General Scaling Behavior Research Articles

Work statistics across a quantum critical surface.

We study the universality of work statistics of a system quenched through a quantum critical surface. By using the adiabatic perturbation theory, we obtain the general scaling behavior for all cumulants of work. These results extend the studies of Kibble-Zurek mechanism scaling of work statistics from an isolated quantum critical point to a critical surface. As an example, we study the scaling behavior of work statistics in the two-dimensional (2D) Kitaev honeycomb model featured with a critical line. By utilizing the trace formula for quadratic fermionic Hamiltonian, we obtain the exact characteristic function of work of the 2D Kitaev model at zero temperature. The results confirm our prediction.

General Thermodynamic Efficiency Loss and Scaling Behavior of Eukaryotic Organisms

A simple and general thermodynamic theory is applied to describe the irreversible aspects of the continuous process of functional efficiency loss, which occurs in dissipative biological structures after they reach maturity. Following Prigogine [G. Nicolis and I. Prigogine, Self-organization in Nonequilibrium Systems (Wiley, New York, 1997), pp. 2–3], this theory considers that these dissipative structures perform their functions carrying out cyclic processes per se since they are self-organized far from equilibrium. Starting from the theoretical fact that after biological dissipative systems reach adulthood, the functionality of their organs decreases linearly over time. We show that cumulative damage leads to the exponential law of increasing mortality rate with age for population groups, known as Gompertz’s law. The theory was applied to the determination of functional efficiency loss parameter, [Formula: see text], for 71 living beings as a function of mass covering 18 orders of magnitude. The mathematical adjustment allowed us to conclude that there is a minimum in the value of the [Formula: see text] parameter for a 23.3 kg mass which is close enough to the Homo sapiens one. We obtained useful expressions to describe the [Formula: see text] parameter for smaller masses than those of saccharomyces cerevisiae, so perhaps this theory may contribute to the study of the evolution of some dissipative pre-biological structures.

Impact of isolation and fiducial cuts on qT and N-jettiness subtractions

Kinematic selection cuts and isolation requirements are a necessity in experimental measurements for identifying prompt leptons and photons that originate from the hard-interaction process of interest. We analyze how such cuts affect the application of the qT and N -jettiness subtraction methods for fixed-order calculations. We consider both fixed-cone and smooth-cone isolation methods. We find that kinematic selection and isolation cuts both induce parametrically enhanced power corrections with considerably slower convergence compared to the standard power corrections that are already present in inclusive cross sections without additional cuts. Using analytic arguments at next-to-leading order we derive their general scaling behavior as a function of the subtraction cutoff. We also study their numerical impact for the case of gluon-fusion Higgs production in the H → γγ decay mode and for pp → γγ direct diphoton production. We find that the relative enhancement of the additional cut-induced power corrections tends to be more severe for qT, where it can reach an order of magnitude or more, depending on the choice of parameters and subtraction cutoffs. We discuss how all such cuts can be incorporated without causing additional power corrections by implementing the subtractions differentially rather than through a global slicing method. We also highlight the close relation of this formulation of the subtractions to the projection-to-Born method.

Light Gold: A Colloidal Approach Using Latex Templates

AbstractA new 18 karat light gold, composed of gold single crystals, amyloids, and a polymer latex matrix is developed. It is similar to a glassy plastic, yet lighter than aluminum and of use in watches, jewelry, radiation shielding, catalysis, and electronics. The material is prepared via a hydrogel precursor dried into an aerogel. Annealing of the polystyrene matrix under vacuum gives rise to a homogeneous template. The final apparent density and porosity of the material depend directly on the volumetric concentration of the starting solution used for hydrogel formation. After annealing, a homogeneous microstructure is obtained in which the shining gold single crystal platelets are evenly embedded in a polystyrene matrix. The material has a glass transition temperature of ≈105 °C which allows for annealing and molding above this temperature. A general scaling behavior is found for the Young's modulus of the material with the density. The Young's modulus of the material with a density of 1.7 g cm−3 is ≈50 MPa. The density and stiffness, as well as the color, of the material can be tuned depending on the final application.

