Large Values Of Parameter Research Articles

Complex flow structures beneath rotational depression solitary waves in gravity-capillary flows

Particle trajectories beneath depression solitary gravity-capillary waves in the weakly nonlinear weakly dispersive regime in a sheared channel with finite depth and constant vorticity are investigated. A fifth-order Korteweg–de Vries equation that incorporates the surface tension and the vorticity effects is derived asymptotically from the full Euler equations when the Bond number is nearly a critical value that depends on the vorticity. The velocity field in the bulk fluid is approximated which allow us to study the submarine structures beneath depression solitary waves. The dynamical system of particle trajectories is reformulated in the moving wave frame and its features are seen through the streamlines. We show that for large values of the vorticity parameter there are always stagnation points in the bulk fluid, which produce rich cat’s-eyes structures. In this case, particle trajectories can undergo vertical excursions, describing closed orbits or undergo pure horizontal transport. Furthermore, bifurcation diagrams according to the number of stagnation points and complex flow structures beneath depression solitary waves with multiple local extrema are shown.

Градиентная модель изгиба неоднородной пьезоэлектрической балки

The problem of bending a horizontally inhomogeneous piezoelectric cantilever beam is studied taking into account scale effects. The lower and upper surfaces of the beam are electroplated. Three types of loading are considered: load uniformly distributed along the length; transverse force at the other end of the beam; supply of electric potential to the upper electrode. The beam bending is modeled based on the Euler-Bernoulli hypotheses and the quadratic distribution of the electric potential. Based on the application of the variational principle of gradient electroelasticity, a system of differential equations of bending and electrostatics is obtained, as well as an extended range of boundary conditions. To find the bending moment and deflection of the middle line of a homogeneous beam, exact analytical expressions are obtained. In the case of an inhomogeneous beam at large values of the scale parameter, the solution is based on the shooting method. On specific examples, the calculations of moments and deflection are carried out, both in the case of a homogeneous and inhomogeneous beam. The influence of the mechanical and electrostatic gradient parameters, the electromechanical coupling coefficient, and the inhomogeneity parameter on the distribution of deflections has been clarified.

Observational constraints on maximum mass limit and physical properties of anisotropic strange star models by gravitational decoupling in Einstein–Gauss–Bonnet gravity

ABSTRACT In this work, we are guided by the gravitational wave events GW 170817 and GW 190814 together with observations of neutron stars PSR J1614-2230, PSR J1903+6620, and LMC X-4 to model compact objects within the framework of Einstein–Gauss–Bonnet (EGB) gravity. In addition, we employ the extended gravitational decoupling (EGD) method to explore the impact of anisotropy by varying the decoupling parameter. We model strange quark stars in which the interior stellar fluid obeys the MIT Bag equation of state which represents a degenerated Fermi gas comprising of up, down, and strange quarks. In order to close the system of field equations describing the seed solution, we employ the Buchdahl ansatz for one of the metric functions. The θ sector is solved under the bifurcation: $\epsilon =\theta ^0_0$ and $P_r=\theta ^1_1$ leading to two new families of solutions. In order to test the physical viability of the models, we vary the EGB parameter (α) or the decoupling constant (β) to achieve the observed masses and radii of compact objects. Our models are able to account for low-mass stars for a range of β values while α is fixed. The present models mimic the secondary component of the GW 190814 with a mass range of 2.5–2.67 M⊙ and radii typically of the order of 11.76$^{+0.14}_{-0.19}$ km for large values of the EGB parameter and the decoupling constant. The energy exchange between fluids inside the stellar object is sensitive to model parameters which lead to stable configurations.

Modeling Sequences of Earthquakes and Aseismic Slip (SEAS) in Elasto‐Plastic Fault Zones With a Hybrid Finite Element Spectral Boundary Integral Scheme

