Power-law Decay Exponent Research Articles

Quasi-two-dimensionality of three-dimensional, magnetically dominated, decaying turbulence

Decaying magnetohydrodynamic (MHD) turbulence is important in various astrophysical contexts, including early universe magnetic fields, star formation, turbulence in galaxy clusters, magnetospheres and solar corona. Previously known in the nonhelical case of magnetically dominated decaying turbulence, we show that magnetic reconnection is important also in the fully helical case and is likely the agent responsible for the inverse transfer of energy. Again, in the fully helical case, we find that there is a similarity in power law decay exponents in both 2.5D and 3D simulations. To understand this intriguing similarity, we investigate the possible quasi-two-dimensionalization of the 3D system. We perform Minkowski functional analysis and find that the characteristic length scales of a typical magnetic structure in the system are widely different, suggesting the existence of local anisotropies. Finally, we provide a quasi-two-dimensional hierarchical merger model which recovers the relevant power law scalings. In the nonhelical case, we show that a helicity-based invariant cannot constrain the system, and the best candidate is still anastrophy or vector potential squared, which is consistent with the quasi-two-dimensionalization of the system.

Tracking Eruption Column Thermal Evolution and Source Unsteadiness in Ground‐Based Thermal Imagery Using Spectral‐Clustering

AbstractVolcanic eruption columns typically have unsteady source conditions, where mass and heat fluxes from the vent evolve or fluctuate on time scales from seconds to hours. However, integral plume models routinely assume source conditions that are statistically stationary, and the degree to which source unsteadiness influences the mechanics of column rise and air entrainment has not been established with quantitative predictions. We address this knowledge gap by examining eruptions with varying unsteady character at Sabancaya Volcano, Peru. Using a novel tracking algorithm based on spectral clustering, we track the spatiotemporal evolution of coherent turbulent structures in columns using ground‐based, thermal infrared imagery. For turbulent structures tracked in time and space, we calculate the power law decay exponent of excess temperature with height. In general, the starting pulses of transient events are characterized by power law exponents matching theoretical predictions for an instantaneous point release of buoyancy (i.e., a thermal), which evolve with sustained emissions to values consistent with steady plumes. Our results support previous findings from field evidence and laboratory experiments that entrainment and gravitational stability in unsteady volcanic columns are inadequately captured by time‐averaging or constant entrainment coefficients. We propose a quantitative definition for column source unsteadiness which captures the timing and magnitude of source fluctuations on time scales that influence entrainment mechanics, and which provisionally predicts our observed differences in power law behavior. We argue for systematic experimental and numerical studies of the relationship between source unsteadiness and entrainment to implement unsteady entrainment parameterizations for integral plume models.

Numerical investigation of the spatial integration effect on the velocity spectrum: Consequences in the wind or tidal turbine power spectrum

We numerically investigate the effects of spatially integrating turbulent velocity signals and their impact on the power spectrum. Possible applications concern turbine power spectra. To this end, a 2D synthetic database built with the aim to mimic a realistic Atmospheric turbulent Boundary Layer (ABL) is used to infer previous observations from laboratory experiments. The size of the computational domain is supposed to be smaller than the integral length scale of the flow. In this case, it is demonstrated that, when spatially averaged along N direction(s), an anisotropic turbulent flow initially satisfying the Kolmogorov’s “−5/3 law” exhibits a −5/3−2N/3 slope in the inertial range of its velocity spectrum. The synthetic database is further used to assess an equivalent turbine power spectrum computed from a 2D-spatial average (over the blade area) coupled with an average over the number of blades of the incoming velocity field. It is then confirmed that such an equivalent turbine power spectrum exhibits a power law decay exponent of −11/3 in the inertial range. Finally, several 1D databases are generated to study the spatial averaging procedure as a function of the number of points per integral length scale and the number of statistically independent velocity samples. We show that the additional −2/3 in the power law decay of the spatially averaged velocity spectrum is favorably observed in the case of a sufficient number of points (superior to 90) per integral length scale, regardless of the number of statistically independent velocity samples, even when the length of the domain is smaller than the integral length scale.

