Power-law Term Research Articles

Landscape Higgs boson and sparticle mass predictions from a logarithmic soft term distribution

Recent work on calculating string theory landscape statistical predictions for the Higgs and sparticle mass spectrum from an assumed power-law soft term distribution yields an expectation for m(h)~ 125 GeV with sparticles (save light higgsinos) somewhat beyond reach of high-luminosity LHC. A recent examination of statistics of SUSY breaking in IIB string models with stabilized moduli suggests a power-law for models based on KKLT stabilization and uplifting while models based on large-volume scenario (LVS) instead yield an expected logarithmic soft term distribution. We evaluate statistical distributions for Higgs and sparticle masses from the landscape with a log soft term distribution and find the Higgs mass still peaks around ~125 GeV with sparticles beyond LHC reach, albeit with somewhat softer distributions than those arising from a power-law.

Evolution of dissipative and nondissipative universes in holographic cosmological models with a power-law term

Density perturbations related to structure formations are expected to be different in dissipative and non-dissipative universes, even if the background evolution of the two universes is the same. To clarify the difference between the two universes, first-order density perturbations are studied, using two types of holographic cosmological models. The first type is a "$\Lambda(t)$ model" similar to a time-varying $\Lambda(t)$ cosmology for the non-dissipative universe. The second type is a "BV model" similar to a bulk viscous cosmology for the dissipative universe. To systematically examine the two different universes, a power-law term proportional to $H^{\alpha}$ is applied to the $\Lambda(t)$ and BV (bulk-viscous-cosmology-like) models, assuming a flat Friedmann--Robertson--Walker model for the late universe. Here, $H$ is the Hubble parameter and $\alpha$ is a free parameter whose value is a real number. The $\Lambda(t)$-$H^{\alpha}$ and BV-$H^{\alpha}$ models are used to examine first-order density perturbations for matter, in which the background evolution of the two models is equivalent. In addition, thermodynamic constraints on the two models are discussed, with a focus on the maximization of entropy on the horizon of the universe, extending previous analyses [Phys. Rev. D 100, 123545 (2019) (arXiv:1911.08306); 102, 063512 (2020) (arXiv:2006.09650)]. Consequently, the $\Lambda(t)$-$H^{\alpha}$ model for small $|\alpha|$ values is found to be consistent with observations and satisfies the thermodynamic constraints, compared with the BV-$H^{\alpha}$ model. The results show that the non-dissipative universe described by the $\Lambda(t)$-$H^{\alpha}$ model similar to lambda cold dark matter models is likely favored.

Entropy production due to adiabatic particle creation in a holographic dissipative cosmology

Cosmological adiabatic particle creation results in the generation of irreversible entropy. The evolution of this entropy is examined in a flat Friedmann--Robertson--Walker universe at late times, using a dissipative model with a power-law term (proportional to the power of the Hubble parameter $H$). In a dissipative universe, the irreversible entropy included in the Hubble volume is found to be proportional to $H^{-1}$, unlike for the case of the Bekenstein--Hawking entropy on the horizon of the universe. In addition, the evolution of the horizon entropy is examined, extending the previous analysis of a non-dissipative universe [Phys.\ Rev.\ D \textbf{100}, 123545 (2019) (arXiv:1911.08306)]. In the present model, the generalized second law of thermodynamics is always satisfied, whereas the maximization of entropy is satisfied under specific conditions. The dissipative universe should be constrained by the entropy maximization as if the universe behaves as an ordinary, isolated macroscopic system. The thermodynamic constraints are likely to be consistent with constraints on a transition from a decelerating universe to an accelerating universe.

A fractional subgrid-scale model for turbulent flows: Theoretical formulation and a priori study

Coherent structures/motions in turbulence inherently give rise to intermittent signals with sharp peaks, heavy-skirt, and skewed distributions of velocity increments, highlighting the non-Gaussian nature of turbulence. This suggests that the spatial nonlocal interactions cannot be ruled out of the turbulence physics. Furthermore, filtering the Navier–Stokes equations in the large eddy simulation of turbulent flows would further enhance the existing nonlocality, emerging in the corresponding subgrid scale fluid motions. This urges the development of new nonlocal closure models, which respect the corresponding non-Gaussian statistics of the subgrid stochastic motions. To this end and starting from the filtered Boltzmann equation, we model the corresponding equilibrium distribution function with a Lévy-stable distribution, leading to the proposed fractional-order modeling of subgrid-scale stresses. We approximate the filtered equilibrium distribution function with a power-law term and derive the corresponding filtered Navier–Stokes equations. Subsequently in our functional modeling, the divergence of subgrid-scale stresses emerges as a single-parameter fractional Laplacian, (−Δ)α(·), α ∈ (0, 1], of the filtered velocity field. The only model parameter, i.e., the fractional exponent, appears to be strictly dependent on the filter-width and the flow Reynolds number. We furthermore explore the main physical and mathematical properties of the proposed model under a set of mild conditions. Finally, the introduced model undergoes a priori evaluations based on the direct numerical simulation database of forced and decaying homogeneous isotropic turbulent flows at relatively high and moderate Reynolds numbers, respectively. Such analysis provides a comparative study of predictability and performance of the proposed fractional model.

