Symmetric Limit Research Articles

Strangeness-correlations on the pseudocritical line in ( 2+1 )-flavor QCD

We present some lattice QCD results on first (χ1i) and second (χ2i) cumulants of and correlations (χ11ij) among net baryon-number (B), strangeness (S) and electric charge (Q) along the pseudocritical line [Tpc(μB)] in the temperature (T)–baryon chemical potential (μB) phase diagram of (2+1)-flavor QCD. We point out that violations of sum rules among second order cumulants, which hold in the isospin symmetric limit of vanishing electric charge chemical potential, are small along the Tpc(μB) for the entire range of μB covered in the RHIC beam energy scan. For the strangeness neutral matter produced in heavy-ion collisions this leads to a close relation between χ11BS and χ11QS. We compare lattice QCD results for χ11BS/χ2S along the Tpc(μB) line with preliminary experimental measurements of χ11BS/χ2S for collision energies 7.7 GeV≤sNN≤62.4 GeV. While we find good agreements for sNN≥39 GeV, differences are sizeable at smaller values of sNN. Moreover, we compare lattice QCD results for the ratio of the strangeness (μS) to baryon (μB) chemical potentials, which define a strangeness neutral system with fixed electric charge to baryon number density, with experimental results obtained by the STAR collaboration for μS/μB using strange baryon yields on the freeze-out line. Finally, we determine the baryon chemical potential at the freeze-out (μBf) by comparing χ1B/χ2B along the Tpc(μB) with the experimentally measured net-proton cumulants χ1p/χ2p. We find that {μBf,Tpc(μBf)} are consistent with the freeze-out parameters of the statistical-model fits to experimentally measured hadron yields for sNN≥11.5 GeV. Published by the American Physical Society 2024

Kaon mixing beyond the standard model with physical masses

We present nonperturbative results for beyond the standard model kaon mixing matrix elements in the isospin symmetric limit (mu=md) of QCD, including a complete estimate of all dominant sources of systematic error. Our results are obtained from numerical simulations of lattice QCD with Nf=2+1 flavors of dynamical domain wall fermions. For the first time, these quantities are simulated directly at the physical pion mass mπ∼139 MeV for two different lattice spacings. We include data at three lattice spacings in the range a=0.11–0.07 fm and with pion masses ranging from the physical value up to 450 MeV. Compared to our earlier work, we have added both direct calculations at physical quark masses and a third lattice spacing making the removal of discretization effects significantly more precise and eliminating the need for any significant mass extrapolation beyond the range of simulated data. We renormalize the lattice operators nonperturbatively using RI-SMOM off-shell schemes. These schemes eliminate the need to model and subtract nonperturbative pion poles that arises in the RI-MOM scheme and, since the calculations are performed with domain wall fermions, the unphysical mixing between chirality sectors is suppressed. Our results for the bag parameters in the MS¯ scheme at 3 GeV are BK≡B1=0.5240(17)(54), B2=0.4794(25)(35), B3=0.746(13)(17), B4=0.897(02)(10) and B5=0.6882(78)(94), where the first error is from lattice uncertainties and the second is the uncertainty due to the perturbative matching to MS¯. Published by the American Physical Society 2024

Investigation of bound state energy spectra for fermionic particles in the presence of ultra generalized exponential hyperbolic potential model

By considering the ultra generalized exponential hyperbolic potential, which covers many potential types, the solutions of the Dirac equation with spin/pseudo-spin symmetric limits are achieved. In both approaches, the relation giving the bound state energy eigenvalues is obtained in a closed form. By using these relations, the energy values are calculated numerically for both symmetry cases via the software program. In addition, it has been identified how the bound state energy eigenvalues depend on the parameters. Besides, the energy equations for the Schrödinger and Klein–Gordon particles in the limit states are derived.

