Distinct Exponents Research Articles

Spatial-segregation limit for exclusion processes with two components under unbalanced reaction

We consider exclusion processes with two types of particles which compete strongly with each other. In particular, we focus on the case where one species does not diffuse at all and killing rates of two species are given by monomials with distinct exponents. We study limiting behavior of interfaces which appear by such a strong competition. Consequently, three kinds of limiting behavior of interfaces (vanishing, moving and immovable interfaces as in [9]) are derived directly from our interacting particle system taking advantage of hydrodynamic limit procedure with singular limit for annihilation dynamics.

Anomalous Diffusion in Dipole- and Higher-Moment-Conserving Systems.

The presence of global conserved quantities in interacting systems generically leads to diffusive transport at late times. Here, we show that systems conserving the dipole moment of an associated global charge, or even higher-moment generalizations thereof, escape this scenario, displaying subdiffusive decay instead. Modeling the time evolution as cellular automata for specific cases of dipole- and quadrupole conservation, we numerically find distinct anomalous exponents of the late time relaxation. We explain these findings by analytically constructing a general hydrodynamic model that results in a series of exponents depending on the number of conserved moments, yielding an accurate description of the scaling form of charge correlation functions. We analyze the spatial profile of the correlations and discuss potential experimentally relevant signatures of higher-moment conservation.

Upper critical field and superconductor-metal transition in ultrathin niobium films

Recent studies suggest that in disordered ultrathin films superconducting (SC) state may be intrinsically inhomogeneous. Here we investigate the nature of SC state in ultrathin Nb films, of thickness d ranging from 1.2 to 20 nm, which undergo a transition from amorphous to polycrystalline structure at the thickness d simeq 3.3 nm. We show that the properties of SC state are very different in polycrystalline and amorphous films. The upper critical field (H_{c2}) is orbitally limited in the first case, and paramagnetically limited in the latter. The magnetic field induced superconductor-metal transition is observed, with the critical field approximately constant or decreasing as a power-law with the film conductance in polycrystalline or amorphous films, respectively. The scaling analysis indicates distinct scaling exponents in these two types of films. Negative contribution of the SC fluctuations to conductivity exists above H_{c2}, particularly pronounced in amorphous films, signaling the presence of fluctuating Cooper pairs. These observations suggest the development of local inhomogeneities in the amorphous films, in the form of proximity-coupled SC islands. An usual evolution of SC correlations on cooling is observed in amorphous films, likely related to the effect of quantum fluctuations on the proximity-induced phase coherence.

Mechanical Forcing of Convection by Cold Pools: Collisions and Energy Scaling.

Forced mechanical lifting through cold pool gust fronts can trigger new convection and, as previous work highlights, is enhanced when cold pools collide. However, as shown by conceptual models, the organization of the convective cloud field emerging from two versus three colliding cold pools differs strongly. In idealized dry large‐eddy simulations we therefore compare collisions between two and three cold pools. The triggering likelihood is quantified in terms of the cumulative vertical mass flux of boundary layer air and the instantaneous updraft strength, generated at the cold pool gust fronts. We find that cold pool expansion can be well described by initial potential energy alone. Cold pool expansion monotonically slows but shows an abrupt transition between an axisymmetric and a broken‐symmetric state mirrored by a sudden drop in expansion speed. We characterize these two dynamic regimes by two distinct power law exponents and explain the transition by the onset of “lobe‐and‐cleft” instabilities at the cold pool head. Two‐cold pool collisions produce the strongest instantaneous updrafts in the lower boundary layer, which we expect to be important in environments with strong convective inhibition. Three‐cold pool collisions generate weaker but deeper updrafts and the strongest cumulative mass flux and are thus predicted to induce the largest midlevel moistening, which has been identified as a precursor for the transition from shallow to deep convection. Combined, our findings may help decipher the role of cold pools in spatially organizing convection and precipitation.

How relevant is the decision of containment measures against COVID-19 applied ahead of time?

The cumulative number of confirmed infected individuals by the new coronavirus outbreak until April 30th, 2020, is presented for the countries: Belgium, Brazil, United Kingdom (UK), and the United States of America (USA). After an initial period with a low incidence of newly infected people, a power-law growth of the number of confirmed cases is observed. For each country, a distinct growth exponent is obtained. For Belgium, UK, and USA, countries with a large number of infected people, after the power-law growth, a distinct behavior is obtained when approaching saturation. Brazil is still in the power-law regime. Such updates of the data and projections corroborate recent results regarding the power-law growth of the virus and their strong Distance Correlation between some countries around the world. Furthermore, we show that act in time is one of the most relevant non-pharmacological weapons that the health organizations have in the battle against the COVID-19, infectious disease caused by the most recently discovered coronavirus. We study how changing the social distance and the number of daily tests to identify infected asymptomatic individuals can interfere in the number of confirmed cases of COVID-19 when applied in three distinct days, namely April 16th (early), April 30th (current), and May 14th (late). Results show that containment actions are necessary to flatten the curves and should be applied as soon as possible.

