Short-scale Fluctuations Research Articles

Pulsed interactions unify reaction–diffusion and spatial nonlocal models for biological pattern formation

The emergence of a spatially organized population distribution depends on the dynamics of the population and mediators of interaction (activators and inhibitors). Two broad classes of models have been used to investigate when and how self-organization is triggered, namely reaction–diffusion and spatially nonlocal models. Nevertheless, these models implicitly assume smooth propagation scenarios, neglecting that individuals interact many times by exchanging short and abrupt pulses of the mediating substance. A recently proposed framework has made advances in properly accounting for these short-scale fluctuations by applying a coarse-graining procedure on the pulse dynamics. In this paper, we generalize the coarse-graining procedure and apply the extended formalism to new scenarios in which mediators influence individuals’ reproductive success or their motility. We show that, in the slow- and fast-mediator limits, pulsed interactions recover, respectively, the reaction–diffusion and nonlocal models, providing a mechanistic connection between them. Furthermore, at each limit, the spatial stability condition is qualitatively different, leading to a timescale-induced transition where spatial patterns emerge as mediator dynamics becomes sufficiently fast.

Renormalization of the 3D exciton spectrum by the disorder

Effect of short-range disorder on the excited states of the exciton is studied. Disorder causes an obvious effect of broadening. Microscopically, an exciton, as an entity, is scattered by the large-scale disorder fluctuations. Much less trivial is that short-scale fluctuations, with a period of the order of the Bohr radius, cause a well-defined down-shift of the exciton levels. We demonstrate that this shift exceeds the broadening parametrically and study the dependence of this shift on the orbital number. Difference of the shifts for neighboring levels leads to effective renormalization of the Bohr energy. Most remarkable effect is the disorder-induced splitting of S and P exciton levels. The splitting originates from the fact that disorder lifts the accidental degeneracy of the hydrogen-like levels. We draw an analogy between this splitting and the Lamb shift in quantum electrodynamics.

Polytropic Behavior of Solar Wind Protons Observed by Parker Solar Probe

Abstract A polytropic process describes the transition of a fluid from one state to another through a specific relationship between the fluid density and temperature. The value of the polytropic index that governs this relationship determines the heat transfer and the effective degrees of freedom during a specific process. In this study, we analyze solar wind proton plasma measurements, obtained by the Faraday cup instrument on board the Parker Solar Probe. We examine the large-scale variations of the proton plasma density and temperature within the inner heliosphere explored by the spacecraft. We then address the polytropic behavior in the density and temperature fluctuations in short time intervals, which we analyze in order to derive the effective polytropic index of small-scale processes. The large-scale variations of the solar wind proton density and temperature, which are associated with the plasma expansion into the heliosphere, follow a polytropic model with a polytropic index ∼5/3. On the other hand, the short-scale fluctuations, which are potentially associated with turbulence, follow a model with a larger polytropic index. We investigate possible correlations between the polytropic index of short-scale fluctuations and the plasma speed, plasma β, and the magnetic field direction. We discuss candidate mechanisms leading to this behavior including energy transfer and possible mechanisms restricting the effective particle degrees of freedom at smaller scales.

Behavior Stability and Individual Differences in Pavlovian Extended Conditioning.

How stable and general is behavior once maximum learning is reached? To answer this question and understand post-acquisition behavior and its related individual differences, we propose a psychological principle that naturally extends associative models of Pavlovian conditioning to a dynamical oscillatory model where subjects have a greater memory capacity than usually postulated, but with greater forecast uncertainty. This results in a greater resistance to learning in the first few sessions followed by an over-optimal response peak and a sequence of progressively damped response oscillations. We detected the first peak and trough of the new learning curve in our data, but their dispersion was too large to also check the presence of oscillations with smaller amplitude. We ran an unusually long experiment with 32 rats over 3,960 trials, where we excluded habituation and other well-known phenomena as sources of variability in the subjects' performance. Using the data of this and another Pavlovian experiment by Harris et al. (2015), as an illustration of the principle we tested the theory against the basic associative single-cue Rescorla–Wagner (RW) model. We found evidence that the RW model is the best non-linear regression to data only for a minority of the subjects, while its dynamical extension can explain the almost totality of data with strong to very strong evidence. Finally, an analysis of short-scale fluctuations of individual responses showed that they are described by random white noise, in contrast with the colored-noise findings in human performance.

