Domain Of Parameter Space Research Articles

Shrinking shrimp-shaped domains and multistability in the dissipative asymmetric kicked rotor map.

An interesting feature in dissipative nonlinear systems is the emergence of characteristic domains in parameter space that exhibit periodic temporal evolution, known as shrimp-shaped domains. We investigate the parameter space of the dissipative asymmetric kicked rotor map and show that, in the regime of strong dissipation, the shrimp-shaped domains repeat themselves as the nonlinearity parameter increases while maintaining the same period. We analyze the dependence of the length of each periodic domain with the nonlinearity parameter, revealing that it follows a power law with the same exponent regardless of the dissipation parameter. Additionally, we find that the distance between adjacent shrimp-shaped domains is scaling invariant with respect to the dissipation parameter. Furthermore, we show that for weaker dissipation, a multistable scenario emerges within the periodic domains. We find that as the dissipation gets weaker, the ratio of multistable parameters for each periodic domain increases, and the area of the periodic basin decreases as the nonlinearity parameter increases.

Searching for axion resonances in vacuum birefringence with three-beam collisions

We consider birefringent (i.e., polarization changing) scattering of x-ray photons at the superposition of two optical laser beams of ultrahigh intensity and study the resonant contributions of axions or axionlike particles, which could also be short lived. Applying the specifications of the Helmholtz International Beamline for Extreme Fields (HIBEF), we find that this setup can be more sensitive than previous light-by-light scattering (birefringence) or light-shining-through-wall experiments in a certain domain of parameter space. By changing the pump and probe laser orientations and frequencies, one can even scan different axion masses, i.e., chart the axion propagator. Published by the American Physical Society 2024

Entanglement witnesses in the XY chain: Thermal equilibrium and postquench nonequilibrium states

We use entanglement witnesses to detect entanglement in the XY chain in thermal equilibrium and determine the temperature bound below which the state is detected as entangled. We consider the entanglement witness based on the Hamiltonian. Such a witness detects a state as entangled if its energy is smaller than the energy of separable states. We also consider a family of entanglement witnesses related to the entanglement negativity of the state. We test the witnesses in infinite and finite systems. We study how the temperature bounds obtained are influenced by a quantum phase-transition or a disorder line in the ground state. Very strong finite-size corrections are observed in the ordered phase due to the presence of a quasi-degenerate excitation. We also study the postquench states in the thermodynamic limit after a quench when the parameters of the Hamiltonian are changed suddenly. In the case of the Ising model, we find that the mixed postquench state is detected as entangled by the two methods if the parameters of the Hamiltonian before and after the quench are close to each other. We find that the two witnesses give qualitatively similar results, showing that energy-based entanglement witnesses are efficient in detecting the nearest-neighbor entanglement in spin chains in various circumstances. For other XY models, we find that the negativity based witnesses also detect states in some parameter regions where the energy-based witness does not, in particular, if the quench is performed from the paramagnetic phase to the ferromagnetic phase and vice versa. The domains in parameter space corresponding to postquench states detected as entangled by the energy-based witness have been determined analytically, which stresses further the utility of our method.

Massive gauge particles versus Goldstone bosons in non-Hermitian non-Abelian gauge theory

We investigate the Englert–Brout–Higgs–Guralnik–Hagen–Kibble mechanism for non-Hermitian field theories with local non-Abelian gauge symmetry in different regions of their parameter spaces. We demonstrate that the two aspects of the mechanism, that is giving mass to gauge vector bosons and at the same time preventing the existence of massless Goldstone bosons, remain to be synchronized in all regimes characterized by a modified CPT symmetry. In the domain of parameter space where the “would be Goldstone bosons” can be identified the gauge vector bosons become massive and the Goldstone bosons cease to exist. The mechanism is also in tact at the standard exceptional points. However, at the zero exceptional points, that is when the eigenvalues of the mass squared matrix vanish irrespective of the symmetry breaking, the mechanism breaks down as the Goldstone bosons cannot be identified and the gauge vector bosons remain massless. This breakdown coincides with the vanishing of the CPT inner product of symmetry breaking vacua defined on the eigenvector space of mass squared matrix. We verify this behaviour for a theory with SU(2) symmetry in which the complex scalar fields are taken in the fundamental as well as in the adjoint representation.