AbstractWe present a coupled finite element spectral boundary integral framework for modeling sequences of earthquakes and aseismic slip on a 2‐D planar rate‐and‐state fault with off‐fault visco‐plastic response in the plane strain approximation. The model resolves both slow aseismic deformation and inertia effects during rapid slip. As an application, we perform two sets of simulations with different choices of cohesion to explore the co‐evolution of fault slip, bulk plasticity and local stress fields. The first set implements a relatively large value of the cohesion parameter, which results in limiting inelastic strain accumulation to dynamic rupture phases. The second set implements a smaller cohesion, allowing for plastic strain to accumulate in both seismic and aseismic phases. For the first model, our results indicate that the extent and distribution of plastic strain depend on the angle of maximum compressive principal stress. At larger angles, inelastic strain accumulates on the extensional side of a dynamically propagating rupture. At smaller angles, the extent of plasticity is limited to the compressional side of the domain. At smaller cohesion values, off‐fault plasticity may occur during aseismic slip, which alters the nucleation characteristics and earthquake sequence pattern. Furthermore, our results at lower cohesion values indicate that plastic strain accumulation may occur in both the extensional and compressional sides of the off‐fault bulk even at higher angles of maximum compression. This produces damage patterns that deviate from the traditional off‐fault fan‐like distribution observed in dynamic rupture simulations and emphasizes the significance of long‐term deformation in interpreting observations.

Analysis of Ordinary Least Square and Geographically Weighted Regression on the Human Development Index of North Sumatra 2021

The Human Development Index has a big contribution to human development in a region, the HDI value is useful for the government as development planning and allocating funds to improve welfare. This research will look for the HDI model in North Sumatra with OLS and GWR, as well as look at the factors that have the greatest influence on HDI in North Sumatra in 2021. Based on the analysis carried out using OLS, one model for the HDI for North Sumatra province with the largest parameter value is the average value. average length of school. Using the GWR, 33 HDI models were obtained for each district/city in North Sumatra. Furthermore, by using OLS and GWR on HDI in North Sumatra, it is obtained that the factor that has the greatest influence on HDI scores in North Sumatra by looking at the value of the largest parameter estimator is the average length of schooling.

Stable rotating regular black holes

We present a rotating regular black hole whose inner horizon has zero surface gravity for any value of the spin parameter, and is therefore stable against mass inflation. Our metric is built by combining two successful strategies for regularizing singularities, i.e. by replacing the mass parameter with a function of $r$ and by introducing a conformal factor. The mass function controls the properties of the inner horizon, whose displacement away from the Kerr geometry's inner horizon is quantified in terms of a parameter $e$; while the conformal factor regularizes the singularity in a way that is parametrized by the dimensionful quantity $b$. The resulting line element not only avoids the stability issues that are common to regular black hole models endowed with inner horizons, but is also free of problematic properties of the Kerr geometry, such as the existence of closed timelike curves. While the proposed metric has all the phenomenological relevant features of singular rotating black holes -- such as ergospheres, light ring and innermost stable circular orbit -- showing a remarkable similarity to a Kerr black hole in its exterior, it allows nonetheless sizable deviations, especially for large values of the spin parameter $a$. In this sense, the proposed rotating "inner-degenarate" regular black hole solution is not only amenable to further theoretical investigations but most of all can represent a viable geometry to contrast to the Kerr one in future phenomenological tests.

Coexistence of Active and Hydrodynamic Turbulence in Two-Dimensional Active Nematics.

In active nematic liquid crystals, activity is able to drive chaotic spatiotemporal flows referred to as active turbulence. Active turbulence has been characterized through theoretical and experimental work as a low Reynolds number phenomenon. We show that, in two dimensions, the active forcing alone is able to trigger hydrodynamic turbulence leading to the coexistence of active and inertial turbulence. This type of flow develops for sufficiently active and extensile flow-aligning nematics. We observe that the combined effect of an extensile nematic and large values of the flow-aligning parameter leads to a broadening of the elastic energy spectrum that promotes a growth of kinetic energy able to trigger an inverse energy cascade.

Prediction of tunnelling induced ground movement in clay using principle of minimum total potential energy

The accurate prediction of tunnelling induced ground movement is of practical and theoretical significance. This paper proposes a mixed empirical-analytical method based on the principle of minimum total potential energy to predict the ground movement due to tunnelling in undrained clay. The proposed method considers the plastic behaviour of the soil. Based on the theory of curvilinear Euler beam, the proposed method considers the soil-lining interaction, which is simplified as a constant force in classical MSD methods. Moreover, the proposed method can deal with the deformation mechanism with multiple undetermined parameters. The tunnelling-induced ground movement can be found by minimizing the total potential energy of the concerned system composed of soil and lining. Four well-documented tunnelling projects are adopted to evaluate the applicability of the proposed method. The results reveal that our method provides better predictions of both surface and subsurface settlements above the tunnel than the other two semi-analytical methods. Moreover, our method excels the other two methods in predicting the tunnelling projects with large gap parameter values as it considers the plastic behaviour of the soil.

Statistical mechanics of phase transitions in elastic media with vanishing thermal expansion.