Chiral charge dynamics in Abelian gauge theories at finite temperature

We study fermion number non-conservation (or chirality breaking) in Abelian gauge theories at finite temperature. We consider the presence of a chemical potential μ for the fermionic charge, and monitor its evolution with real-time classical lattice simula- tions. This method accounts for short-scale fluctuations not included in the usual effective magneto-hydrodynamics (MHD) treatment. We observe a self-similar decay of the chemi- cal potential, accompanied by an inverse cascade process in the gauge field that leads to a production of long-range helical magnetic fields. We also study the chiral charge dynamics in the presence of an external magnetic field B, and extract its decay rate {varGamma}_5equiv frac{d log mu }{dt} . We provide in this way a new determination of the gauge coupling and magnetic field de- pendence of the chiral rate, which exhibits a best fit scaling as {varGamma}_5{propto}^{raisebox{1ex}{11}!left/ !raisebox{-1ex}{2}right.}{B}^2 . We confirm numerically the fluctuation-dissipation relation between Γ5 and Γdiff , the Chern-Simons diffusion rate, which was obtained in a previous study. Remarkably, even though we are outside the MHD range of validity, the dynamics observed are in qualitative agreement with MHD predictions. The magnitude of the chiral/diffusion rate is however a factor ∼ 10 times larger than expected in MHD, signaling that we are in reality exploring a dif- ferent regime accounting for short scale fluctuations. This discrepancy calls for a revision of the implications of fermion number and chirality non-conservation in finite tempera- ture Abelian gauge theories, though no definite conclusion can be made at this point until hard-thermal-loops are included in the lattice simulations.

Functional data analysis by matrix completion

Functional data analyses typically proceed by smoothing, followed by functional PCA. This paradigm implicitly assumes that rough variation is due to nuisance noise. Nevertheless, relevant functional features such as time-localised or short scale fluctuations may indeed be rough relative to the global scale, but still smooth at shorter scales. These may be confounded with the global smooth components of variation by the smoothing and PCA, potentially distorting the parsimony and interpretability of the analysis. The goal of this paper is to investigate how both smooth and rough variations can be recovered on the basis of discretely observed functional data. Assuming that a functional datum arises as the sum of two uncorrelated components, one smooth and one rough, we develop identifiability conditions for the recovery of the two corresponding covariance operators. The key insight is that they should possess complementary forms of parsimony: one smooth and finite rank (large scale), and the other banded and potentially infinite rank (small scale). Our conditions elucidate the precise interplay between rank, bandwidth and grid resolution. Under these conditions, we show that the recovery problem is equivalent to rank-constrained matrix completion, and exploit this to construct estimators of the two covariances, without assuming knowledge of the true bandwidth or rank; we study their asymptotic behaviour, and then use them to recover the smooth and rough components of each functional datum by best linear prediction. As a result, we effectively produce separate functional PCAs for smooth and rough variation.

Optimization of Open Boundary Conditions in a 3D Internal Tidal Model with the Adjoint Method around Hawaii

Based on the theory of inverse problem, the optimization of open boundary conditions (OBCs) in a 3D internal tidal model is investigated with the adjoint method. Fourier coefficients ofM2internal tide on four open boundaries, which are regarded as OBCs, are inverted simultaneously. During the optimization, the steepest descent method is used to minimize cost function. The reasonability and feasibility of the model are tested by twin experiments (TEs). In TE1, OBCs on four open boundaries are successfully inverted by using independent point (IP) strategy, suggesting that IP strategy is useful in parameter estimation. Results of TE2 indicate that the model is effective even by assimilating inaccurate “observations.” Based on conclusions of TEs, theM2internal tide around Hawaii is simulated by assimilating T/P data in practical experiment. The simulated cochart shows good agreement with that obtained from the Oregon State University tidal model and T/P observations. Careful inspection shows that the major difference between simulated results and OSU model results is short-scale fluctuations superposed on coamplitude lines, which can be treated as the surface manifestation modulated by the internal tide. The computed surface manifestation along T/P tracks is comparable to the estimation in previous work.

Where the ocean influences the impulse response and its effect on synchronous changes of acoustic travel time

In 1983, sounds at 133 Hz, 0.06 s resolution were transmitted in the Pacific for five days at 2 min intervals over 3709 km between bottom-mounted instruments maintained with atomic clocks. In 1989, a technique was developed to measure changes in acoustic travel time with an accuracy of 135 microseconds at 2 min intervals for selected windows of travel time within the impulse response. The data have short-lived 1 to 10 ms oscillations of travel time with periods less than a few days. Excluding tidal effects, different windows exhibited significant synchronized changes in travel time for periods shorter than 10 h. In the 1980s, this phenomenon was not understood because internal waves have correlation lengths of a few kilometers which are smaller than the way sound was thought to sample the ocean along well-separated and distinct rays corresponding to different windows. The paradox's resolution comes from modern theories that replace the ray-picture with finite wavelength representations that predict sound can be influenced in the upper ocean over horizontal scales such as 20 km or more. Thus, different windows are influenced by the same short-scale fluctuations of sound speed. This conclusion is supported by the data and numerical simulations of the impulse response.