Scaling behavior of the stationary states arising from dissipation at continuous quantum transitions

We study the critical behavior of the nonequilibrium dynamics and of the steady states emerging from the competition between coherent and dissipative dynamics close to quantum phase transitions. The latter is induced by the coupling of the system with a Markovian bath, such that the evolution of the system's density matrix can be effectively described by a Lindblad master equation. We devise general scaling behaviors for the out-of-equilibrium evolution and the stationary states emerging in the large-time limit for generic initial conditions in terms of the parameters of the Hamiltonian providing the coherent driving and those associated with the dissipative interactions with the environment. Our framework is supported by numerical results for the dynamics of a one-dimensional lattice fermion gas undergoing a quantum Ising transition in the presence of dissipative mechanisms which include local pumping and decay of particles.

Competing coherent and dissipative dynamics close to quantum criticality

We investigate the competition of coherent and dissipative dynamics in many-body systems at continuous quantum transitions. We consider dissipative mechanisms that can be effectively described by Lindblad equations for the density matrix of the system. The interplay between the critical coherent dynamics and dissipation is addressed within a dynamic finite-size scaling framework, which allows us to identify the regime where they develop a nontrivial competition. We analyze protocols that start from critical many-body ground states and put forward general dynamic scaling behaviors involving the Hamiltonian parameters and the coupling associated with the dissipation. This scaling scenario is supported by a numerical study of the dynamic behavior of a one-dimensional lattice fermion gas undergoing a quantum Ising transition in the presence of dissipative mechanisms such as local pumping, decaying, and dephasing.

Variation of the transition energies and oscillator strengths for the 3C and 3D lines of the Ne-like ions under plasma environment

We present the results of a detailed theoretical study which meets the spatial and temporal criteria of the Debye–Hückel approximation on the variation of the transition energies as well as the oscillator strengths for the (3C line) and the (3D line) transitions of the Ne-like ions subject to external plasma. Our study shows that the redshifts of the transition energy follow the general scaling behaviors similar to the ones for the simple H-like and He-like ions. Whereas the oscillator strength for the 3C line decreases, the oscillator strength for the spin-flipped 3D line increases as the strength of the outside plasma increases. As a result, their ratio is amplified subject to outside plasma environment. We further demonstrate that the plasma-induced variation between the relative strength of the 3C and 3D transitions is mainly due to the spin-dependent interactions which dictate the mixing of the 1P1 component in the 3D1 upper state of the 3D transition. In addition, we are able to find that the ratio between the relative oscillator strengths of the 3C and 3D lines in the presence of the plasma to their respective plasma-free values varies as a nearly universal function of , with Z the nuclear charge and D the Debye length. The results of this study should be of great help in the modelling and diagnostic of astrophysical plasmas as well as laboratory plasmas.

Geometrical optics of constrained Brownian excursion: from the KPZ scaling to dynamical phase transitions

We study a Brownian excursion on the time interval , conditioned to stay above a moving wall such that , and . For a whole class of moving walls, typical fluctuations of the conditioned Brownian excursion are described by the Ferrari–Spohn (FS) distribution and exhibit the Kardar–Parisi–Zhang (KPZ) dynamic scaling exponents 1/3 and 2/3. Here we use the optimal fluctuation method (OFM) to study atypical fluctuations, which turn out to be quite different. The OFM provides their simple description in terms of optimal paths, or rays, of the Brownian motion. We predict two singularities of the large deviation function, which can be interpreted as dynamical phase transitions, and they are typically of third order. Transitions of a fractional order can also appear depending on the behavior of in a close vicinity of . Although the OFM does not describe typical fluctuations, it faithfully reproduces the near tail of the FS distribution and therefore captures the KPZ scaling. If the wall function is not parabolic near its maximum, typical fluctuations (which we probe in the near tail) exhibit a more general scaling behavior with a continuous one-parameter family of scaling exponents.