A Comprehensive Report on Ultrasonic Attenuation of Engineering Materials, Including Metals, Ceramics, Polymers, Fiber-Reinforced Composites, Wood, and Rocks

In this paper, ultrasonic attenuation of engineering materials is evaluated comprehensively, covering metals, ceramics, polymers, fiber-reinforced composites, wood, and rocks. After verifying two reliable experimental methods, 336 measurements are conducted and their results are tabulated. Attenuation behavior is determined over broadband spectra, extending up to 15 MHz in low attenuating materials. The attenuation spectra are characterized in combination with four power law terms, with many showing linear frequency dependence, with or without Rayleigh scattering. Dislocation damping effects are re-evaluated and a new mechanism is proposed to explain some of the linear frequency dependencies. Additionally, quadratic and cubic dependencies due to Datta–Kinra scattering and Biwa scattering, respectively, are used for some materials to construct model relations. From many test results, some previously hidden behaviors emerged upon data evaluation. Effects of cold working, tempering, and annealing are complex and sometimes contradictory. Comparison to available literature was attempted for some, but most often prior data were unavailable. This collection of new attenuation data will be of value in materials selection and in designing structural health monitoring and non-destructive inspection protocols.

Thermostatistics of overdamped motion with anisotropic drag forces

We investigate the consequences of anisotropic drag forces for the thermostatistics of systems of interacting particles in the overdamped motion regime. Systems of confined particles interacting via short-range forces and performing overdamped motion exhibit interesting thermodynamic features, and constitute useful models for various problems in physics and other areas. In particular, they proved useful for the study of interacting vortices in type-II superconductors. The dynamics of the above mentioned many-particle systems admits an effective description based on nonlinear Fokker-Planck equations with power-law diffusion terms. Most works studying this kind of systems, and their relationship with nonlinear Fokker-Planck equations, assume isotropic drag forces. In the present work we consider the effects of anisotropic drag forces on this kind of systems. We derive the corresponding nonlinear Fokker-Planck equations and investigate some of their main properties.

The axion mass from 5D small instantons

We calculate a new contribution to the axion mass that arises from gluons propagating in a 5th dimension at high energies. By uplifting the 4D instanton solution to five dimensions, the positive frequency modes of the Kaluza-Klein states generate a power-law term in the effective action that inversely grows with the instanton size. This causes 5D small instantons to enhance the axion mass in a way that does not spoil the axion solution to the strong CP problem. Moreover this enhancement can be much larger than the usual QCD contribution from large instantons, although it requires the 5D gauge theory to be near the non-perturbative limit. Thus our result suggests that the mass range of axions (or axion-like particles), which is important for ongoing experimental searches, can depend sensitively on the UV modification of QCD.

Geometric inflation and dark energy with axion F(R) gravity

We present a model of $F(R)$ gravity in the presence of a string theory motivated misalignment axion like particle materialized in terms of a canonical scalar field minimally coupled with gravity, and we study the cosmological phenomenology of the model, emphasizing mainly on the late-time era. The main result of the paper is that inflation and the dark energy era may be realized in a geometric way by an $F(R)$ gravity, while the axion is the dark matter constituent of the Universe. The $F(R)$ gravity model consists of an ${R}^{2}$ term, which as we show dominates the evolution during the early time, thus producing a viable inflationary phenomenology, and a power law term $\ensuremath{\sim}{R}^{\ensuremath{\delta}}$ with $\ensuremath{\delta}\ensuremath{\ll}1$ and positive, which eventually controls the late-time era. The axion field remains frozen during the inflationary era, which is an effect known for misalignment axions, but as the Universe expands, the axion starts to oscillate, and its energy density scales eventually as we show, as ${\ensuremath{\rho}}_{a}\ensuremath{\sim}{a}^{\ensuremath{-}3}$. After appropriately rewriting the gravitational equations in terms of the redshift $z$, we study in detail the late-time phenomenology of the model, and we compare the results with the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model and the latest Planck 2018 data. As we show, the model for small redshifts $0<z<5$ is phenomenologically similar to the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model, however at large redshifts and deeply in the matter domination era, the results are different from those of the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model due to the dark energy oscillations. For the late-time study we investigate the behavior of several well-known statefinder quantities, like the deceleration parameter, the jerk and $Om(z)$, and we demonstrate that the statefinders which contain lower derivatives of the Hubble rate have similar behavior for both the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ and the axion $F(R)$ gravity model. We conclude that the axion $F(R)$ gravity model can unify in a geometric way the inflationary epoch with the dark energy era, and with the axion being the main dark matter constituent.