Geometrically consistent approach to stochastic DBI inflation

Stochastic effects during inflation can be addressed by averaging the quantum inflaton field over Hubble-patch--sized domains. The averaged field then obeys a Langevin-type equation into which short-scale fluctuations enter as a noise term. We solve the Langevin equation for an inflaton field with a Dirac-Born-Infeld (DBI) kinetic term perturbatively in the noise and use the result to determine the field value's probability density function (PDF). In this calculation, both the shape of the potential and the warp factor are arbitrary functions, and the PDF is obtained with and without volume effects due to the finite size of the averaging domain. DBI kinetic terms typically arise in string-inspired inflationary scenarios in which the scalar field is associated with some distance within the (compact) extra dimensions. The inflaton's accessible range of field values therefore is limited because of the extra dimensions' finite size. We argue that in a consistent stochastic approach the inflaton's PDF must vanish for geometrically forbidden field values. We propose to implement these extra-dimensional spatial restrictions into the PDF by installing absorbing (or reflecting) walls at the respective boundaries in field space. As a toy model, we consider a DBI inflaton between two absorbing walls and use the method of images to determine its most general PDF. The resulting PDF is studied in detail for the example of a quartic warp factor and a chaotic inflaton potential. The presence of the walls is shown to affect the inflaton trajectory for a given set of parameters.

Human activities predominate in determining changing incidence of tick-borne encephalitis in Europe

Explanations for the dynamics of tick-borne disease systems usually focus on changes in the transmission potential in natural enzootic cycles. These are undoubtedly important, but recent analyses reveal that they may not be quantitatively the most significant side of the interaction between infected ticks and humans. Variation in human activities that may impact inadvertently but positively on both the enzootic cycles and the degree of human exposure to those cycles, provide more robust explanations for recent upsurges in tick-borne encephalitis in Europe. This can account for long-term increases in incidence that coincided with post-soviet political independence, for small-scales spatial variation in incidence within a country, and for short-scale fluctuations such as annual spikes in incidence. The patterns of relevant human activities, typically those related to the use of forest resources, are evidently driven and/or constrained by the cultural and socio-economic circumstances of each population, resulting in contrasting national epidemiological outcomes.

Inflation and reheating in induced gravity

Inflation is studied in the context of induced gravity (IG) γσ2R, where R is the Ricci scalar, σ a scalar field and γ a dimensionless constant. We study in detail cosmological perturbations in IG and examine both a Landau–Ginzburg (LG) and a Coleman–Weinberg (CW) potential toy models for small field and large field (chaotic) inflation and find that small field inflationary models in IG are constrained to γ≲3×10−3 by WMAP 5-yrs data. Finally we describe the regime of coherent oscillations in induced gravity by an analytic approximation, showing how the homogeneous inflaton can decay in its short-scale fluctuations when it oscillates around a non-zero value σ0.

Shell architecture, element composition, and stable isotope signature of the giant deep-sea oyster Neopycnodonte zibrowii sp. n. from the NE Atlantic