Fast magnetosonic solitonic structures in a quasi-neutral collision-free finite-beta plasma

The equations of the model of two fluids of a two component collision-free, isotropic and fully ionized plasma in thermal equilibrium consisting of singly-ionized ions and electrons in a uniform magnetic field with heated ions and electrons are treated. We focus our attention on determining the global hydromagnetic fast magnetosonic traveling solitonic waves for plane wave equations. Ordinary solitary waves, bifurcating from the zero wave number, exist for the angles of inclination θ of the magnetic field vector to the direction x of the wave propagation, located in some left neighborhood of π/2. A global family of solitary waves containing solitary waves of all possible amplitudes is numerically determined. The dynamic stability of these solitary waves is investigated by numerical methods: the problem of the evolution of solitary waves via the time dependent field equations of the quasi-neutral collision-free finite beta-plasma is analyzed. We also concern the domains in parameter space where traveling generalized and envelope solitary waves exist and compute the possible forms of these waves and of so-called multi-soliton waves with several humps. The evolution of a localized perturbation is also treated numerically.

Domains identification by the parameter values in multidimensional space

As a result of cluster and discriminant data analysis, the objects are distributed among different classes represented in the multidimensional space of parameter values. At the next stage, it is relevant to use the results obtained in various applications. The most frequently solved task is the diagnostics of a newly received object when the class of the object is determined through parameter values. In terms of a data view model, the problem can be reduced to determining a domain in parameter space, the new object belonging to this domain. The solution to this problem depends on the way the data analysis results are described and presented. Previously the graphic data model was considered to describe the domains separated by surfaces in the multidimensional space. Moreover, a constructive approach was proposed to describe an error in the representation of the boundaries, making it possible to take into account the experimental data errors. The mathematical model proposed in the given article is used to develop a domain identification algorithm by the parameter values in the multidimensional space. The proof of correctness and the estimation of computational complexity are provided for the algorithm. The results obtained make it possible to use the algorithm to calculate various characteristics of objects: state, intervals of existence, etc.

Black holes in torsion bigravity

We study spherically symmetric black hole solutions in a four-parameter Einstein-Cartan-type class of theories, called "torsion bigravity". These theories offer a geometric framework (with a metric and an independent torsionfull connection) for a modification of Einstein's theory that has the same spectrum as bimetric gravity models. In addition to an Einsteinlike massless spin-2 excitation, there is a massive spin-2 one (of range $\kappa^{-1}$) coming from the torsion sector, rather than from a second metric. We prove the existence of three broad classes of spherically-symmetric black hole solutions in torsion bigravity. First, the Schwarzschild solution defines an asymptotically-flat torsionless black hole for all values of the parameters. [And we prove that one cannot deform a Schwarzschild solution, at the linearized level, by adding an infinitesimal torsion hair.] Second, when considering finite values of the range, we find that there exist non-asymptotically-flat torsion-hairy black holes in a large domain of parameter space. Third, we find that, in the limit of infinite range, there exists a two-parameter family of asymptotically flat torsion-hairy black holes. The latter black hole solutions give an interesting example of non-Einsteinian (but still purely geometric) black hole structures which might be astrophysically relevant when considering a range of cosmological size.

Stopbands in fast ion-acoustic soliton propagation revisited

It was recently discovered that, in a multispecies plasma with two positive ion species (one cold and one warm adiabatic) and Boltzmann-distributed electrons, a “stopband” could occur, i.e., there was a range of velocities where no fast ion-acoustic solitons could propagate between two ranges where propagation was possible. Several extensions were subsequently investigated, including the effects of the cool ions having finite temperature and of nonthermal electron distributions. Efforts were made to estimate existence domains in plasma parameter space, often by ad hoc arguments, but the illustrations were invariably restricted to the same specific set of parameter values or their neighborhoods. In contrast, here, a systematic and structured study is given: physical arguments determine a range of compositional parameters so that a Sagdeev pseudopotential analysis establishes in a consistent way the various curves limiting the existence domains in parameter space. This is done for four models, namely, Boltzmann, nonthermal Cairns, superthermal kappa, and nonextensive Tsallis electron distributions, and for each, existence domains are plotted in the space of ion charge-to-mass ratio and inverse electron temperature, and detailed examples are presented. Contrary to reports in the literature, stopbands are shown to exist for large deviations from isothermality. However, their range in parameter space is shifted from that obtained for Boltzmann electrons. This establishes that the stopband phenomenon is robust and governed primarily by the cold and warm ion properties and the electron temperature, the form of the electron distribution having only a quantitative effect.