Dirac-Type Nodal Spin Liquid Revealed by Refined Quantum Many-Body Solver Using Neural-Network Wave Function, Correlation Ratio, and Level Spectroscopy

Pursuing fractionalized particles that do not bear properties of conventional measurable objects, exemplified by bare particles in the vacuum such as electrons and elementary excitations such as magnons, is a challenge in physics. Here we show that a machine-learning method for quantum many-body systems that has achieved state-of-the-art accuracy reveals the existence of a quantum spin liquid (QSL) phase in the region $0.49\lesssim J_2/J_1\lesssim0.54$ convincingly in spin-1/2 frustrated Heisenberg model with the nearest and next-nearest neighbor exchanges, $J_1$ and $J_2$, respectively, on the square lattice. This is achieved by combining with the cutting-edge computational schemes known as the correlation ratio and level spectroscopy methods to mitigate the finite-size effects. The quantitative one-to-one correspondence between the correlations in the ground state and the excitation spectra enables the reliable identification and estimation of the QSL and its nature. The spin excitation spectra containing both singlet and triplet gapless Dirac-like dispersions signal the emergence of gapless fractionalized spin-1/2 Dirac-type spinons in the distinctive QSL phase. Unexplored critical behavior with coexisting and dual power-law decays of N\'{e}el antiferromagnetic and dimer correlations is revealed. The power-law decay exponents of the two correlations differently vary with $J_2/J_1$ in the QSL phase and thus have different values except for a single point satisfying the symmetry of the two correlations. The isomorph of excitations with the cuprate $d$-wave superconductors implies a tight connection between the present QSL and superconductivity. This achievement demonstrates that the quantum-state representation using machine learning techniques, which had mostly been limited to benchmarks, is a promising tool for investigating grand challenges in quantum many-body physics.

Signature of elastic turbulence of viscoelastic fluid flow in a single pore throat.

When a viscoelastic fluid, such as an aqueous polymer solution, flows through a porous medium, the fluid undergoes a repetitive expansion and contraction as it passes from one pore to the next. Above a critical flow rate, the interaction between the viscoelastic nature of the polymer and the pore configuration results in spatial and temporal flow instabilities reminiscent of turbulentlike behavior, even though the Reynolds number Re≪1. To investigate whether this is caused by many repeated pore body-pore throat sequences, or simply a consequence of the converging (diverging) nature present in a single pore throat, we performed experiments using anionic hydrolyzed polyacrylamide (HPAM) in a microfluidic flow geometry representing a single pore throat. This allows the viscoelastic fluid to be characterized at increasing flow rates using microparticle image velocimetry in combination with pressure drop measurements. The key finding is that the effect, popularly known as "elastic turbulence," occurs already in a single pore throat geometry. The critical Deborah number at which the transition in rheological flow behavior from pseudoplastic (shear thinning) to dilatant (shear thickening) strongly depends on the ionic strength, the type of cation in the anionic HPAM solution, and the nature of pore configuration. The transition towards the elastic turbulence regime was found to directly correlate with an increase in normal stresses. The topology parameter, Q_{f}, computed from the velocity distribution, suggests that the "shear thickening" regime, where much of the elastic turbulence occurs in a single pore throat, is a consequence of viscoelastic normal stresses that cause a complex flow field. This flow field consists of extensional, shear, and rotational features around the constriction, as well as upstream and downstream of the constriction. Furthermore, this elastic turbulence regime, has high-pressure fluctuations, with a power-law decay exponent of up to |-2.1| which is higher than the Kolmogorov value for turbulence of |-5/3|.