Self-similar segmentation and multifractality of post-stack seismic data

Layering detection is an important step in petroleum engineering. Time series of post-stack seismic data and wire-line log data belong to subsurface layering. They exhibit multifractal properties with complex patterns because of the heterogeneity and different genetic properties in the earth layers. In a multifractal configuration, any piece of a series has a distinct Hurst exponent that reflects its nature and can be used for zone detection. Time series are post-stack seismic traces and wire-line log data near the well-bores. Self-similar Autoregressive Exogenous (SAE) model is a modified method which can place self-similar post-stack seismic and wire-line log segments across layers with the same lithology. The results satisfy the capability of layering identification from seismic data by SAE model.

Fracton hydrodynamics

We introduce new classes of hydrodynamic theories inspired by the recently discovered fracton phases of quantum matter. Fracton phases are characterized by elementary excitations (fractons) with restricted mobility. The hydrodynamic theories we introduce describe thermalization in systems with fractonlike mobility constraints, including fluids where charge and dipole moment are both locally conserved, and fluids where charge is conserved along every line or plane of a lattice. Each of these fluids is subdiffusive and constitutes a new universality class of hydrodynamic behavior. There are infinitely many such classes, each with distinct subdiffusive exponents, all of which are captured by our formalism. Our framework naturally explains recent results on dynamics with constrained quantum circuits, as well as recent experiments with ultracold atoms in tilted optical lattices. We identify crisp experimental signatures of these novel hydrodynamics and explain how they may be realized in near term ultracold atom experiments.Received 15 May 2020Revised 1 July 2020Accepted 2 July 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.033124Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum statistical mechanicsTechniquesHydrodynamicsSymmetries in condensed matterCondensed Matter, Materials & Applied PhysicsFluid DynamicsStatistical PhysicsQuantum Information

Questioning a fundamental assumption of rheology: Observation of noninteger power expansions

We report the most complete experimental evidence to date of noninteger power-law expansions for nonlinear viscoelastic properties. Our observations, made with a capillary suspension of spherical poly(methyl methacrylate) (PMMA) particles, falsify the universality of the standard assumption where shear stress nonlinearities arise as the amplitude cubed, e.g., σ ∼ O ( γ 0 3 ) in an oscillatory shear test at small amplitudes. In terms of material properties, our measurements require noninteger Taylor expansions about a linear reference state. Furthermore, distinct power-law exponents are found for the storage and loss signals. In this work, we conclusively demonstrate that the noninteger scaling is real and not an experimental artifact. Our experimental and data analysis methods ensure that we report the most complete result to date. While the noninteger scaling remains to be associated with underlying microstructural physics, the thorough experimental data reported herein demonstrate that such theoretical studies are worth pursuing.

On the number of distinct exponents in the prime factorization of an integer

Let $f(n)$ be the number of distinct exponents in the prime factorization of the natural number $n$. We prove some results about the distribution of $f(n)$. In particular, for any positive integer $k$, we obtain that $$ \#\{n \leq x : f(n) = k\} \sim A_k x $$ and $$ \#\{n \leq x : f(n) = \omega(n) - k\} \sim \frac{B x (\log \log x)^k}{k! \log x} , $$ as $x \to +\infty$, where $\omega(n)$ is the number of prime factors of $n$ and $A_k, B > 0$ are some explicit constants. The latter asymptotic extends a result of Akta\c{s} and Ram Murty about numbers having mutually distinct exponents in their prime factorization.

A comprehensive analysis of Universal Soil Loss Equation‐based models at the Sparacia experimental area

AbstractImproving Universal Soil Loss Equation (USLE)‐based models has large interest because simple and reliable analytical tools are necessary in the perspective of a sustainable land management. At first, in this paper, a general definition of the event rainfall‐ runoff erosivity factor for the USLE‐based models, REFe = (QR)b1(EI30)b2, in which QR is the event runoff coefficient, EI30 is the single‐storm erosion index, and b1 and b2 are coefficients, was introduced. The rainfall‐runoff erosivity factors of the USLE (b1 = 0 and b2 = 1), USLE‐M (b1 = b2 = 1), USLE‐MB (b1 ≠ 1 and b2 = 1), USLE‐MR (b1 = 1 and b2 ≠ 1), USLE‐MM (b1 = b2 ≠ 1), and USLE‐M2 (b1 ≠ b2 ≠ 1) can be defined using REFe. Then the different expressions of REFe were simultaneously tested against a data set of normalized bare plot soil losses, AeN, collected at the Sparacia (south Italy) site. As expected, the poorest AeN predictions were obtained with the USLE. The observed tendency of this model to overestimate small AeN values and underestimate high AeN values was reduced by introducing in the soil loss prediction model both QR and an exponent for the erosivity term. The fitting to the data was poor with the USLE‐MR as compared with the USLE‐MB and the USLE‐MM. Estimating two distinct exponents (USLE‐M2) instead of a single exponent (USLE‐MB, USLE‐MR, and USLE‐MM) did not appreciably improve soil loss prediction. The USLE‐MB and the USLE‐MM were recognized to be the best performing models among the possible alternatives, and they performed similarly with reference to both the complete data set and different sub‐data sets, only including small, intermediate, and severe erosion events. In conclusion, including the runoff coefficient in the soil loss prediction model is important to improve the quality of the predictions, but a great importance has to be paid to the mathematical structure of the model.