Single particle dark-field spectroscopy of spherical dimers with down to sub-10 nm gaps fabricated by the annealing of nano-pillars

Abstract In this paper we present a method for the fabrication of plasmonic spherical dimers and oligomers with narrow gaps and tunable distances. High-aspect-ratio nano-pillars are created by the two-step evaporation of gold on structured substrates. By using electron beam lithography, it is possible to control the close spacing of the pillars. Rapid thermal annealing causes the pillars to adopt a spherical shape. Since by melting the spheres gain in diameter compared to the initial nano-pillars, the distance between two adjacent spheres can be reduced to below 10 nm. Dimers with different distances were fabricated and optically characterized by single particle dark-field spectroscopy. The characteristic red-shift of the longitudinal mode due to stronger coupling for smaller distances could be clearly observed and follows a general scaling behavior.

Magnetoresistance mechanisms in carbon-nanotube yarns

Carbon nanotube (CNT) yarns are novel CNT-based materials that extend the advantages of CNT from the nanoscale to macroscale applications. Herein we have modeled the electrical properties of carbon nanotube yarn as a function of temperature and magnetic field. The conductivity was well explained by 3D Mott Variable Range Hopping (VRH) law at T < 100 K. The hopping effective dimension is reduced with increasing of magnetic field. Negative magnetoresistance (MR) was observed at different magnetic field range. A quadratic MR was found at small magnetic fields up to BD2, where a deviation occurred from the quadratic magnetic field dependence of the MR. In the intermediate magnetic field region, the negative MR shows linear magnetic field dependence up to the magnetic crossover field of BD1. It was found that physical parameters such as the localization length and the density of states at the Fermi level are temperature and magnetic field dependent. In addition, a general scaling behavior was found for the MR as a function of (B/B*)1/3, where B* is a crossover magnetic field.

Dynamic Off-Equilibrium Transition in Systems Slowly Driven across Thermal First-Order Phase Transitions.

We study the off-equilibrium behavior of systems with short-range interactions, slowly driven across a thermal first-order transition, where the equilibrium dynamics is exponentially slow. We consider a dynamics that starts in the high-T phase at time t=t_{i}<0 and ends at t=t_{f}>0 in the low-T phase, with a time-dependent temperature T(t)/T_{c}≈1-t/t_{s}, where t_{s} is the protocol time scale. A general off-equilibrium scaling (OS) behavior emerges in the limit of large t_{s}. We check it at the first-order transition of the two-dimensional q-state Potts model with q=20 and 10. The numerical results show evidence of a dynamic transition, where the OS functions show a spinodal-like singularity. Therefore, the general mean-field picture valid for systems with long-range interactions is qualitatively recovered, provided the time dependence is appropriately (logarithmically) rescaled.

Scale-invariant radio jets and varying black hole spin

Compact radio cores associated with relativistic jets are often observed in both active galactic nuclei and X-ray binaries. Their radiative properties follow some general scaling laws which primarily depend on their masses and accretion rates. However, it has been suggested that the black hole spin can also strongly influence the power and radio flux of these. Here, we attempt to estimate the dependency of the radio luminosity of steady jets launched by accretion disks on black hole mass, accretion rate and spin using numerical simulations. We make use of 3D GRMHD simulations of accretion disks around low-luminosity black holes in which the jet radio emission is produced by the jet sheath. We find that the radio flux increases roughly by a factor of 6 as the back hole spin increases from a~0 to a=0.98. This is comparable to the increase in accretion power with spin, meaning that the ratio between radio jet and accretion power is hardly changing. Although our jet spine power scales as expected for the Blandford-Znajek process, the dependency of jet radio luminosity on the black hole spin is somewhat weaker. Also weakly rotating black holes can produce visible radio jets. The overall scaling of the radio emission with black hole mass and accretion rate is consistent with the scale-invariant analytical models used to explain the fundamental plane of black hole activity. Spin does not introduce a significant scatter in this model. The jet-sheath model can describe well resolved accreting systems, such as SgrA* and M87, as well as the general scaling behavior of low-luminosity black holes. Hence the model should be applicable to a wide range of radio jets in sub-Eddington black holes. The black hole spin has an effect on the production of visible radio jet, but it may not be the main driver to produce visible radio jets. An extension of our findings to powerful quasars remains speculative.