More current with less particles due to power-law hopping

We reveal interesting universal transport behavior of ordered one-dimensional fermionic systems with power-law hopping. We restrict ourselves to the case where the power-law decay exponent , so that the thermodynamic limit is well-defined. We explore the quantum phase-diagram of the non-interacting model in terms of the zero temperature Drude weight, which can be analytically calculated. Most interestingly, we reveal that for , there is a phase where the zero temperature Drude weight diverges as filling fraction goes to zero. Thus, in this regime, counter intuitively, reducing number of particles increases transport and is maximum for a sub-extensive number of particles. Being a statement about zero-filling, this transport behavior is immune to adding number conserving interaction terms. We have explicitly checked this using two different interacting systems. We propose that measurement of persistent current due to a flux through a mesoscopic ring with power-law hopping will give an experimental signature of this phase. In persistent current, the signature of this phase survives up to a finite temperature for a finite system. At higher temperatures, a crossover is seen. The maximum persistent current shows a power-law decay at high temperatures. This is in contrast with short ranged systems, where the persistent current decays exponentially with temperature.

Topographic effects on frequency-size distribution of landslides triggered by the Hokkaido Eastern Iburi Earthquake in 2018

This study examined the frequency-size distribution of 6117 landslides spread over 440 km2 in Iburi Subprefecture, Hokkaido, Japan, induced by the Hokkaido Eastern Iburi Earthquake (Mw 6.6) on September 6, 2018. The study area is characterized by gently undulating terrain that is finely dissected by shallow streams and covered predominantly by layers of volcanic products with high water content. Most of the landslides were shallow landslides, and their slip surfaces often formed in a layer of volcanic soil called the “Ta-d,” deposited at 9000 ybp. Low ridges separating small catchments allowed individual landslides to coalesce in many locations. The average size of landslides was 7160 m2. Landslide size tended to increase with slope angle up to 20° to 25° and then decrease with further increase of slope angle. About half of the landslides occurred in a feature with both concave planform and profile curvature, and their average size was 8720 m2. In contrast, 17% of the total landslides occurred in the case of both curvatures being convex, and their average size was 5190 m2. The results indicated that the accumulation of saturated soil in concave features provided more opportunities for landslides of large sizes. The frequency-size distribution of the landslides presented high rollover, 5.0 × 10−3 km2, but the exponent of power law decay for medium to large landslides, − 2.46, was not largely different from those of studies in other locations. Compared with other seismically caused examples, the landslides triggered by the Hokkaido Eastern Iburi Earthquake can be characterized as more clustered, more numerous, and larger in size for the moment magnitude of the earthquake. Conversely, the magnitude scale for the landslide event estimated from the total landslide area was equivalent to that of a region struck by an earthquake of Mw = 7.0 to 7.4. This study demonstrated that gently undulating regions can produce unexpectedly large and frequent landslides when struck by an intense earthquake, and when soil layers vulnerable to ground shaking cover the ground.

Jet Geometry and Rate Estimate of Coincident Gamma-Ray Burst and Gravitational-wave Observations

Abstract Short gamma-ray burst (SGRB) progenitors have long been thought to be coalescing binary systems of two neutron stars (NSNS) or a neutron star and a black hole. The 2017 August 17th detection of the GW170817 gravitational-wave (GW) signal by Advanced LIGO and Advanced Virgo in coincidence with the electromagnetic observation of the SGRB GRB 170817A confirmed this scenario and provided new physical information on the nature of these astronomical events. We use SGRB observations by the Neil Gehrels Swift Observatory Burst Alert Telescope and GW170817/GRB 170817A observational data to estimate the detection rate of coincident GW and electromagnetic observations by a GW detector network and constrain the physical parameters of the SGRB jet structure. We estimate the rate of GW detections coincident with SGRB electromagnetic detections by the Fermi Gamma-ray Burst Monitor to be between ∼0.1 and ∼0.6 yr−1 in the third LIGO-Virgo observing run and between ∼0.3 and ∼1.8 yr−1 for the LIGO-Virgo-KAGRA network at design sensitivity. Assuming a structured model with a uniform ultrarelativistic jet surrounded by a region with power-law decay emission, we find the jet half-opening angle and the power-law decay exponent to be θ c ∼ 7°–22° and s ∼ 5–30 at a 1σ confidence level, respectively.