Dynamical Systems on Graph Limits and Their Symmetries

AbstractThe collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to capture the network, one often resorts to graph limits and the dynamics thereon. We elucidate the symmetry properties of dynamical systems on graph limits—including graphons and graphops—and analyze how the symmetry shapes the dynamics, for example through invariant subspaces. In addition to traditional symmetries, dynamics on graph limits can support generalized noninvertible symmetries. Moreover, as asymmetric networks can have symmetric limits, we note that one can expect to see ghosts of symmetries in the dynamics of large but finite asymmetric networks.

Electroweak Multi-Higgs Production: A Smoking Gun for the Type-I Two-Higgs-Doublet Model.

Extending the Higgs sector of the standard model (SM) by just one additional Higgs doublet field leads to the two-Higgs-doublet model (2HDM). In the type-I Z_{2}-symmetric limit of the 2HDM, all the five new physical Higgs states can be fairly light, O(100) GeV or less, without being in conflict with current data from the direct Higgs boson searches and the B-physics measurements. In this Letter, we establish that the new neutral as well as the charged Higgs bosons in this model can all be simultaneously observable in the multi-b final state. The statistical significance of the signature for each of these Higgs states, resulting from the electroweak (EW) production of their pairs, can exceed 5σ at the 13TeV high-luminosity Large Hadron collider (HL-LHC). Since the parameter space configurations where this is achievable are precluded in the other, more extensively pursued, 2HDM types, an experimental validation of our findings would be a clear indication that the true underlying Higgs sector in nature is the type-I 2HDM.

Analytic design of constrained control laws for nonlinear dynamic systems with symmetric and asymmetric limits

In this article, we formulate and investigate dynamic optimisation of systems with control limits. Aerial, electronic, electromechanical, mechatronic and robotic systems exhibit symmetric and asymmetric bounds. Applying a Hamiltonian optimisation, and, minimisation of specified-by-constraints nonquadratic performance functionals result in analytically designed bounded control laws. Closed form solution of an optimisation problem is found. Continuous control algorithms ensure consistency to physical systems and homogeneous performance. Findings in dynamic optimisation and constrained control are analytically, numerically and experimentally substantiated. Experimental studies and results are documented for a dc-dc switching regulator and permanent-magnet synchronous motor.

Electromagnetic time-like form factors

We present the calculation of charged pion and kaon electromagnetic form factors in the time-like regime using Schwinger-Dyson equations and the Poincare covariant Bethe-Salpeter equations within an SU(2) isospin symmetric limit. To accurately represent the behavior of a time-like photon, we have incorporated non-valence contributions into the system of equations, enabling the decays ρ → ππ and φ → KK. The inclusion of these decay mechanisms is essential for capturing the expected behavior of the electromagnetic pion and kaon form factors. Our results for the form factors reasonably reproduce the experimental data for a time-like photon.

Study of geometrical properties of 96Mo, 98Ru and 100Pd isotones within interacting boson model

The software package for interacting boson model-1 and for the geometrical boson model has been used to calculate energy levels and potential energy surfaces for and by estimating a set of parameters which are used to predict the behavior of even-even and isotones. According to a framework, the interaction is prominent between the two parameters (and). This means that vibrational structures are constant rises with opposite of rotational. Thus, the potential energy surfaces are considered as a pointer of and distortions for even-even and isotones. The behaviors of the potential energy surfaces with minimum β (-0.84356,- 0.39928, and -0.19045) have circular contours centered at this point that indicates a good agreement with the typical axially symmetric limits. The results of the calculated energy levels were in acceptable agreement with the experimental data. There is no pure vibrational property of these isotones which is clearly shown in the behavior of potential energy surfaces.