Analysis of a generalized Fujikawa's growth model.

We analyze a generalized form of the Fujikawas growth model which involves an adaptation function that enhances the representation of the lag phase. This model is autonomous, and combines a power law term, a saturation term and an adaptation function that suppresses the growth rate during initial period corresponding to the lag phase. The properties of the adaptation function are determined, and the proposed model is examined separately for the regular measure and the logarithmic measure, including: Convergence and boundedness properties; population at the inflection point; conditions for the existence of the inflection point and lag phase; effect of model parameters on the existence of the inflection point and lag phase; population size of the inflection point under limiting values of the model parameters; and parameter values that lead to inflection point located at the mean value of the curve. Different combinations of model parameters lead to different possibilities for the existence of the inflection point and the lag phase. It was noticed that the power law term has a strong effect on the representation of the exponential growth phase, whereas the adaptation function has a strong effect on the representation of the lag phase. The lag phase duration depends on the exponent parameter of the adaptation function, and its dependence with respect to the power law parameter is low. Also, an approach is proposed for the analytical determination of the lag time, based on the application of the classical approach to a simplified model. Ascertained lag time values were obtained, what confirms the assumptions. At last, the model is applied to experimental data.

Horizon thermodynamics in holographic cosmological models with a power-law term

Thermodynamics on the horizon of a flat universe at late times is studied in holographic cosmological models that assume an associated entropy on the horizon. In such models, a $\Lambda(t)$ model similar to a time-varying $\Lambda(t)$ cosmology is favored because of the consistency of energy flows across the horizon. Based on this consistency, a $\Lambda(t)$ model with a power-law term proportional to $H^{\alpha}$ is formulated to systematically examine the evolution of the Bekenstein--Hawking entropy. Here, $H$ is the Hubble parameter and $\alpha$ is a free parameter whose value is a real number. The present model always satisfies the second law of thermodynamics on the horizon. In particular, the universe for $\alpha <2$ tends to approach thermodynamic equilibrium-like states. Consequently, when $\alpha < 2$, the maximization of the entropy should be satisfied as well, at least in the last stage of the evolution of an expanding universe. A relaxation-like process before the last stage is also examined from a thermodynamics viewpoint.

Power-law Sérsic profiles in hydrostatic stellar galaxy discs

ABSTRACT Previously, we showed that surface density profiles of the form of a power-law times a Sérsic function satisfy the hydrostatic Jeans equations, a variety of observational constraints, and the condition of a minimal radial entropy profile in two-dimensional galaxy discs with fixed power law, halo potentials. It was assumed that such density profiles are generated by star scattering by clumps, waves, or other inhomogeneities. Here, we generalize these models to self-gravitating discs. The cylindrically symmetric Poisson equation imposes strong constraints. Scattering processes favour smoothness, so the smoothest solutions, which minimize entropy gradients, are preferred. In the case of self-gravitating discs (e.g. inner discs), the gravity, surface density, and radial velocity dispersion in these smoothest models are all of the form 1/r times an exponential. When vertical balance is included, the vertical velocity dispersion squared has the same form as the surface density, and the scale height is constant. In combined self-gravitating plus halo gravity cases, the radial dispersion has an additional power-law term. None the less, the surface density profile has the same form at all radii, without breaks, satisfying the ‘disc–halo conspiracy’. The azimuthal velocity and velocity dispersions are smooth, though the former can have a distinct peak. In these models the vertical dispersion increases inwards, and scattering may mediate a transition to a secular bulge. If halo gravity dominates vertically in the outer disc, it flares. The models suggest a correlation between disc mass and radial scale length. The combination of smoothness, simplicity, ability to match generic observational features, and physical constraints is unique to these models.

An index of Chinese surname distribution and its implications for population dynamics.