Orthogonality catastrophe in Coulomb systems

The orthogonality catastrophe (OC) problem is considered solved for 50 years. It has important consequences for numerous dynamic phenomena in fermionic systems, including Kondo effect, X-ray spectroscopy, and quantum diffusion of impurities, and is often used in the context of metals. However, the key assumptions on which the known solution is based---impurity potentials with finite cross-section and non-interacting fermions---are both highly inaccurate for problems involving charged particles in metals. As far as we know, the OC problem for the "all Coulomb" case has never been addressed systematically, leaving it unsolved for the most relevant practical applications. In this work we include effects of dynamic screening in a consistent way and demonstrate that for short-range impurity potentials the non-interacting Fermi-sea approximation radically overestimates the power-law decay exponent of the overlap integral. We also find that the dynamically screened Coulomb potential leads to a larger exponent than the often used static Yukawa potential. Finally, by employing the Diagrammatic Monte Carlo technique, we quantify effects of a finite impurity mass and reveal how OC physics leads to small, but finite, impurity residues.

Quantitative approach to multifractality induced by correlations and broad distribution of data

We analyze quantitatively the effect of spurious multifractality induced by the presence of fat-tailed symmetric and asymmetric probability distributions of fluctuations in time series. In the presented approach different kinds of symmetric and asymmetric broad probability distributions of synthetic data are examined starting from Levy regime up to those with finite variance. We use nonextensive Tsallis statistics to construct all considered data in order to have good analytical description of frequencies of fluctuations in the whole range of their magnitude and simultaneously the full control over exponent of power-law decay for tails of probability distribution. The semi-analytical compact formulas are then provided to express the level of spurious multifractality generated by the presence of fat tails in terms of Tsallis parameter q̃ and the scaling exponent β of the asymptotic decay of cumulated probability density function (CDF). The results are presented in Hurst and Hölder languages — more often used in study of multifractal phenomena. According to the provided semi-analytical relations, it is argued how one can make a clear quantitative distinction for any real data between true multifractality caused by the presence of nonlinear correlations, spurious multifractality generated by fat-tailed shape of distributions — eventually with their asymmetry, and the correction due to linear autocorrelations in analyzed time series of finite length. In particular, the spurious multifractal effect of fat tails is found basic for proper quantitative estimation of all spurious multifractal effects. Examples from stock market data are presented to support these findings.

Diffusion-Mediated Delayed Fluorescence by Singlet Fission and Geminate Fusion of Correlated Triplets

Singlet fission (SF) has been extensively studied through the use of magnetic field effects and analyzed by the Johnson–Merrifield model or its extended models. We extended the Johnson–Merrifield model to study delayed fluorescence originating from diffusion-mediated reversible geminate fusion of triplets; the emission intensity was shown to decay by a A/tβ law, where β = 3/2 in one and three dimensions and β = 1 in two dimensions. Analytical expressions for the amplitude as well as the exponent of the asymptotic power law decay were obtained. We have shown that a wide range of SF materials from polyene-based molecular crystals to amorphous rubrene exhibit A/t3/2 asymptotic decay. The temperature dependence of the asymptotic emission decay supports a mechanism involving delayed fluorescence mediated by diffusion. Moreover, we show that the decay lines at different field strengths will not cross each other when fission occurs effectively. In the opposite limit when fusion occurs effectively the two decay lines will cross each other.

Charged particle dynamics in the presence of non-Gaussian Lévy electrostatic fluctuations

Full orbit dynamics of charged particles in a 3-dimensional helical magnetic field in the presence of α-stable Lévy electrostatic fluctuations and linear friction modeling collisional Coulomb drag is studied via Monte Carlo numerical simulations. The Lévy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space resulting from intermittent electrostatic turbulence. The probability distribution functions of energy, particle displacements, and Larmor radii are computed and showed to exhibit a transition from exponential decay, in the case of Gaussian fluctuations, to power law decay in the case of Lévy fluctuations. The absolute value of the power law decay exponents is linearly proportional to the Lévy index α. The observed anomalous non-Gaussian statistics of the particles' Larmor radii (resulting from outlier transport events) indicate that, when electrostatic turbulent fluctuations exhibit non-Gaussian Lévy statistics, gyro-averaging and guiding centre approximations might face limitations and full particle orbit effects should be taken into account.