A conspicuous new deep-sea oyster, Neopycnodonte zibrowii sp. n., is described from the Azores Archipelago, where it thrives in 420 to >500 m water depth in high densities concealed underneath overhangs. The new species reaches a relatively large size, which may exceed 20 cm, and is characterised by a very unusual hinge line morphology, straight without a bulge of the resilium. It is compared to the extant Indo-Pacific Empressostrea kostini Huber and Lorenz, 2007 and to the cosmopolitan Neopycnodonte cochlear (Poli, 1791), which has a broadly sympatric distribution at shallower depths in the Azores and Bay of Biscay. Radiocarbon dating reveals that individuals reach an impressive lifespan of one to more than five centuries, placing them among the longest-lived molluscs known to date. They often grow on top of each other, forming stacks that resemble dish piles—an effective measure to optimise shell stability with minimal biomineralisation effort, but with the drawback of increased bioerosion ultimately leading to detachment. Three microstructure types are developed in N. zibrowii: (1) the cross-foliated, calcitic, dorsal to central endostracum and aragonitic ligostracum, (2) the porous vesicular structure of the calcitic ventral endostracum, and (3) the simple prismatic aragonitic myostracum. Foliated and vesicular shell portions show sub-millimetre-scale first-order increments delineated by conchiolin-rich growth breaks (interpreted as reproductive cyclicity), and less distinct second-order increments (interpreted as annual in nature). This pattern is clearly reflected by the elemental composition with the primary growth breaks lacking Ca and Sr but including Mg and S as organic matrix constituents. The second-order increments within the calcite are mirrored by moderately co-varying Mg/Ca and S/Ca fluctuations at stable Sr concentrations, reflecting varying proportions of organic matrix. Dorsal and central endostracum transects reveal a low inter-valve, but considerable inter-specimen variability with high Mg/Ca molar ratios and fluctuations (22.5±17.6 mmol/mol), low Sr/Ca values (0.2±0.1 mmol/mol), and a typical to high S/Ca content (6.9±2.2 mmol/mol), when compared to other calcitic bivalves. Unlike short-lived, shallow-water oysters, N. zibrowii thrives under very stable environmental conditions. Minimal temperature fluctuations and stable open marine salinity provide an optimal basis to recognise biological fractionation processes. Strong Mg/Ca fluctuations indicate a physiological control related to metabolism and biomineralisation, prohibiting the use of this ratio as a temperature or ocean chemistry proxy. Low Sr/Ca ratios indicate rather constant and low long-term accretion rates, while short-scale fluctuations may be attributed to short-term variations in growth rate and Mg incorporation. Oxygen isotopes yield a considerable spread of 1.8‰ with a mean of 2.0±0.3‰ δ 18O V-PDB, and low correlation between different contemporaneous parts of the shell and between specimens. These values surprisingly exceed expected equilibrium conditions, calculated from in situ temperature data (annual mean 12.3±0.3 °C) and seawater isotopic composition (0.5±0.1‰ δ 18O SMOW), by 0.5‰ on average. Such positively shifting vital effects, previously reported for limpets and barnacles, are often overlooked in high-temperature and high-amplitude settings and may be more common than is currently believed. Carbon isotopes range from 0.2 to 3.5‰ δ 13C V-PDB (mean 1.8±0.7‰) and show an ontogenetic decrease, but may incorporate an environmental signal in adult portions, indicated by a strong correspondence of peaks between specimens. This signal is likely driven by a complex interplay of different factors, such as primary production, current-based food supply and metabolism.

Quasi‐linear Magnetic Field Lines: Anomalous Transport and Self‐Similarity, from the Analytic to the Numerical

Charged energetic particles propagating in solar wind magnetic fields span field irregularities down to very short turbulent scales, not described by the original quasi-linear theory for weak magnetic turbulence. This theory only predicts a field line diffusion on the largest scales, well above the correlation length, inverse of the spectral flattening wavenumber. The quasi-linear prediction for the transport and behavior of magnetic field lines is generalized here to all scales and arbitrary three-dimensional turbulence spectra. New analytical expressions are derived for the field line mean square cross-field displacement Δx2, and analytical proof is presented for the anomalous transport of the field lines. We find Δx2 ∝ (Δz)β, where Δz is the elapsed distance along the average field and β, the transport exponent, can take any value between 0 and 2. A decreasing turbulence spectrum results in a field line supradiffusion (β > 1), while an inverted spectrum implies a subdiffusion (β < 1). Simple expressions are derived for the transport exponent and coefficient. A powerful new method is presented to compute magnetic field lines in the quasi-linear regime of turbulence that allows rapid computation of field lines generated from any three-dimensional turbulence spectrum, including some 1015 modes and more. Individual field lines computed with this method show how a spectral steepening results in a smoothing of the field lines and how harder spectra give increasingly more short-scale fluctuations. The field line self-similarity, characteristic of power-law spectra, is demonstrated visually, and the anomalous transport of the field lines is confirmed numerically.

Excitation of short-scale fluctuations by parametric decay of helicon waves into ion–sound and Trivelpiece–Gould waves

The helicon wave field and the excitation of short-scale electrostatic fluctuations in a helicon-produced plasma are closely related as both the helicon wave damping and the fluctuation level are shown to increase with the launched rf power. Correlation methods using electrostatic probes as well as microwave back-scattering at the upper-hybrid resonance are applied to obtain the dispersion relations of the fluctuations in the low-frequency and high-frequency ranges. The frequency and wavenumber spectra measured for all components of the wave vector allow us to identify the fluctuations as ion–sound and Trivelpiece–Gould waves that originate from parametric decay of the helicon pump wave. The growth rates and thresholds inferred from the evolution of the fluctuations in a wide range of helicon plasma parameters are in good agreement with predictions for the parametric decay instability that takes into account realistic damping rates for the decay waves as well as non-vanishing parallel wavenumber of the helicon pump.

