergence to the sought‐after scale invariance. [ABSTRACT FROM AUTHOR]

A dynamics of quark-gluon plasmas has been defined by the evolution parameter, which at high energies depends on collision energy of atomic nuclei for appropriate multiplicities of secondary hadrons. The paper is based on the solution of evolution equation for patrons momentum distribution. A transition from regular propagation to irregular chaotic is an indicator of the quark-gluon plasma emerging. Nonlinear renormalization group equation has been solved by the method of Poincaré mappings. The equation is a model of the evolution of the momentum distribution of partons due to competing processes of their creation and fusion. As the energy increases, sequential bifurcation (doubling) of phase trajectories occurs, and scale-invariant fractal structures are to create. At sufficiently high energies of quarks and gluons, a dynamically determined quarkgluon system, corresponding to QGP, arises in space. There are also hadron-like structures. Quantum coherence effects follow by dynamic chaos. As a result, quarks and gluons merge into stable attractor structures with their subsequent decay into hadrons. The nonlinear equation introduced for quark-gluon cascade, which comprises dynamical chaos, has include effects of parton recombination. The chaotic dynamics has been connected specifically to the transverse momenta of partons. Clearly, the formation of dynamically determined stable structures should be unknown before, attractor mechanism of quark hadronization. [ABSTRACT FROM AUTHOR]

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This paper shows that below a critical value of dimensionality that lies between two and three, the potential between objects begins to fall as the energy levels increase. For dimensionality below two, the potential becomes constant irrespective of separation and the force between them disappears, which represents a new paradigm of asymptotic freedom. Since asymptotic freedom is at the basis of many applications such as those associated with strange metals, unconventional superconductors, and fractional quantum Hall states, the new paradigm can have novel applications. It also is of relevance to the study of anomalous mechanical effects that are important in metamaterials. [ABSTRACT FROM AUTHOR]

We provide a short characterization of p-asymptotic uniform smoothability and asymptotic uniform flatenability of operators and of Banach spaces. We use these characterizations to show that many asymptotic uniform smoothness properties pass to injective tensor products of operators and of Banach spaces. In particular, we prove that the injective tensor product of two asymptotically uniformly smooth Banach spaces is asymptotically uniformly smooth. We prove that for 1

Abstract In the framework of perturbative QCD and nonrelativistic bound state formalism, we calculate the production of B c and B c ⁎ mesons at the conditions of the CDF and LHCb experiments. We derive first estimations for the B c wave function from a comparison with the available data. [ABSTRACT FROM AUTHOR]

Abstract Fluctuations of conserved quantities such as baryon number, charge, and strangeness are sensitive to the correlation length of the hot and dense matter created in relativistic heavy-ion collisions and can be used to search for the QCD critical point. We report the first measurements of the moments of net-kaon multiplicity distributions in Au+Au collisions at s NN = 7.7 , 11.5, 14.5, 19.6, 27, 39, 62.4, and 200 GeV. The collision centrality and energy dependence of the mean (M), variance (σ 2), skewness (S), and kurtosis (κ) for net-kaon multiplicity distributions as well as the ratio σ 2 / M and the products Sσ and κ σ 2 are presented. Comparisons are made with Poisson and negative binomial baseline calculations as well as with UrQMD, a transport model (UrQMD) that does not include effects from the QCD critical point. Within current uncertainties, the net-kaon cumulant ratios appear to be monotonic as a function of collision energy. [ABSTRACT FROM AUTHOR]

In this research, a miniaturized humanoid robot is constructed to ride and pedal a bicycle of comparable size. The design of the controller for the robot to balance and steer the bicycle using the handlebar is of particular interest. The controller possesses the capability to estimate the uncertain center of gravity of the robot-bicycle system and then incorporate such an estimation to enhance control performance. A general control framework which can achieve asymptotic stability under uncertain measurement biases is adopted for controller design. Using the framework, the stability of the control system is analytically guaranteed and its control parameters can be determined in a systematic manner. Both simulations and experiments verify that the proposed controller can automatically counteract the mass imbalance in the robot-bicycle system and allow it to perform straight-line steering without using camera visual feedback. [ABSTRACT FROM AUTHOR]