Extensive numerical investigations on the ergodic properties of two coupled Pomeau–Manneville maps

We present extensive numerical investigations on the ergodic properties of two identical Pomeau–Manneville maps interacting on the unit square through a diffusive linear coupling. The system exhibits anomalous statistics, as expected, but with strong deviations from the single intermittent map: Such differences are characterized by numerical experiments with densities which do not have singularities in the marginal fixed point, escape and Poincaré recurrence time statistics that share a power-law decay exponent modified by a clear dimensional scaling, while the rate of phase-space filling and the convergence of ensembles of Lyapunov exponents show a stretched instead of pure exponential behavior. In spite of the lack of rigorous results about this system, the dependence on both the intermittency and the coupling parameters appears to be smooth, paving the way for further analytical development. We remark that dynamical exponents appear to be independent of the (nonzero) coupling strength.

Dynamics of correlations in two-dimensional quantum spin models with long-range interactions: a phase-space Monte-Carlo study

Interacting quantum spin models are remarkably useful for describing different types of physical, chemical, and biological systems. Significant understanding of their equilibrium properties has been achieved to date, especially for the case of spin models with short-range couplings. However, progress toward the development of a comparable understanding in long-range interacting models, in particular out-of-equilibrium, remains limited. In a recent work, we proposed a semiclassical numerical method to study spin models, the discrete truncated Wigner approximation (DTWA), and demonstrated its capability to correctly capture the dynamics of one- and two-point correlations in one-dimensional (1D) systems. Here we go one step forward and use the DTWA method to study the dynamics of correlations in two-dimensional (2D) systems with many spins and different types of long-range couplings, in regimes where other numerical methods are generally unreliable. We compute spatial and time-dependent correlations for spin-couplings that decay with distance as a power-law and determine the velocity at which correlations propagate through the system. Sharp changes in the behavior of those velocities are found as a function of the power-law decay exponent. Our predictions are relevant for a broad range of systems including solid state materials, atom–photon systems and ultracold gases of polar molecules, trapped ions, Rydberg, and magnetic atoms. We validate the DTWA predictions for small 2D systems and 1D systems, but ultimately, in the spirt of quantum simulation, experiments will be needed to confirm our predictions for large 2D systems.

Trimer superfluid induced by photoassocation on the state-dependent optical lattice

We use the mean-field method, the Quantum Monte-carlo method and the Density matrix renormalization group method to study the trimer superfluid phase and the quantum phase diagram of the Bose-Hubbard model in an optical lattice, with explicit trimer tunneling term. Theoretically, we derive the explicit trimer hopping terms, such as $a_i^{3\dagger}a_j^3$, by the Schrieffer-Wolf transformation. In practice, the trimer super\-fluid described by these terms is driven by photoassociation. The phase transition between the trimer super\-fluid phase and other phases are also studied. Without the on-site interaction, the phase transition between the trimer superfluid phase and the Mott Insulator phase is continuous. Turning on the on-site interaction, the phase transitions are first order with Mott insulators of atom filling $1$ and $2$. With nonzero atom tunneling, the phase transition is first order from the atom superfluid to the trimer superfluid. In the trimer superfluid phase, the win\-ding numbers can be divided by three without any remainders. In the atom superfluid and pair superfluid, the vorticities are $1$ and $1/2$, respectively. However, the vorticity is $1/3$ for the trimer superfluid. The power law decay exponents is $1/2$ for the non diagonal correlation $a_i^{\dagger 3} a_j^{3}$, i.e. the same as the exponent of the correlation $a_i^{\dagger}a_j$ in hardcore bosons. The density dependent atom-tunneling term $n_i^2a_i^{\dagger}a_j$ and pair tunneling term $n_ia_i^{\dagger2}a_j^2$ are also studied. With these terms, the phase transition from the empty phase to atom superfluid is first order and different from the cases without the density dependent terms. The ef\-fects of temperature are studied. Our results will be helpful in realizing the trimer superfluid by a cold atom experiment.