Dynamics of Predator-Prey Community with Age Structures and Its Changing Due To Harvesting

The paper studies dynamic modes of discrete-time model of structured predator-prey community like “arctic fox – rodent” and changing its dynamic modes due to interspecific interaction. We paid special attention to the analysis of situations in which changes in the dynamic modes are possible. In particularly, 3-cycle emerging in prey population can result in predator extinction. Moreover, this solution corresponding to an incomplete community simultaneously coexists with the solution describing dynamics of complete community, which can be both stable and unstable. The anthropogenic impact on the community dynamics is studied, that is realized as harvest of some part of predator or prey population. It is shown that prey harvesting leads to expansion of parameter space domain with non-trivial stable numbers of community populations. In this case, the prey harvest has little effect on the predator dynamics; changes are mainly associated with multistability areas. In particular, the multistability domain narrows, in which changing initial conditions leads to different dynamic regimes, such as the transition to a stable state or periodic oscillations. As a result, community dynamics becomes more predictable. It is shown that the dynamics of prey population is sensitive to its harvesting. Even a small harvest rate results in disappearance of population size fluctuations: the stable state captures the entire phase space in multistability areas. In the case of the predator population harvest, stability domain of the nontrivial fixed point expands along the parameter of the predator birth rate. Accordingly, a case where predator determines the prey population dynamics is possible only at high values of predator reproductive potential. It is shown that in the case of predator harvest, a change in the community dynamic mode is possible because of a shifting dynamic regime in the prey population initiating the same nature fluctuations in the predator population. The dynamic regimes emerging in the community models with and without harvesting were compared.

Dynamics of Predator-Prey Community with Age Structures and Its Changing Due To Harvesting

The paper studies dynamic modes of discrete-time model of structured predator-prey community like “arctic fox – rodent” and changing its dynamic modes due to interspecific interaction. We paid special attention to the analysis of situations in which changes in the dynamic modes are possible. In particularly, 3-cycle emerging in prey population can result in predator extinction. Moreover, this solution corresponding to an incomplete community simultaneously coexists with the solution describing dynamics of complete community, which can be both stable and unstable. The anthropogenic impact on the community dynamics is studied, that is realized as harvest of some part of predator or prey population. It is shown that prey harvesting leads to expansion of parameter space domain with non-trivial stable numbers of community populations. In this case, the prey harvest has little effect on the predator dynamics; changes are mainly associated with multistability areas. In particular, the multistability domain narrows, in which changing initial conditions leads to different dynamic regimes, such as the transition to a stable state or periodic oscillations. As a result, community dynamics becomes more predictable. It is shown that the dynamics of prey population is sensitive to its harvesting. Even a small harvest rate results in disappearance of population size fluctuations: the stable state captures the entire phase space in multistability areas. In the case of the predator population harvest, stability domain of the nontrivial fixed point expands along the parameter of the predator birth rate. Accordingly, a case where predator determines the prey population dynamics is possible only at high values of predator reproductive potential. It is shown that in the case of predator harvest, a change in the community dynamic mode is possible because of a shifting dynamic regime in the prey population initiating the same nature fluctuations in the predator population. The dynamic regimes emerging in the community models with and without harvesting were compared.

On the sample-mean method for computing hyper-volumes

Abstract Estimating hyper-volumes of convex and non-convex sets are of interest in a number of areas. In this article we develop further a simple geometric Monte Carlo method, known also as the sample-mean method, which transforms the domain to an equivalent hyper-sphere with the same volume. We first examine the performance of the method to compute the volumes of star-convex unit balls and show that it gives accurate estimates of their volumes. We then examine the use of this method for computing the volumes of nonstar-shaped domains. In particular, we develop two algorithms, which couple the sample-mean method with algebraic and geometric techniques, to generate and compute the volumes of low-dimensional stability domains in parameter space.