Thermalization of mutual information in hyperscaling violating backgrounds

We study certain features of scaling behaviors of the mutual information during a process of thermalization, more precisely we extend the time scaling behavior of mutual information which has been discussed in \cite{Alishahiha:2014jxa} to time-dependent hyperscaling violating geometries. We use the holographic description of entanglement entropy for two disjoint system consisting of two parallel strips whose widths are much larger than the separation between them. We show that during the thermalization process, the dynamical exponent plays a crucial rule in reading the general time scaling behavior of mutual information (\emph{e.g.,} at the pre-local-equilibration regime). It is shown that the scaling violating parameter can be employed to define an effective dimension.

Scale Dependency of Total Water Variance and Its Implication for Cloud Parameterizations

Abstract The scale dependency of variance of total water mixing ratio is explored by analyzing data from a general circulation model (GCM), a numerical weather prediction model (NWP), and large-eddy simulations (LESs). For clarification, direct numerical simulation (DNS) data are additionally included, but the focus is placed on defining a general scaling behavior for scales ranging from global down to cloud resolving. For this, appropriate power-law exponents are determined by calculating and approximating the power density spectrum. The large-scale models (GCM and NWP) show a consistent scaling with a power-law exponent of approximately −2. For the high-resolution LESs, the slope of the power density spectrum shows evidence of being somewhat steeper, although the estimates are more uncertain. Also the transition between resolved and parameterized scales in a current GCM is investigated. Neither a spectral gap nor a strong scale break is found, but a weak scale break at high wavenumbers cannot be excluded. The evaluation of the parameterized total water variance of a state-of-the-art statistical scheme shows that the scale dependency is underestimated by this parameterization. This study and the discovered general scaling behavior emphasize the need for a development of scale-dependent parameterizations.

Throughput analysis in mobile ad hoc networks with directional antennas

A major obstacle stunting the application of mobile ad hoc networks (MANETs) is the lack of a general throughput analysis theory for such networks. The available works in this area mainly focus on asymptotic throughput study (order sense) in MANETs with omnidirectional antennas or directional antennas. Although the order sense results can help us to understand the general scaling behaviors, it tells us little about the exact achievable throughput. This paper studies the achievable throughput of a MANET where each node is equipped with a directional antenna of beamwidth θ for transmission. A generalized two hop relay scheme with packet redundancy f is adopted for packet routing. Based on the Markov chain and automatic feedback theory, we explore a general theoretical framework that enables the achievable throughput analysis to be conducted for a directional antenna-based MANET. Based on the results of the achievable per node throughput, we further explore the throughput optimization problem for a fixed beamwidth θ and determine the corresponding optimal setting of f to achieve the optimal throughput. Numerical studies are also conducted to demonstrate the efficiency of these models.It shows that the maximum achievable throughput obtained from our theoretical framework matches nicely (with at most 7% difference) with that obtained from simulation under a realistic model.