ObjectiveWe propose an index to characterize the key feature of Chinese surname distributions and investigate its implications for population structure and dynamics.Materials and methodsThe surname dataset was obtained from the National Citizen Identity Information Center, which contains 1.28 billion Chinese citizens enrolled in 2007, excluding those of Hong Kong, Macao, and Taiwan. An index, the coverage ratio of stretched exponential distribution (CRSED), is proposed based on the crossover point of stretched exponential truncated power‐law distribution, where the stretched exponential term and the power‐law term contribute equally. We use multidimensional scaling technique to demonstrate the dependence of the similarity of one prefecture to the others on the CRSED.ResultsThe CRSEDs of 362 prefectures exhibit an uneven distribution. The consistency of this index is evident by strong positive correlations of CRSEDs at the three administrative levels. This new index has a strong negative correlation with the proportion of the rare surnames. The prefectures with similar CRSEDs tend to adjoin each other on the administrative map, resulting in several distinct regions, each of which shares similar terrain features or historical migrations. The prefectures with lower CRSEDs are more dissimilar to the other prefectures, while the ones with higher CRSEDs are more similar to the others.DiscussionThe population dynamics of the prefectures with higher CRSEDs are more likely dominated by migratory movements, the dominant evolutionary forces of the prefectures with lower CRSEDs can be attributed to drift and mutation.

Effect of iron oxide nanoparticles on fibrin gel formation and its fractal dimension.

In this paper, we studied the influence of nonmagnetic iron oxide nanoparticles on fibrin gel formation and its structure using dynamic light scattering. The surface of nanoparticles produced by a new method in acoustoplasma discharge with cavitation has specific morphology and accelerates the rate of fibrin gel formation, i.e., activates the enzyme thrombin. We studied changes in the form of autocorrelation functions of the scattered light intensity for fibrinogen-thrombin samples with different thrombin concentrations as well as the nanoparticles addition. Appearance of the power-law term in the function was an indicator of gel formation in the sample. Application of Martin's theory allows estimating the exponent φ of power-law function and the contribution of the diffusive mode of protofibrils. We found that an increase in thrombin concentration or its activation with iron oxide nanoparticles leads to decreasing contribution of the diffusive mode, and increasing contribution of the exponent of power-law function. The values of fractal dimension Df calculated using Muthukumar's theory are 1.61 ± 0.13 and 1.69 ± 1.11 for samples with low and high concentrations of thrombin respectively and 1.77 ± 0.08 for the sample with thrombin activated by nanoparticles. Such an increase in fractal dimension shows an increase in the complexity of the fibrin gel structure (or density).

Reconstruction of $f(R)$ gravity models for an accelerated universe using the Raychaudhuri equation

A new strategy for the reconstruction of $f(R)$ gravity models have been attempted using Raychaudhuri equation. Two examples, one for an eternally accelerating universe and the other for one that mimics a ${\Lambda}$CDM expansion history have been worked out. For both the cases, the relevant $f=f(R)$ could be found out analytically. In the first case, $f(R)$ is found to be a combination of power-law terms and in the expression for the second case involves hypergeometric functions. The evolution history of the universe, given as specific values of the kinematical quantities like the jerk or the deceleration parameter, serve as the input. It is found that the corresponding $f(R)$ gravity models, in both the examples, are not viable options.

Holographic approach to entanglement entropy in disordered systems

We investigate the entanglement entropy of a two-dimensional disordered system holographically. In particular, we study the evolution of the entanglement entropy along renormalization group flows for a conformal theory at the UV fixed point, that is perturbed by weak disorder into a Lifshitz theory at the IR fixed point. Through numerical fitting, we find that the disorder correlations leads to a sub-leading power-law term in the entanglement entropy that vanishes at the IR fixed point. Interestingly, the exponent that controls the power-law vanishing of the sub-leading term seems to be almost universal as it depends very weakly on the strength of the disorder. We show that our results can be put in the context of the c-theorem by defining an effective central charge that decreases along the RG flow. We also investigate disorder induced long-range correlations between the two subsystems by studying the holographic mutual information.

Rationally Derived Three-Parameter Models for Elastomeric Suspension Bushings: Theory and Experiment

Abstract Linear, causal, and time-invariant viscoelastic material response models are of practical interest in many areas, including our interest in automotive suspension bushings. Empirical fits to experimental data may involve several fitted parameters which, if chosen arbitrarily, violate theoretical restrictions derived from causality, linearity, and time invariance. Here, we retain a correction term in an asymptotic expansion for Bode’s representation of the famous Kramers-Kronig relations. We then derive two new mathematical forms that both satisfy theoretical restrictions and fit experimental data well. Both forms proposed in this article have three free parameters each. The first form has logarithms and power law terms and is valid if the index in the power law is small. The second form has only logarithmic terms and satisfies restrictions exactly. Both forms successfully fit the test data for four different automotive suspension bushings in a frequency range of 1–30 Hz. The first form, with the power law, is more complicated but fits the data slightly better. Because the frequency response involves both a real and imaginary part, simultaneously fitting both parts well with merely three parameters validates the approximations proposed in this article.