Quantum criticality of semi-Dirac fermions in 2+1 dimensions

Two-dimensional semi-Dirac fermions are quasiparticles that disperse linearly in one direction and quadratically in the other. We investigate instabilities of semi-Dirac fermions towards charge, spin-density wave and superconducting orders, driven by short-range interactions. We analyze the critical behavior of the Yukawa theories for the different order parameters using Wilson momentum shell RG. We generalize to a large number $N_f$ of fermion flavors to achieve analytic control in 2+1 dimensions and calculate critical exponents at one-loop order, systematically including $1/N_f$ corrections. The latter depend on the specific form of the bosonic infrared propagator in 2+1 dimensions, which needs to be included to regularize divergencies. The $1/N_f$ corrections are surprisingly small, suggesting that the expansion is well controlled in the physical dimension. The order-parameter correlations inherit the electronic anisotropy of the semi-Dirac fermions, leading to correlation lengths that diverge along the spatial directions with distinct exponents, even at the mean-field level. We conjecture that the proximity to the critical point may stabilize novel modulated order phases.

Cooper pairing of incoherent electrons: An electron-phonon version of the Sachdev-Ye-Kitaev model

We introduce and solve a model of interacting electrons and phonons that is a natural generalization of the Sachdev-Ye-Kitaev-model and that becomes superconducting at low temperatures. In the normal state two Non-Fermi liquid fixed points with distinct universal exponents emerge. At weak coupling superconductivity prevents the onset of low-temperature quantum criticality, reminiscent of the behavior in several heavy-electron and iron-based materials. At strong coupling, pairing of highly incoherent fermions sets in deep in the Non-Fermi liquid regime, a behavior qualitatively similar to that in underdoped cuprate superconductors. The pairing of incoherent time-reversal partners is protected by a mechanism similar to Anderson's theorem for disordered superconductors. The superconducting ground state is characterized by coherent quasiparticle excitations and higher-order bound states thereof, revealing that it is no longer an ideal gas of Cooper pairs, but a strongly coupled pair fluid. The normal-state incoherency primarily acts to suppress the weight of the superconducting coherence peak and reduce the condensation energy. Based on this we expect strong superconducting fluctuations, in particular at strong coupling.

Microscopic Nature of Magnetic Ground State in CeAuSb2

The synergistic investigation of ground‐state magnetic correlation in the single‐crystal heavy fermion compound CeAuSb2 using detailed neutron scattering measurements and density functional calculations is reported. Unlike the previous reports of single antiferromagnetic transition at TN ≈ 6 K, three successive transitions with distinct critical exponents at TN = 5.3, 4.46, and 3.76 K, respectively, are detected in CeAuSb. The low‐temperature ground‐state magnetic correlation is described by the spin density wave order in the basal plane with propagation wave vector τ = (0.135, 0.135, 0.5) rlu. The spin density wave order arises due to the nesting of hole pockets in the Fermi surface, with parallel surfaces being separated by the experimentally found propagation vector τ. The comprehensive investigation of magnetic ground‐state properties is expected to provide new insights in understanding the emerging quantum magnetism in this system, including the debated quantum critical state and magnetic field‐induced metamagnetic transitions at low temperature.

Fragility and Cooperative dynamics correlations in GexSe1-x chalcogenide glasses

In our thermal studies correlation between Cooperativity and Angell's fragility index neatly delineates homogeneous floppy, heterogeneous isostatic, and semi-homogeneous stressed rigidity-phases of the GexSe1-x system. These phases are manifestation of network evolutions due to doping of Ge into selenium polymer chains. In present experiments/data analysis distinct power law exponents (positive and negative) in fragility and cooperative dynamics correlation are observed. Their explanations are provided for three phases across GexSe1-x glass series. Temperature scanning study by ramp method was performed and data was analyzed with Vogel-Fulcher type. Isothermal measurements were performed and data was analyzed with Kohlarausch stretched exponential type. However, the Kohlrausch-Williams-Watts (KWW) nonlinearity exponent β parametrizing stretched-exponential relaxations [~ exp.{−(t/τ)β}] does not discern between the three phases, in its covariance with mAngell. In present study theoretical models for confirmation the result for correlations among properties of glasses are being suggested.