We consider a minimal spin model for Ising transitions in an isotropic elastic medium in the zero thermal expansion (ZTE) limit. We set up the elastic theory for this system. We use this theory to identify and study the nature of the fluctuations in the system near the second order phase transitions at T_{c} in the ZTE limit given by dT_{c}/dV=0, where V is the system volume, and explore anomalous elasticity. Allowing for the local strain to couple asymmetrically or selectively with the states of the order parameter, we uncover the dramatic effects of these couplings on the fluctuations of the local displacements near T_{c}, and also on the nature of the phase transition itself. Near second-order phase transitions and with weak asymmetry in the order parameter-strain couplings, the variance of the displacement fluctuations in two dimensions scale with the system size L in a universal fashion as [ln(L/a_{0})]^{2/3}; a_{0} is a small-scale cutoff. Likewise, the correlation functions of the difference of the local displacements at two different points separated by r scale as [ln(r/a_{0})]^{2/3} for large r. For stronger selectivity above a finite threshold, this variance diverge as L exceeds beyond a (nonuniversal) size, determined by the model parameters, signaling a transition to a phase with only short-range order or the loss of the positional order of the elastic medium. At dimensions higher than two, for sufficiently weak selectivity, the variance of the displacement fluctuations is L-independent corresponding to long-range order. However, if the selectivity parameters rise beyond a dimension-dependent threshold value, then again the positional order is lost with a concomitant transition to a phase with short-range order. Large values of the order parameter-strain couplings can turn the phase transition into a first order as well. Our theory establishes a one-to-one correspondence between the order of phase transitions and anomalous elasticity near the transitions. Our theory should be a useful guide to possible synthesis of appropriate ZTE materials.

New Solutions of Fractional Jeffrey Fluid with Ternary Nanoparticles Approach

The existing work deals with the Jeffrey fluid having an unsteady flow, which is moving along a vertical plate. A fractional model with ternary, hybrid, and nanoparticles is obtained. Using suitable dimensionless parameters, the equations for energy, momentum, and Fourier's law were converted into non-dimensional equations. In order to obtain a fractional model, a fractional operator known as the Prabhakar operator is used. To find a generalized solution for temperature as well as a velocity field, the Laplace transform is used. With the help of graphs, the impact of various parameters on velocity as well as temperature distribution is obtained. As a result, it is noted that ternary nanoparticles approach can be used to increase the temperature than the results obtained in the recent existing literature. The obtained solutions are also useful in the sense of choosing base fluids (water, kerosene and engine oil) for nanoparticles to achieved the desired results. Further, by finding the specific value of fractional parameters, the thermal and boundary layers can be controlled for different times. Such a fractional approach is very helpful in handling the experimental data by using theoretical information. Moreover, the rate of heat transfer for ternary nanoparticles is greater in comparison to hybrid and mono nanoparticles. For large values of fractional parameters, the rate of heat transfer decreases while skin friction increases. Finally, the present results are the improvement of the results that have already been published recently in the existing literature. Fractional calculus enables us to control the boundary layers as well as rate of heat transfer and skin friction for finding suitable values of fractional parameters. This approach can be very helpful in electronic devices and industrial heat management system.

Influence of coherent structure on turbulence characteristics of 0814 strong typhoon Hagupit

In order to explore the formation mechanism of the nonstationary wind speed in the eye wall regions and eye region of a typhoon, taking the measured data of No.0814 strong typhoon Hagupit as the research object, we identify and extract the coherent structure of the measured wind field by discrete wavelet transform combined with hypothesis testing, and analyze the influence of the coherent structure on the nonstationary and non-Gaussian wind speed and study the influence of the coherent structure on the wind turbulence characteristics. The results show that for the 0814 typhoon Hagupit process, the coherent structure is the main reason that leads to the nonstationary and non-Gaussian fluctuating winds in the typhoon field, and with the coherent structures being exacted from the original winds, the nonstationary and non-Gaussian characteristics of the nonstationary wind samples are significantly weakened. The average contribution of the coherent structure to the turbulence parameters ranges from 6.42% to 32.40%. The duration of the coherent structure is about 10.60% of the sample duration, however, its contribution to turbulent kinetic energy is up to 40.50%. The coherent structure has the characteristics of short duration and high energy content, which is the cause of the abnormally large turbulence parameter value. This study can provide a reference for the refined wind resistance design of structures under the action of nonstationary wind.