Ghost stochastic resonance induced by a power-law distributed noise in the FitzHugh–Nagumo neuron model

We numerically investigate the ghost stochastic resonance phenomenon induced by a power-law distributed noise in the neuron FitzHugh–Nagumo model. The input noise considered is produced by a Langevin process including both multiplicative and additive Gaussian noise sources. In this process, the power-law decay exponent of the resulting noise distribution is governed by the off-set of the multiplicative noise, thus allowing us to probe both regimes of Gaussian and strongly non-Gaussian noises. Ghost stochastic resonance, i.e., stochastic resonance in a missing fundamental harmonic, occurs in this model. Deviations from the Gaussianity of the input noise are shown to reduce both the additive noise intensity corresponding to the optimal identification of the missing fundamental as well as the number of firing events at the ghost stochastic resonance condition.

Localization properties at band edge of local density of states in two-dimensional Thue–Morse photonic systems

The spatial distribution of the local density of states (LDOS) at band edges on large-sized two-dimensional Thue–Morse dielectric systems has been investigated by means of a parallel implementation of the multipole expansion method. From the study of the LDOS participation number, the optical modes have been classified as critical, namely as intermediate between uniformly extended and exponentially localized. The exponent of power-law decay of their envelopes has been determined. Furthermore, multifractal analysis by a standard box-counting method has been performed. Almost all of the investigated modes exhibit a strong multifractal character. These results can be exploited for the designing of novel light source devices based on aperiodic order.

A model for transit time distributions through organs that accounts for fractal heterogeneity

It has been shown that density functions of organ transit time distributions of vascular markers (washout curves) are characterized by a power-law tail, reflecting the fractal nature of the vascular network. Yet, thus far, no closed-form model is available that can be fitted to such organ outflow data. Here we propose a model that accounts for the existing data. The model is a continuous mixture of inverse Gaussian densities, implying flow heterogeneity in the organ. It has been fitted to outflow data from the rabbit heart and rat liver. The power-law decay with exponent -3 observed in the heart, corresponds to an intra-organ flow distribution with a relative dispersion of about 35%.

Sensor models and localization algorithms for sensor networks based on received signal strength

Received signal strength (RSS) can be used in sensor networks as a ranging measurement for positioning and localization applications. This contribution studies the realistic situation where neither the emitted power nor the power law decay exponent be assumed to be known. The application in mind is a rapidly deployed network consisting of a number of sensor nodes with low-bandwidth communication, each node measuring RSS of signals traveled through air (microphones) and ground (geophones). The first contribution concerns validation of a model in logarithmic scale, that is, linear in the unknown nuisance parameters (emitted power and power loss constant). The parameter variation is studied over time and space. The second contribution is a localization algorithm based on this model, where the separable least squares principle is applied to the non-linear least squares (NLS) cost function, after which a cost function of only the unknown position is obtained. Results from field trials are presented to illustrate the method, together with fundamental performance bounds. The ambition is to pave the way for sensor configuration design and more thorough performance evaluations as well as filtering and target tracking aspects.

Long-range self-avoiding walk converges to α-stable processes

Nous considérons un modèle à longue portée de la marche aléatoire auto-évitante en dimension d > 2(α ∧ 2), où d est la dimension et α l’exposant de décroissance polynomiale de la fonction de couplage. Après un rééchelonnage approprié, nous démontrons la convergence vers un mouvement brownien pour α ≥ 2 et vers un processus de Lévy α-stable pour α < 2. Ce résultat complète celui de Slade [J. Phys. A 21 (1988) L417–L420] qui démontre la convergence vers le mouvement brownien pour une marche auto-évitante à plus proche voisin en grande dimension.