Breaking the Fluctuation-Dissipation Relation by Universal Transport Processes.

Universal phenomena far from equilibrium exhibit additional independent scaling exponents and functions as compared to thermal universal behavior. For the example of an ultracold Bose gas we simulate nonequilibrium transport processes in a universal scaling regime and show how they lead to the breaking of the fluctuation-dissipation relation. As a consequence, the scaling of spectral functions (commutators) and statistical correlations (anticommutators) between different points in time and space become linearly independent with distinct dynamic scaling exponents. As a macroscopic signature of this phenomenon, we identify a transport peak in the statistical two-point correlator, which is absent in the spectral function showing the quasiparticle peaks of the Bose gas.

Phase separation and emergence of collective motion in a one-dimensional system of active particles.

We study numerically a one-dimensional system of self-propelled particles, where the state of the particles is given by their moving direction (left or right), which is encoded by a spin-like variable, and their position. Particles interact by short-ranged, spring-like attractive forces and do not possess spin-spin interactions (i.e., velocity alignment). Newton's third law is broken in this model by assuming an asymmetric interaction range that is larger in the direction of the moving direction of the particle. We show that in this nonequilibrium system, due to the absence of the action-reaction symmetry, there exists an intimate link between phase separation and the formation of highly coherent, spatially localized, moving flocks (i.e., collective motion). More specifically, we prove the existence of two fundamentally different types of active phase separation, which we refer to as neutral phase separation (NPS) and polar phase separation. Furthermore, we indicate that NPS is subdivided in two classes with distinct critical exponents. These results are of key importance to understand that in active matter, there exist several phase-separation classes and that the emergence of polar, self-organized patterns (i.e., flocks) does not require the presence of a velocity alignment.

Aspects of the Morphophonology of the Verb in Latin and in German and English

Aspects of the Morphophonology of the Verb in Latin and in German and English

Interference and Outage Analysis of Random D2D Networks Underlaying Millimeter-Wave Cellular Networks

Device-to-device (D2D) networks underlaying a millimeter-wave cellular network have great potential for capacity growth. Thus, it is important to characterize the outage of such a D2D link incorporating millimeter-wave propagation effects, user association rules, power control, and spatial randomness. To this end, we model the locations of cellular transmitters and receivers as homogeneous Poisson point processes and those of the D2D nodes as a Matern cluster process, and incorporate blockages due to random objects, sectored antenna patterns, log-distance path loss, and Nakagami- $m$ fading. Furthermore, we consider antenna gain inversion-based power control, and peak power constraints for D2D devices along with distinct path loss exponents and distinct fading severities for line-of-sight (LOS) and non-LOS scenarios. With the aid of stochastic geometry tools, we derive closed-form expressions of the moment generating function of the aggregate interference on a D2D receiver node and its outage probability for two transmitter–receiver association schemes— nearest association and LOS association. We finally show that the feasibility of millimeter-wave D2D communication relies heavily on the D2D cluster radii, peak power thresholds, and node densities. Furthermore, these parameters affect the performance of the desired link more than the interference and noise.

A Theoretical Analysis of the Rheological Parameters Associated with DDRX

The macroscopic strain rate sensitivity m and apparent activation energy Q are derived from their microscopic counterparts associated with strain hardening, grain boundary mobility, and nucleation rate in the case of steady state discontinuous dynamic recrystallization (DDRX). The case of solid solutions, involving effects of the solute concentration on strain hardening and boundary mobility, is also taken into consideration. Moreover, three distinct Derby exponents are introduced to refine the correlation between steady state flow stress and average grain size. Hot torsion data and micrographic observations on a set of nickel-niobium alloys are used to assess the predictions of this tentative approach.

Supersymmetric quantum spherical spins

In this work we investigate properties of a supersymmetric extension of the quantum spherical model from an off-shell formulation directly in the superspace. This is convenient to safely handle the constraint structure of the model in a way compatible with supersymmetry. The model is parametrized by an interaction energy, , which governs the interactions between the superfields of different sites. We briefly discuss some consequences when corresponds to the case of first-neighbor interactions. After computing the partition function via saddle point method for a generic interaction, , we focus in the mean-field version, which reveals an interesting critical behavior. In fact, the mean-field supersymmetric model exhibits a quantum phase transition without breaking supersymmetry at zero temperature, as well as a phase transition at finite temperature with broken supersymmetry. We compute critical exponents of the usual magnetization and susceptibility in both cases of zero and finite temperature. Concerning the susceptibility, there are two regimes in the case of finite temperature characterized by distinct critical exponents. The entropy is well behaved at low temperature, vanishing as .