We consider the Euler-Maruyama discretization of stochastic volatility model dSt = σtStdWt, dσt = ωσtdZt, t ∈ [0, T], which has been widely used in financial practice, where Wt,Zt, t ∈ [0, T], are two uncorrelated standard Brownian motions. Using asymptotic analysis techniques, the moderate deviation principles for log Sn (or log |Sn| in case Sn is negative) are obtained as n → ∞ under different discretization schemes for the asset price process St and the volatility process σt. Numerical simulations are presented to compare the convergence speeds in different schemes. [ABSTRACT FROM AUTHOR]

We exhibit a new concentration phenomenon for the supercritical problem - Δ ⁢ v = λ ⁢ v + | v | p - 2 ⁢ v in ⁢ Ω , v = 0 on ⁢ ∂ ⁡ Ω , -\Delta v=\lambda v+|v|^{p-2}v\quad\text{in }\Omega,\qquad v=0\quad\text{on }% \partial\Omega, as p → 2 N , m ∗ {p\rightarrow 2_{N,m}^{\ast}} from below, where 2 N , m ∗ := 2 ⁢ ( N - m ) N - m - 2 {2_{N,m}^{\ast}:=\frac{2(N-m)}{N-m-2}} , 1 ≤ m ≤ N - 3 {1\leq m\leq N-3} , is the so-called ( m + 1 ) {(m+1)} -th critical exponent. We assume that Ω is of the form Ω := { ( x 1 , x 2 ) ∈ ℝ m + 1 × ℝ N - m - 1 : ( | x 1 | , x 2 ) ∈ Θ } , \Omega:=\bigl{\{}(x_{1},x_{2})\in\mathbb{R}^{m+1}\times\mathbb{R}^{N-m-1}:(|x_% {1}|,x_{2})\in\Theta\bigr{\}}, where Θ is a bounded smooth domain in ℝ N - m {\mathbb{R}^{N-m}} such that Θ ¯ ⊂ ( 0 , ∞ ) × ℝ N - m - 1 {\overline{\Theta}\subset(0,\infty)\times\mathbb{R}^{N-m-1}}. Under some symmetry assumptions, we show that there exists λ ∗ ≥ 0 {\lambda_{\ast}\geq 0} such that for each λ ∈ ( - ∞ , λ ∗ ) ∪ { 0 } {\lambda\in(-\infty,\lambda_{\ast})\cup\{0\}} , there exist a sequence p k ∈ ( 2 , 2 N , m ∗ ) {p_{k}\in(2,2_{N,m}^{\ast})} with p k → 2 N , m ∗ {p_{k}\rightarrow 2_{N,m}^{\ast}} and a sequence of solutions v k {v_{k}} which concentrate and blow up along an m-dimensional sphere of minimal radius contained in ∂ ⁡ Ω {\partial\Omega} , developing a single sign-changing layer as p k → 2 N , m ∗ {p_{k}\rightarrow 2_{N,m}^{\ast}}. In contrast with previous results, the asymptotic profile of this layer on each space perpendicular to the blow-up sphere is not a sum of positive and negative bubbles, but a rescaling of a sign-changing solution to the critical problem - Δ ⁢ u = | u | 4 / ( N - m - 2 ) ⁢ u , u ∈ D 1 , 2 ⁢ ( ℝ N - m ) . -\Delta u=|u|^{{4}/({N-m-2})}u,\quad u\in D^{1,2}(\mathbb{R}^{N-m}). Moreover, λ ∗ > 0 {\lambda_{\ast}>0} if m ≥ 2 {m\geq 2}. [ABSTRACT FROM AUTHOR]

In this paper we establish a Harnack inequality for non-negative solutions of L ⁢ u = f ⁢ ( u ) {Lu=f(u)} where L is a non-divergence structure uniformly elliptic operator and f is a non-decreasing function that satisfies an appropriate growth conditions at infinity. [ABSTRACT FROM AUTHOR]

By a perturbative argument, we construct solutions for a plasma-type problem with two opposite-signed sharp peaks at levels 1 and - γ {-\gamma} , respectively, where 0 < γ < 1 {0<\gamma<1}. We establish some physically relevant qualitative properties for such solutions, including the connectedness of the level sets and the asymptotic location of the peaks as γ → 0 + {\gamma\to 0^{+}}. [ABSTRACT FROM AUTHOR]