Decoherence and quantum steering of accelerated qubit–qutrit system

The bidirectional steerability between different-size subsystems is discussed for a single parameter accelerated qubit–qutrit system. The decoherence due to the mixing and acceleration parameters is investigated, where for the total system and the qutrit, it increases as the mixing parameter increases, while it decreases for the qubit. The non-classical correlations are quantified by using the local quantum uncertainty, where the uncertainty increases at large values of the acceleration parameter. The possibility that each subsystem steers each other is studied, where the behavior of the steering inequality predicts that the qubit has a large ability to steer the qutrit. The degree of steerability decays gradually when the qubit is accelerated. However, it decays suddenly when the qutrit or both subsystems are accelerated. The degree of steerability is shown for the qutrit vanishes at small values of the acceleration, while the qubit at large acceleration. The difference between the degrees of steerability depends on the initial state settings and the size of the accelerated subsystem.

Recurrence quantification and bifurcation analysis of electrical activity in resistive/memristive synapse coupled Fitzhugh–Nagumo type neurons

Temporal response of excitable individual and coupled different neuronal circuits i.e., Cell-I and Cell-II, of Fitzhugh–Nagumo type have been numerically simulated with a view to understand and characterize the complexities of involved dynamical processes. FHN neuronal circuit Cell-I and Cell-II have been shown to exhibit supercritical Hopf bifurcation, when excited by an external steady stimulus. For time varying sinusoidal excitation, the temporal action potential behavior of these neuronal circuits, when analyzed using measures of recurrence quantification analysis (RQA) and bifurcation diagram reveals period-1, period-2, multi-periodic, chaotic and reverse period doubling characteristics as observed earlier experimentally in giant squid axon and other biological cell assemblies. Phase portrait, bifurcation diagrams and recurrence plot (RPs), of (i) unidirectional and (ii) bidirectional coupled FHN Cell-I and Cell-II, through a gap junction resistor, suggest the possibility of transition to intermittent state besides the transition of respective action potential from periodic to multi-periodic to chaotic state in an ordered or disordered fashion, depending on values of system parameters that control the complexities. Further, for both the configurations (i) and (ii), synchronization of FHN neuron Cell-I with Cell-II is also shown to occur for large values of coupling parameter, ξ. The dynamical effect of electromagnetic radiation on individual FHN neuron circuits has also been investigated using a flux controlled memristor that couples the magnetic flux with the individual FHN neurons. Phase portrait, bifurcation and RQA analysis have also been used to characterize the electrical activities of excitable cell assemblies involving memristive synapse coupled FHN neuronal Cell-I and Cell-II in settings (i) and (ii) respectively.

Thermoelectric properties of Rashba compounds KSnX (X = Sb, Bi)

Here, we have presented the results of the detailed theoretical study of thermoelectric properties of two Rashba compounds KSnSb and KSnBi using first principles calculations based on density functional theory and Boltzmann transport theory taking spin–orbit coupling (SOC) into account. As these compounds have layered-type crystal structures, their transport parameters are found to be highly anisotropic. For KSnBi (KSnSb), the calculated lattice thermal conductivity κl along its crystallographic c axis is found to have ultralow value of 0.49 W m−1 K−1 (0.78 W m−1 K−1) even at room temperature, whereas almost twofold larger value of κl is estimated along its crystallographic a axis. However, large values of other transport parameters like electrical conductivity σ and thermopower S desirable for a high power factor (S2σ) are found along the a axis of these compounds. For KSnSb, the optimum a axis ZT=2.6 can be reachable for an electron concentration of 3.3 × 1019 cm−3 and at a temperature of 800 K. Comparable value of optimum a axis ZT=2.5 is also noted for KSnBi despite its strong susceptibility to bipolar conduction. Both these non-centrosymmetric compounds exhibit SOC-driven Rashba spin splitting of electronic bands, which affects both thermopower and electrical conductivity of these compounds. However, such Rashba spin splitting induced change in thermopower is almost negated by the concomitant change in electrical conductivity, resulting in no appreciable impact on power factor and hence ZT of the studied compounds.

Asymptotic Behavior of Solutions of the Cauchy Problem for a Hyperbolic Equation with Periodic Coefficients II

The paper is devoted to studying the behavior of solutions of the Cauchy problem for large values of time—more precisely, obtaining an asymptotic expansion characterizing the behavior of the solution of the Cauchy problem for a one-dimensional second-order hyperbolic equation with periodic coefficients for large values of the time parameter t. To obtain this asymptotic expansion as t→∞, methods of the spectral theory of differential operators are used, as well as the properties of the spectrum of a non-positive Hill operator with periodic coefficients.