Fermion masses, critical behavior and universality

We look for signals of critical behavior in the Yukawa sector. By reviewing a set of models for the fermion masses, we select those where a symmetry-breaking order parameter sits at a transition point between a disordered phase and an ordered one. Many models based on ordinary flavor symmetries are formulated in terms of small corrections to a symmetric limit, which can hardly be interpreted unambiguously as a sign of near-criticality. Different is the case of nonlinearly realized flavor symmetries when the system is always in the broken phase. By inspecting a large number of modular and CP invariant models of lepton masses, we find that most of them cluster around the fixed point τ = i, where the system enjoys enhanced symmetry. Since a priori all values of the modulus τ are equally acceptable to describe the fermion spectrum, we regard this preference as a hint of near-criticality. We analyze in detail these models in the vicinity of all fixed points, showing that only one possibility provides a good description of neutrino masses and mixing angles. Near the fixed points the models exhibit a universal behavior. Mass ratios and mixing angles scale with appropriate powers of the order parameter, independently of the details of the theory, a feature reminiscent of systems belonging to the same universality class in second-order phase transitions. The observations of this work are inspired by the role near-criticality might play in solving the naturalness problem and are motivated by the fascinating possibility that most of the free parameters of the Standard Model could find a common explanation.

Chiral critical behavior of 3D lattice fermionic models with quartic interactions

We study the critical behavior of the three-dimensional Gross-Neveu (GN) model with ${N}_{f}$ four-component Dirac fermionic flavors and quartic interactions, at the chiral ${\mathbb{Z}}_{2}$ transition in the massless ${\mathbb{Z}}_{2}$-symmetric limit. For this purpose, we consider a lattice GN model with staggered Kogut-Susskind fermions and a scalar field coupled to the scalar bilinear fermionic operator, which effectively realizes the attractive four-fermion interaction. We perform Monte Carlo simulations for ${N}_{f}=4$, 8, 12, 16. By means of finite-size scaling analyses of the numerical data, we obtain estimates of the critical exponents, which are compared with the large-${N}_{f}$ predictions obtained using the continuum GN field theory. We observe a substantial agreement. This confirms that lattice GN models with staggered fermions provide a nonperturbative realization of the GN quantum field theory, even though the lattice interactions explicitly break the flavor $\mathrm{U}({N}_{f})\ensuremath{\bigotimes}\mathrm{U}({N}_{f})$ symmetry of the GN field theory, which is only recovered in the critical limit.

Localization of electronic states in hybrid nanoribbons in the nonperturbative regime

We investigate the localization of low-energy single quasi-particle states in the 7/9-hybrid nanoribbon system in the presence of strong interactions and within a finite volume. We consider two scenarios, the first being the Hubbard model at half-filling and perform quantum Monte Carlo simulations for a range $U$ that includes the strongly correlated regime. In the second case we add a nearest-neighbor superconducting pairing $\Delta$ and take the symmetric line limit, where $\Delta$ is equal in magnitude to the hopping parameter $t$. In this limit the quasi-particle spectrum and wavefunctions can be directly solved for general onsite interaction $U$. In both cases we extract the site-dependent quasi-particle wavefunction densities and demonstrate that localization persists in these non-perturbative regimes under particular scenarios.

An enhanced two‐quantile Wilks methodology for engineering uncertainty analysis

AbstractComplex computational engineering uncertainty analyses have become more prevalent. When input parameters of such engineering models are uncertain, the output metric's uncertainty distribution is of an unknown parametric form. Since Wilks' method, named after the seminal paper by SS Wilks in 1941 entitled “Determination of sample sizes for setting tolerance limits”, is a nonparametric statistical procedure, it has received renewed interest, in particular in nuclear and chemical safety engineering. Unfortunately, the prevailing Wilks' method applied relies on arbitrary specification of order statistics' ranks with undue influence on the sample size recommendations that follow. Herein, a novel modification of Wilks' method involving two quantiles is proposed resolving that arbitrary rank selection. Together with a confidence level to be exceeded, these quantiles uniquely determine the parameters of an order statistics' beta distribution which drive the selection of symmetric tolerance limits. The modified procedure is demonstrated in two illustrative engineering uncertainty analysis examples drawn from the nuclear and chemical engineering domains.

Phase transitions in non-linear urns with interacting types

We investigate reinforced non-linear urns with interacting types, and show that where there are three interacting types there are phenomena which do not occur with two types. In a model with three types where the interactions between the types are symmetric, we show the existence of a double phase transition with three phases: as well as a phase with an almost sure limit where each of the three colours is equally represented and a phase with almost sure convergence to an asymmetric limit, which both occur with two types, there is also an intermediate phase where both symmetric and asymmetric limits are possible. In a model with anti-symmetric interactions between the types, we show the existence of a phase where the proportions of the three colours cycle and do not converge to a limit, alongside a phase where the proportions of the three colours can converge to a limit where each of the three is equally represented.