A standard approach to estimating structural parameters in life‐cycle models imposes sufficient assumptions on the data to identify the “age profile” of outcomes, then chooses model parameters so that the model's age profile matches this empirical age profile. I show that this approach is both incorrect and unnecessary: incorrect, because it generally produces inconsistent estimators of the structural parameters, and unnecessary, because consistent estimators can be obtained under weaker assumptions. I derive an estimation method that avoids the problems of the standard approach. I illustrate the method's benefits analytically in a simple model of consumption inequality and numerically by reestimating the classic life‐cycle consumption model of Gourinchas and Parker (2002). [ABSTRACT FROM AUTHOR]

We have studied the existence of self-dual effective compact and true compacton configurations in Abelian Higgs models with generalized dynamics. We have named an effective compact solution the one whose profile behavior is very similar to the one of a compacton structure but still preserves a tail in its asymptotic decay. In particular, we have investigated the electrically neutral configurations of the Maxwell-Higgs and Born-Infeld-Higgs models and the electrically charged ones of the Chern-Simons-Higgs and Maxwell-Chern-Simons-Higgs models. The generalization of the kinetic terms is performed by means of dielectric functions in gauge and Higgs sectors. The implementation of the BPS formalism without the need to use a specific Ansatz has led us to the explicit determination for the dielectric function associated with the Higgs sector to be proportional to λϕ2λ-2, λ>1. Consequently, the followed procedure allows us to determine explicitly new families of self-dual potential for every model. We have also observed that, for sufficiently large values of λ, every model supports effective compact vortices. The true compacton solutions arising for λ=∞ are analytical. Therefore, these new self-dual structures enhance the space of BPS solutions of the Abelian Higgs models and they probably will imply interesting applications in physics and mathematics. [ABSTRACT FROM AUTHOR]

Schrödinger equation with potential − g / r 2 exhibits a limit cycle, described in the literature in a broad range of contexts using various regularizations of the singularity at r = 0 . Instead, we use the renormalization group transformation based on Gaussian elimination, from the Hamiltonian eigenvalue problem, of high momentum modes above a finite, floating cutoff scale. The procedure identifies a richer structure than the one we found in the literature. Namely, it directly yields an equation that determines the renormalized Hamiltonians as functions of the floating cutoff: solutions to this equation exhibit, in addition to the limit-cycle, also the asymptotic-freedom, triviality, and fixed-point behaviors, the latter in vicinity of infinitely many separate pairs of fixed points in different partial waves for different values of g . [ABSTRACT FROM AUTHOR]

We define the β -function of a perturbative quantum field theory in the mathematical framework introduced by Costello – combining perturbative renormalization and the BV formalism – as the cohomology class of a certain functional measuring scale dependence of the effective interaction. We show that the one-loop β -function is a well-defined element of the obstruction–deformation complex for translation-invariant and classically scale-invariant theories, and furthermore that it is locally constant as a function on the space of classical interactions and computable as a rescaling anomaly, or as the logarithmic one-loop counterterm. We compute the one-loop β -function in first-order Yang–Mills theory, recovering the famous asymptotic freedom for Yang–Mills in a mathematical context. [ABSTRACT FROM AUTHOR]

On the one hand, we prove that almost surely, for large dimension, there is no eigenvalue of a Hermitian polynomial in independent Wigner and deterministic matrices, in any interval lying at some distance from the supports of a sequence of deterministic probability measures, which is computed with the tools of free probability. On the other hand, we establish the strong asymptotic freeness of independent Wigner matrices and any family of deterministic matrices with strong limiting distribution. [ABSTRACT FROM AUTHOR]

The analytical method of the QCD running coupling constant is extended to a model with an all-order beta function which is inspired by the famous Novikov-Shifman-Vainshtein-Zakharov beta function of $$N=1$$ supersymmetric gauge theories. In the approach presented here, the running coupling is determined by a transcendental equation with non-elementary integral of the running scale $$\mu $$ . In our approach $$\alpha _\text {an}(0)$$ , which reads 0.30642, does not rely on any dimensional parameters. This is in accordance with results in the literature on the analytical method of the QCD running coupling constant. The new 'analytically improved' running coupling constant is also compatible with the property of asymptotic freedom. [ABSTRACT FROM AUTHOR]