Investigations of short-scale fluctuations in a helicon plasma by cross-correlation enhanced scattering

Correlation enhanced scattering (CES) near the upper hybrid resonance has been applied for studying small-scale plasma density fluctuations excited by the rf fields in a helicon discharge. The turbulent fluctuations are diagnosed for conditions where the electron plasma frequency exceeds the electron cyclotron frequency considerably. The frequency and wave number spectra of the fluctuations are measured both in the plasma core as well as in outer region of the helicon discharge. The spectral measurements evidence the short-scale fluctuations to originate from a parametric decay instability. The low-frequency fluctuations obey the ion-sound dispersion relation while the lower sideband of the helicon wave frequency satisfies the Trivelpiece–Gould wave dispersion relation. In order to gain more insight in the experimental results and, in particular, to estimate the fluctuation level the backscattering process is analyzed both numerically and analytically for high-density plasma conditions. A fully electromagnetic model was developed that takes into account the radial density distribution of the plasma column as well as the antenna diagram of the rectangular emitting/receiving horn. Using this model the relative amplitude of ion-sound density fluctuations in the core of the helicon discharge is estimated as 11%. The role of nonlinear effects on formation of the scattering spectra due to the high fluctuation level in the plasma center is discussed. The findings also demonstrate that the CES diagnostic can be applied to diagnose fluctuations in spherical tokamak plasmas where the probing conditions resemble those of high-density helicon discharges.

Scaling laws of density fluctuations at high-k on Tore Supra

Anomalous transport in tokamaks is generally attributed to turbulent fluctuations. Since a large variety of modes are potentially unstable, a wide range of short-scale fluctuations should be measured, with wavenumbers from kρi ∼ 0.1 to kρi ≫ 1. In the Tore Supra tokamak, a light scattering experiment has made possible fluctuation measurements in the medium- and high-k domains where a transition in the k-spectrum is observed: the fluctuation level decreases much faster than usual observations, typically with a power law S(k) ≡ k−6. A scan of the ion Larmor radius shows that the transition wavenumber scales with ρi around kρi ∼ 1.5. This transition indicates that a characteristic length scale should be involved to describe the fluctuation nonlinear dynamics in this range. The resulting very low level of fluctuations at high-k does not support a strong effect of turbulence driven by the electron temperature gradient. For this gyroradius scan, the characteristics of turbulence also exhibit a good matching with predictions from gyro-Bohm scaling: the typical scale length of turbulence scales with the ion Larmor radius, the typical timescales with a/cs; the turbulence level also scales with ρi, according to the mixing length rule.

Spectra of enhanced scattering by spontaneous density fluctuations in a tokamak

The wavenumber-resolved radar backscattering diagnostics in the upper hybrid resonance (UHR) region was used to study low-frequency short-scale turbulence in the FT-1 tokamak. The scattered spectra were measured for different delay times of the scattered signals. It is shown that the width of the spectrum of enhanced scattering by spontaneous fluctuations is proportional to the delay time. Possible mechanisms for the formation of the scattered spectra are proposed and discussed. The results of simulations and additional experiments were used to determine the dominant mechanisms governing the formation of the scattered spectra in the FT-1 tokamak. These mechanisms are related to the effect of multiple small-angle scattering of both the probing wave and the waves backscattered in the UHR region by long-scale density fluctuations and to the Doppler effect caused by the entrainment of short-scale fluctuations by the long-scale turbulent flow.

Renormalization-group analysis on the stability of large-scale electrostatic fluctuations of two-dimensional plasmas

Stability of large-scale electrostatic fluctuations of forced two-dimensional plasma is studied by the use of the renormalization-group method. Large-scale flows have been rendered important in regulating turbulent plasma states and many recent works focus on their generation out of turbulence. This work is motivated by the recent result that the long-wavelength fluctuations can either grow or decay as a result of the interactions between the short-scale fluctuations depending anisotropically on the spectra of the small-scale turbulence. The Hasegawa–Mima model that is forced by an anisotropic Gaussian power-law noise is used and the renormalized viscosity up to the lowest-order coupling is computed. The result shows that the anisotropic portion of the viscosity may have opposite sign compared to the isotropic part, depending on the strength of the anisotropy.

Disorder-induced first-order transition in superconducting films.

Strong disorder in the two-dimensional XY model is shown to favor the first-order phase transition with nonuniversal properties due to reduction of the effective temperature for short-scale fluctuations. The results seem to be of relevance for high-${\mathit{T}}_{\mathit{c}}$ superconducting films.