Flows with time-reversal symmetric limit sets on surfaces

The Long-time behavior of orbits is one of the most fundamental properties in dynamical systems. Poincaré studied the Poisson stability, which satisfies a time-reversal symmetric condition, to capture the property of whether points return arbitrarily near the initial positions after a sufficiently long time. Birkhoff introduced and studied the concept of non-wandering points, which is one of the time-reversal symmetric conditions. Moreover, minimality and pointwise periodicity satisfy the time-reversal symmetric condition for limit sets. This paper characterizes flows with the time-reversal symmetric condition for limit sets, which refine the characterization of irrational or Denjoy flows by Athanassopoulos. Using the description, we construct flows on a sphere with Lakes of Wada attractors and with an arbitrarily large number of complementary domains, which are flow versions of such examples of spherical homeomorphisms constructed by Boroński, Činč, and Liu.

Development and verification of a high-speed compressible reactive flow solver in OpenFOAM

This paper proposes a newly developed density-based compressible solver called DCRFoam on a basis of OpenFOAM platform for simulating detonation phenomena with detailed chemical kinetics. It employs AUSM+-up scheme to determine the convective fluxes and a four steps low storage Runge-Kutta time integration method for time integration. A total variation diminishing (TVD) and symmetrical flux limiter sgva is implemented for interpolation process. Also, the dynamic mesh adaptation method is applied to refine or coarsen the computational mesh dynamically since the resolution requirements of supersonic combustion are localized. The numerical solver has been validated systematically with many numerical and experimental results reported in the literature, including those from non-reacting cases (Sod’s shock tube problem, two-dimensional shock/cylinder interaction) to reacting flow cases (the ignition sequence in a shock tube, oblique detonation wave (ODW) initiating process and detonation propagating in a bifurcated channel). The results obtained by current schemes are compared with original central upwind Kurganov-Noelle-Petrova (KNP) scheme in official OpenFOAM. The corresponding result demonstrates the robustness and accuracy of the current solver.

Dynamical study of a novel three-dimensional and generalized chaotic system

In this manuscript, a new three-dimensional continuous chaotic model is presented based on the modification in the Lorenz system. The dynamical aspects of the complex system are investigated, covering equilibrium points and linear stability, dissipation, phase portraits, Poincaré mapping, Lyapunov exponent, attractor projection, bifurcations, time series analysis, and sensitivity. The model is also studied numerically using the Haar wavelet scheme with Caputo fractional derivative. The positive exponent reveals that the system is chaotic. The symmetric limit cycle and butterfly type attractors are observed because the trajectories of the model ultimately progress to a bounded region. The existence of the chaotic attractor is shown by Poincaré section. In the Poincaré section, the kindling is integrated and connected as a single attractor. From the sensitivity analysis of the system, it is noted the system is dependent on the initial conditions that show chaos in the system. The evolution of the attractor is depicted by fixing the first two parameters and varying the third. The theoretical and numerical studies exhibit that the model has complex dynamics with certain stimulating physical characteristics.