W-shaped, dark and grey solitary waves in the nonlinear Schrödinger equation competing dual power-law nonlinear terms and potentials modulated in time and space

ABSTRACTThis paper explores the higher-order nonlinear Schrodinger equation with dual power-law nonlinearities and external potential that can depend on space and time coordinates. We constructed exact soliton-like solutions with arbitrary power-law nonlinearities using the similarity transformation approach. We obtained a family of soliton-like solutions: the so-called W-shaped, dark and the grey solitons. These solutions are at first, found by considering just the time modulated nonlinearities, where the frame variable coincides with the characteristic coordinate ξ. Then the nonlinearities coefficients and potential are space–time modulated with a bounded function . In both cases, a numerical study based on appropriate choices of parameters is achieved. For a fixed absolute value of nonlinearities, we examine how different soliton profiles are influenced when increasing the power-law index n. These variations of parameters display some substantial changes in solitary wave profiles; paving the way for many applications.

Solutions of solitary-wave for the variable-coefficient nonlinear Schrödinger equation with two power-law nonlinear terms

In this paper, we consider the variable-coefficient power-law nonlinear Schrödinger equations (NLSEs) with external potential as well as the gain or loss function. First, we generalize the similarity transformation method, which converts the variable coefficient NLSE with two power-law nonlinear terms to the autonomous dual-power NLS equation with constant coefficients. Then, we obtain the exact solutions of the variable-coefficient NLSE. Moreover, we discuss the solitary-wave solutions for equations with vanishing potential, space-quadratic potential and optical lattice potential, which are applied to many branches of physics.

The elusive linkage between CEO pay and performance

ObjetivoDiscutimos o trabalho de Aguinis et al. (2018). Acreditamos que as suas hipóteses são provavelmente verdadeiras, mas a sua metodologia apresenta deficiências e os dados apresentados não suportam as conclusões.Design/metodologiaAnalisamos e comentamos o trabalho de Aguinis et al. (2018).ResultadosOs dados não demonstram adequadamente a existência de uma distribuição de poder-lei porque suas análises não consideram as condições externas que afetam o resultado da empresa e os autores fazem uso impróprio das variáveis dependentes. As análises não mostram que as recompensas dos CEOs seguem uma distribuição da lei do poder porque não tomam em consideração as mudanças no nível ou na composição da remuneração sobre o tempo. As análises não mostram falta de sobreposição entre as duas distribuições, porque não têm em conta a forma como os CEOs são pagos pelos resultados e porque utilizam a retribuição média calculada sobre a antiguidade do CEO.Limitações/implicaçõesUma análise mais convincente da hipótese proposta requer o uso do desempenho total dos acionistas como uma variável de resultados organizacionais e um número muito mais específico de variáveis de controle.Implicações práticasOs autores incentivam os profissionais a pensar mais em termos de uma distribuição da lei de potência quando se define o salário do CEO. Suas análises indicam que os profissionais já pensam em termos dessa distribuição e distribuem as recompensas de forma proporcional a ela. Além do mais, os resultados derivados da teoria da lei de poder podem ser erroneamente usados como uma desculpa para pagar menos para o CEO médio.Implicações sociaisAgregamos uma outra perspectiva no pagamento ao CEO.Originalidade/valorNossa perspectiva é apoiada pelo nosso pesquisa e experiência de consultoria em projetos de remuneração para CEOs.

From the nonlinear Fokker-Planck equation to the Vlasov description and back: Confined interacting particles with drag.

Nonlinear Fokker-Planck equations endowed with power-law diffusion terms have proven to be valuable tools for the study of diverse complex systems in physics, biology, and other fields. The nonlinearity appearing in these evolution equations can be interpreted as providing an effective description of a system of particles interacting via short-range forces while performing overdamped motion under the effect of an external confining potential. This point of view has been recently applied to the study of thermodynamical features of interacting vortices in type II superconductors. In the present work we explore an embedding of the nonlinear Fokker-Planck equation within a Vlasov equation, thus incorporating inertial effects to the concomitant particle dynamics. Exact time-dependent solutions of the q-Gaussian form (with compact support) are obtained for the Vlasov equation in the case of quadratic confining potentials.