Low angular momentum relativistic hot accretion flow around Kerr black holes with variable adiabatic index

We study the relativistic, time-independent, low angular momentum, inviscid, advective accretion flow around Kerr black hole. Considering the relativistic equation of state (REoS), we examine the transonic properties of the flow and find that there exists an upper bound of the location of the physically accepted critical point ($r^{\rm max}_{\rm out}$). However, no such limit exists when an ideal gas equation of state (IEoS) is assumed to describe the flow. Further, we calculate the global accretion solutions that contain shock waves and separate the domain of parameter space in angular momentum ($\lambda$) and energy (${\cal E}$) plane. We find ample disagreement between the shock parameter spaces obtained for REoS and IEoS, respectively. In general, post-shock flow (equivalently post-shock corona, hereafter PSC) is characterized by shock location ($r_s$) and compression ratio ($R$, measure of density compression across the shock front) which are uniquely determined for flow with given input parameters, namely $({\cal E}, \lambda)$. Using $r_s$ and $R$, we empirically compute the oscillation frequency ($\nu_{QPO}$) of the shock front which is in general quasi-periodic (QP) in nature and retrace the domain of shock parameter space in the $r_s-R$ plane in terms of $\nu_{QPO}$ for REoS around the weakly as well as rapidly rotating black holes. Finally, we indicate the relevance of the present work to explain the plausible origin of high frequency QPO (HFQPO) and its connection with the spin ($a_k$) of the Galactic black hole sources.

On the Stability of Multi-Step Finite-Difference-Based Lattice Boltzmann Schemes

Stability of finite-difference-based off-lattice Boltzmann schemes is analyzed. The time derivative in system of discrete Boltzmann equations is approximated by two-step modified central difference. Advective term is approximated by finite differences from first- to fourth-orders of accuracy. Characteristics-based (CB) schemes and schemes with traditional separate approximations of space derivatives are considered. A special class of high-order CB schemes with approximation in the internal nodes of grid patterns is constructed. It is demonstrated that apparent viscosity for the schemes of high-order is equal to kinematic viscosity of the system of Bhatnaghar–Gross–Krook kinetic equations. Stability of the schemes is analyzed by the von Neumann method for the cases of two flow regimes in unbounded domain. Stability is analyzed by the investigation of the stability domains in parameter space. The area of the domain is considered as the main numerical characteristic of the stability. As the main result of the analysis, it must be mentioned that the areas of CB schemes are greater than areas for the schemes with separate approximations.

Exploring the Dynamics of a Third-Order Phase-Locked Loop Model

We study the dynamics and characterize the bifurcation structure of a phase-locked loop (PLL) device modeled by a third-order autonomous differential equation with sinusoidal phase detector. The development of this work was performed using rigorous analysis and numerical experiments. Through theoretical analysis the bifurcation structures related to two fundamental equilibrium points of the system are described. By using extensive numerical experiments we investigate the intricate organization between periodic and chaotic domains in parameter space (named here parameter plane as the PLL model has only two control parameters) and obtain two following remarkable findings: (i) there are self-organized generic stable periodic structures along specific directions in parameter plane, whose periods are defined by a mathematical rule and, (ii) the existence of transient chaos phenomenon responsible for long chaotic temporal evolution preceding the asymptotic (periodic) dynamics for some particular control parameter pairs is characterized. Our theoretical and numerical results present an astonishing concordance. We believe that the present study, specially the parameter plane analysis, may have a great importance to experimental studies and general applications involving PLL devices when, for example, one would like to avoid the chaotic regimes.

Relativistic collapse of axion stars

We study the gravitational collapse of axion dark matter in null coordinates, assuming spherical symmetry. Compared with previous studies, we use a simpler numerical scheme which can run, for relevant parameters, in a few minutes or less on a desktop computer. We use it to accurately determine the domains of parameter space in which the axion field forms a black hole, an axion star or a relativistic Bosenova.

On Solutions and Heteroclinic Orbits of Some Lotka-Volterra Systems

In this work, a principle for getting heteroclinic orbit of a dynamical system has been proposed when the solution is known in a compact form. The proposed principle has been tested through its application to a three species Lotka-Volterra system, which may appear as a mathematical model of human pathogen system. The domain in parameter space involve in the model, and the region of initial condition for the existence of heteroclinic orbit have been derived.