Spin and valley ordering of fractional quantum Hall states in monolayer graphene

We study spin and valley ordering in the quantum Hall fractions in monolayer graphene at Landau level filling factors ${\ensuremath{\nu}}_{G}=\ensuremath{-}2+n/3\phantom{\rule{4pt}{0ex}}(n=2,4,5)$. We use exact diagonalizations on the spherical as well as toroidal geometry by taking into account the effect of realistic anisotropies that break the spin/valley symmetry of the pure Coulomb interaction. We also use a variational method based on eigenstates of the fully $\text{SU}(4)$ symmetric limit. For all the fractions we study, there are two-component states for which the competing phases are generalizations of those occurring at neutrality ${\ensuremath{\nu}}_{G}=0$. They are ferromagnetic, antiferromagnetic, charge-density wave, and K\'ekul\'e phases, depending on the values of Ising or $XY$ anisotropies in valley space. The varying spin-valley content of the states leads to ground-state quantum numbers that are different from the ${\ensuremath{\nu}}_{G}=0$ case. For filling factor ${\ensuremath{\nu}}_{G}=\ensuremath{-}2+5/3$, there is a parent state in the $\text{SU}(4)$ limit that has a flavor content $(1,1/3,1/3,0)$ where the two components that are one-third filled form a two-component singlet. The addition of anisotropies leads to the formation of new states that have no counterpart at ${\ensuremath{\nu}}_{G}=0$. While some of them are predicted by the variational approach, we find notably that negative Ising-like valley anisotropy leads to the formation of a state that is a singlet in both spin and valley space and lies beyond the reach of the variational method. Also fully spin polarized two-component states at $\ensuremath{\nu}=\ensuremath{-}2+4/3$ and $\ensuremath{-}2+5/3$ display an emergent $\text{SU}(2)$ valley symmetry because they do not feel point-contact anisotropies. We discuss implications for current experiments concerning possible spin transitions.

On Enhanced GLM-Based Monitoring: An Application to Additive Manufacturing Process

Innovations in technology assist the manufacturing processes in producing high-quality products and, hence, become a greater challenge for quality engineers. Control charts are frequently used to examine production operations and maintain product quality. The traditional charting structures rely on a response variable and do not incorporate any auxiliary data. To resolve this issue, one popular approach is to design charts based on a linear regression model, usually when the response variable shows a symmetric pattern (i.e., normality). The present work intends to propose new generalized linear model (GLM)-based homogeneously weighted moving average (HWMA) and double homogeneously weighted moving average (DHWMA) charting schemes to monitor count processes employing the deviance residuals (DRs) and standardized residuals (SRs) of the Poisson regression model. The symmetric limits of HWMA and DHWMA structures are derived, as SR and DR statistics showed a symmetric pattern. The performance of proposed and established methods (i.e., EWMA charts) is assessed by using run-length characteristics. The results revealed that SR-based schemes have relatively better performance as compared to DR-based schemes. In particular, the proposed SR-DHWMA chart outperforms the other two, namely SR-EWMA and SR-HWMA charts, in detecting shifts. To illustrate the practical features of the study’s proposal, a real application connected to the additive manufacturing process is offered.

Solution of boundary value problems with moving boundaries by using an approximate method for constructing solutions of integro – differential equations

The problem of oscillations of objects with moving boundaries, formulated as a differential equation with boundary and initial conditions, is a non-classical generalization of a problem of hyperbolic type. To facilitate the construction of a solution to this problem and justify the choice of a solution form, equivalent integro-differential equations are constructed with symmetric and time-dependent kernels and integration limits varying in time. The method for constructing solutions of integro-differential equations is based on the direct integration of differential equations in combination with the standard replacement of the desired function with a new variable. The method is extended to a wider class of model boundary value problems that take into account the bending stiffness of an oscillating object, the resistance of the environment, and the rigidity of the substrate. Particular attention is paid to the consideration of the most common in practice case when external disturbances act at the boundaries. The solution is made in dimensionless variables accurate to second-order values of smallness with respect to small parameters characterizing the speed of the border.

Electric dipole moments of three-nucleon systems in the pionless effective field theory

We calculate the electric dipole moments (EDMs) of three-nucleon systems at leading order in pionless effective field theory. The one-body contributions that arise from permanent proton and neutron EDMs and the two-body contributions that arise from charge-parity-odd nucleon-nucleon interactions are taken into account. Neglecting the Coulomb interaction, we consider the triton and $^{3}\mathrm{He}$, and also investigate them in the Wigner-SU(4) symmetric limit. We also calculate the electric dipole form factor and find numerically that the momentum dependence of the electric dipole form factor in the Wigner limit is, up to an overall constant (and numerical accuracy), the same as the momentum dependence of the charge form factor. Finally, we study the cutoff dependence of these observables and find that they are properly renormalized.