Skyrmion semiclassical quantization in the presence of an isospin chemical potential

The semiclassical description of Skyrmions at small isospin chemical potential ${\ensuremath{\mu}}_{I}$ is carefully analyzed. We show that when the calculation of the energy of a nucleon is performed using the straightforward generalization of the vacuum sector techniques (${\ensuremath{\mu}}_{I}=0$), together with the ``natural'' assumption ${\ensuremath{\mu}}_{I}=\mathcal{O}({N}_{c}^{0})$, the proton and neutron masses are nonlinear in ${\ensuremath{\mu}}_{I}$ in the regime $|{\ensuremath{\mu}}_{I}|&lt;{m}_{\ensuremath{\pi}}$. Although these nonlinearities turn out to be numerically quite small, such a result fails to strictly agree with the very robust prediction that for those values of ${\ensuremath{\mu}}_{I}$ the energy excitations above the vacuum are linear in ${\ensuremath{\mu}}_{I}$. The resolution of this paradox is achieved by studying the realization of the large ${N}_{c}$ limit of QCD in the Skyrme model at finite ${\ensuremath{\mu}}_{I}$. This is done in a simplified context devoid of the technical complications present in the Skyrme model but which fully displays the general scaling behavior with ${N}_{c}$. The analysis shows that the paradoxical result appears as a symptom of using the semiclassical approach beyond its regime of validity and that, at a formal level, the standard methods for dealing with the Skyrme model are only strictly justified for states of high isospin, $I\ensuremath{\sim}{N}_{c}$.

Scaling laws for transverse relaxation times

Simple scaling laws are useful tools in understanding the effect of changing parameters in MRI experiments. In this paper the general scaling behavior of the transverse relaxation times is discussed. We consider the dephasing of spins diffusing around a field inhomogeneity inside a voxel. The strong collision approximation is used to describe the diffusion process. The obtained scaling laws are valid over the whole dynamic range from motional narrowing to static dephasing. The dependence of the relaxation times on the external magnetic field, diffusion coefficients of the surrounding medium, and the characteristic scale of the field inhomogeneity is analyzed. For illustration the generally valid scaling laws are applied to the special case of a capillary, usually used as a model of the myocardial BOLD effect.

Scaling and universality in the aging kinetics of the two-dimensional clock model

We study numerically the aging dynamics of the two-dimensional p -state clock model after a quench from an infinite temperature to the ferromagnetic phase or to the Kosterlitz-Thouless phase. The system exhibits the general scaling behavior characteristic of nondisordered coarsening systems. For quenches to the ferromagnetic phase, the value of the dynamical exponents suggests that the model belongs to the Ising-type universality class. Specifically, for the integrated response function chi(t,s) approximately or = s(-a)chif(t/s), we find a(chi) consistent with the value a(chi)=0.28 found in the two-dimensional Ising model.

The effective temperature in the quenching of coarsening systems to and to belowTC

We overview the general scaling behaviour of the effective temperature inquenches of simple non-disordered systems, such as ferromagnets, to and to belowTC. Emphasis is on the behaviour as the dimensionality is varied.Consequences for the shape of the asymptotic parametric representationare derived. In particular, this is always trivial in critical quenches withTC>0. We clarify that thequench to TC = 0 at the lowercritical dimensionality dL, cannot be regarded as a critical quench. Implications for the behaviour of the exponenta of the ageing response function in quenches to belowTC are developed.

Multiscaling analysis and random cascade modeling of dye infiltration

We aimed at investigating whether the spatial variability of infiltration in field soils, as visualized through dye infiltration experiments, is characterized by a multiscaling behavior. Digitized high‐resolution dye images from three sites in an experimental catchment in Tunisia were analyzed using three indicators of scaling: empirical probability distribution functions, power spectra, and raw statistical moments. The two former indicators suggested a general scaling behavior of the data, which through the moments' analysis was found to be of multiscaling type. Random cascade processes are frequently used to model multiscaling processes, and we fitted the “universal multifractal” (UM) model of Schertzer and Lovejoy [1987] to our data. The UM model closely reproduced the empirical K(q) functions, and simulated fields reproduced key features in the observed ones. The results indicate that multiscaling random cascade modeling is useful for statistically describing flow processes and solute transport under field conditions.