Entanglement entropies of an interval in the free Schrödinger field theory on the half line

We study the entanglement entropies of an interval adjacent to the boundary of the half line for the free fermionic spinless Schrödinger field theory at finite density and zero temperature, with either Neumann or Dirichlet boundary conditions. They are finite functions of the dimensionless parameter given by the product of the Fermi momentum and the length of the interval. The entanglement entropy displays an oscillatory behaviour, differently from the case of the interval on the whole line. This behaviour is related to the Friedel oscillations of the mean particle density on the half line at the entangling point. We find analytic expressions for the expansions of the entanglement entropies in the regimes of small and large values of the dimensionless parameter. They display a remarkable agreement with the curves obtained numerically. The analysis is extended to a family of free fermionic Lifshitz models labelled by their integer Lifshitz exponent, whose parity determines the properties of the entanglement entropies. The cumulants of the local charge operator and the Schatten norms of the underlying kernels are also explored.

Routes to chaos in a class-B laser coupled to a neutral resonator

We study the dynamics of a class-B semiconductor microring laser coupled to a neutral microring resonator for common fabrication parameters. For zero detuning between the resonators, we identify five dynamical regions controlled by the normalized pump rate of the laser and coupling strength between the resonators. These regions show stable lasing with phase locking for either sufficiently small or large coupling strength parameter values. Multistability and chaos arise in between these stable regions where at least one fixed point is attractive. The transition from stable to unstable lasing regions in the parameter space phase diagram is a crossover.

QED effects on phase transition and Ruppeiner geometry of Euler-Heisenberg-AdS black holes* *Supported by the National Natural Science Foundation of China (12075103, 11675064, 12047501) and the 111 Project (B20063)

Considering the quantum electrodynamics (QED) effect, we study the phase transition and Ruppeiner geometry of Euler-Heisenberg anti-de Sitter black holes in the extended phase space. For negative and small positive QED parameters, we observe a small/large black hole phase transition and reentrant phase transition, respectively, whereas a large positive value of the QED parameter ruins the phase transition. Phase diagrams for each case are explicitly shown. Then, we construct the Ruppeiner geometry in thermodynamic parameter space. Different features of the corresponding scalar curvature are shown for both the small/large black hole phase transition and reentrant phase transition cases. Of particular interest is the additional region of positive scalar curvature, indicating a dominant repulsive interaction among black hole microstructures, for the black hole with a small positive QED parameter. Furthermore, universal critical phenomena are observed for the scalar curvature of Ruppeiner geometry. These results indicate that the QED parameter has a crucial influence on the black hole phase transition and microstructure.

Universal Properties of Anisotropic Dipolar Bosons in Two Dimensions

The energy of ultra-dilute quantum many-body systems is known to exhibit a universal dependence on the gas parameter x=n a_0^dx=na0d, with nn the density, dd the dimensionality of the space (d=1,2,3d=1,2,3) and a_0a0 the ss-wave scattering length. The universal regime typically extends up to x\approx 0.001x≈0.001, while at larger values specific details of the interaction start to be relevant and different model potentials lead to different results. Dipolar systems are peculiar in this regard since the anisotropy of the interaction makes a_0a0 depend on the polarization angle \alphaα, so different combinations of n and \alphaα can lead to the same value of the gas parameter x. In this work we analyze the scaling properties of dipolar bosons in two dimensions as a function of the density and polarization dependent scattering length up to very large gas parameter values. Using Quantum Monte Carlo (QMC) methods we study the energy and the main structural and coherence properties of the ground state of a gas of dipolar bosons by varying the density and scattering length for a fixed gas parameter. We find that the dipolar interaction shows relevant scaling laws up to unusually large values of xx that hold almost to the boundaries in the phase diagram where a transition to a stripe phase takes place.

Asymptotic Behavior of Solutions of the Cauchy Problem for a Hyperbolic Equation with Periodic Coefficients (Case: H0 > 0)

The main goal of this article is to study the behavior of solutions of non-stationary problems at large timescales, namely, to obtain an asymptotic expansion characterizing the behavior of the solution of the Cauchy problem for a one-dimensional second-order hyperbolic equation with periodic coefficients at large values of the time parameter t. To obtain an asymptotic expansion as t→∞, the basic methods of the spectral theory of differential operators are used, as well as the properties of the spectrum of the Hill operator with periodic coefficients in the case when the operator is positive: H0>0.