Post-Processing Partitions to Identify Domains of Modularity Optimization.

We introduce the Convex Hull of Admissible Modularity Partitions (CHAMP) algorithm to prune and prioritize different network community structures identified across multiple runs of possibly various computational heuristics. Given a set of partitions, CHAMP identifies the domain of modularity optimization for each partition—i.e., the parameter-space domain where it has the largest modularity relative to the input set—discarding partitions with empty domains to obtain the subset of partitions that are “admissible” candidate community structures that remain potentially optimal over indicated parameter domains. Importantly, CHAMP can be used for multi-dimensional parameter spaces, such as those for multilayer networks where one includes a resolution parameter and interlayer coupling. Using the results from CHAMP, a user can more appropriately select robust community structures by observing the sizes of domains of optimization and the pairwise comparisons between partitions in the admissible subset. We demonstrate the utility of CHAMP with several example networks. In these examples, CHAMP focuses attention onto pruned subsets of admissible partitions that are 20-to-1785 times smaller than the sets of unique partitions obtained by community detection heuristics that were input into CHAMP.

The Design Space of the Embryonic Cell Cycle Oscillator

One of the main tasks in the analysis of models of biomolecular networks is to characterize the domain of the parameter space that corresponds to a specific behavior. Given the large number of parameters in most models, this is no trivial task. We use a model of the embryonic cell cycle to illustrate the approaches that can be used to characterize the domain of parameter space corresponding to limit cycle oscillations, a regime that coordinates periodic entry into and exit from mitosis. Our approach relies on geometric construction of bifurcation sets, numerical continuation, and random sampling of parameters. We delineate the multidimensional oscillatory domain and use it to quantify the robustness of periodic trajectories. Although some of our techniques explore the specific features of the chosen system, the general approach can be extended to other models of the cell cycle engine and other biomolecular networks.

The effect of temperature on generic stable periodic structures in the parameter space of dissipative relativistic standard map

In this work, we have characterized changes in the dynamics of a two-dimensional relativistic standard map in the presence of dissipation and specially when it is submitted to thermal effects modeled by a Gaussian noise reservoir. By the addition of thermal noise in the dissipative relativistic standard map (DRSM) it is possible to suppress typical stable periodic structures (SPSs) embedded in the chaotic domains of parameter space for large enough temperature strengths. Smaller SPSs are first affected by thermal effects, starting from their borders, as a function of temperature. To estimate the necessary temperature strength capable to destroy those SPSs we use the largest Lyapunov exponent to obtain the critical temperature ($T_C$) diagrams. For critical temperatures the chaotic behavior takes place with the suppression of periodic motion, although, the temperature strengths considered in this work are not so large to convert the deterministic features of the underlying system into a stochastic ones.

The continuous modeling of charge-stabilized colloidal suspensions in shear flows

Flows of concentrated colloidal suspensions may exhibit a rich set of behaviors due to both hydrodynamic and colloidal interactions between the particles. Colloidal flows are generally modeled with an effective Navier–Stokes equation and a mass balance for the solid phase involving a diffusion coefficient given by the generalized Stokes–Einstein relation. This picture corresponds to a near equilibrium regime in which entropic and colloidal forces dominate over hydrodynamic interactions, the latter being totally ignored. On the other hand, suspension flows far from equilibrium require the modeling of significant hydrodynamic stresses responsible in particular for shear-induced migration, a phenomenon known to occur in some industrial processes involving colloids, such as ultrafiltration. The choice of the proper model ingredients requires a knowledge of the domains in parameter space in which colloidal or hydrodynamic effects are dominant. In this article, such a phase diagram is established for a channel flow of charge-stabilized colloids with a version of the suspension balance model including both colloidal and hydrodynamic effects at the continuous level. It is shown that the classical Peclet number is not sufficient to characterize the flow regime. The phase boundary between the colloidal and hydrodynamic regimes exhibits an original shape explained by the dependence of electrostatic interactions with the colloidal surface charge, and in particular by the phenomenon of ionic condensation. We also show that the phase diagram can be predicted based on the knowledge of a rescaled Peclet number comparing the hydrodynamic stress scale to the bulk modulus of the suspension. The criterion determined here provides important guidelines for the efficient modeling of colloidal flows.