Recent measurements of the proton–proton total cross section σ t o t at 7 and 8 TeV by the TOTEM and ATLAS Collaborations are characterized by some discrepant values: the TOTEM data suggest a rise of the cross section with the energy faster than the ATLAS data. Attempting to quantify these different behaviors, we develop new analytical fits to σ t o t and ρ data from pp and p ¯ p scattering in the energy region 5 GeV–8 TeV. The dataset comprises all the accelerator data below 7 TeV and we consider three ensembles by adding: either only the TOTEM data (T), or only the ATLAS data (A), or both sets (T + A). For the purposes, we use our previous RRPL γ parametrization for σ t o t ( s ) , consisting of two Reggeons (RR), one critical Pomeron (P) and a leading log-raised-to-gamma (L γ ) contribution (with γ as a free fit parameter), analytically connected to ρ ( s ) through singly-subtracted derivative dispersion relations and energy scale fixed at the physical threshold. The data reductions with ensembles T and A present good agreement with the experimental data analyzed and cannot be distinguished on statistical grounds. The quality of the fit is not as good with ensemble T + A. The fit results provide γ ∼ 2.3 ± 0.1 (T), 2.0 ± 0.1 (A), 2.2 ± 0.2 ( T + A ), with χ 2 / DOF ∼ 1.07 (T), 1.09 (A), 1.14 (T + A), suggesting extrema bounds for γ given by 1.9 and 2.4. Fits with γ = 2 (fixed) are also developed and discussed. [ABSTRACT FROM AUTHOR]

We give explicit and asymptotic lower bounds for the quantity | e s / t − M / N | by studying a generalized continued fraction expansion of e s / t . In cases | s | ≥ 3 we improve existing results by extracting a large common factor from the numerators and the denominators of the convergents of that generalized continued fraction. [ABSTRACT FROM AUTHOR]

The asymptotic behavior of solutions to a family of Dirichlet boundary value problems involving inhomogeneous PDEs in divergence form is studied in an Orlicz-Sobolev setting. Solutions are shown to converge uniformly to the distance function to the boundary of the domain. This implies that a well-known result in the analysis of problems modeling torsional creep continues to hold under much more general constitutive assumptions on the stress. [ABSTRACT FROM AUTHOR]

Characterization of classes of switching signals that ensure stability of switched systems occupies a significant portion of the switched systems literature. This article collects a multitude of stabilizing switching signals under an umbrella framework. We achieve this in two steps: Firstly, given a family of systems, possibly containing unstable dynamics, we propose a new and general class of stabilizing switching signals. Secondly, we demonstrate that prior results based on both point-wise and asymptotic characterizations follow our result. This is the first attempt in the switched systems literature where these switching signals are unified under one banner. [ABSTRACT FROM AUTHOR]

We study the joint asymptotic behavior of the space requirement and the total path length (either summing over all root-key distances or over all root-node distances) in random m-ary search trees. The covariance turns out to exhibit a change of asymptotic behavior: it is essentially linear when [ABSTRACT FROM AUTHOR]

The evolving Kingman coalescent is the tree-valued process which records the time evolution undergone by the genealogies of Moran populations. We consider the associated process of total external tree length of the evolving Kingman coalescent and its asymptotic behaviour when the number of leaves of the tree tends to infinity. We show that on the time-scale of the Moran model slowed down by a factor equal to the population size, the (centred and rescaled) external length process converges to a stationary Gaussian process with almost surely continuous paths and covariance function $$c(s,t)=\Big ( \frac{2}{2+|s-t|} \Big )^2$$ . A key role in the evolution of the external length is played by the internal lengths of finite orders in the coalescent at a fixed time which behave asymptotically in a multivariate Gaussian manner [see Dahmer and Kersting (Ann Appl Probab 25(3):1325-1348, 2015)]. A coupling of the Moran model with a critical branching process is used. We also derive a central limit result for normally distributed sums endowed with independent random coefficients. [ABSTRACT FROM AUTHOR]

Standard condition number (SCN) detector is a promising detector that can work efficiently in uncertain environments. In this paper, we consider a Cognitive Radio (CR) system with large number of antennas (eg. Massive MIMO) and we provide an accurate and simple closed form approximation for the SCN distribution using the generalized extreme value (GEV) distribution. The approximation framework is based on the moment-matching method where the expressions of the moments are approximated using bi-variate Taylor expansion and results from random matrix theory. In addition, the performance probabilities and the decision threshold are considered. Since the number of antennas and/or the number of samples used in the sensing process may frequently change, this paper provides simple form decision threshold and performance probabilities offering dynamic and real-time computations. Simulation results show that the provided approximations are tightly matched to relative empirical ones. [ABSTRACT FROM AUTHOR]