Scaling Regime Research Articles

Friction on ALP domain walls and gravitational waves

We study the early Universe evolution of axion-like particle (ALP) domain walls taking into account the effect of friction from particles in the surrounding plasma, including the case of particles in thermal equilibrium and frozen out species. We characterize the friction force from interactions within the ALP effective theory, providing new results for the fermion contribution as well as identifying simple conditions for friction to be relevant during the domain wall life time. When friction dominates, the domain wall network departs from the standard scaling regime and the corresponding gravitational wave emission is affected. As a relevant example, we show how this can be the case for ALP domain walls emitting at the typical frequencies of Pulsar Timing Array experiments, when the ALP couples to the SM leptons. We then move to a general exploration of the gravitational wave prospects in the ALP parameter space. We finally illustrate how the gravitational wave signal from ALP domain walls is correlated with the quality of the underlying U(1) symmetry.

Noisy pursuit by a self-steering active particle in confinement (a)

The properties of a cognitive, self-propelled, and self-steering particle in the presence of a stationary target are analyzed theoretically and by simulations. In particular, the effects of confinement in competition with activity and steering are addressed. The pursuer is described as an intelligent active Ornstein-Uhlenbeck particle (iAOUP), confined in a harmonic potential. For the free pursuer, we find universal scaling regimes for the pursuer-target distance in terms of the Péclet number and maneuverability. Steering results in a novel constant mean-distance regime, which broadens with increasing maneuverability. Confinement strongly affects the propulsion direction and leads to a scaling at large Péclet numbers similar to that in the absence of confinement, yet with a pronounced dependence on confinement strength.

Large is different: Nonmonotonic behavior of elastic range scaling in polymeric turbulence at large Reynolds and Deborah numbers.

We use direct numerical simulations to study homogeneous and isotropic turbulent flows of dilute polymer solutions at high Reynolds and Deborah numbers. We find that for small wave numbers k, the kinetic energy spectrum shows Kolmogorov-like behavior that crosses over at a larger k to a novel, elastic scaling regime, E(k) ∼ k-ξ, with ξ ≈ 2.3. We study the contribution of the polymers to the flux of kinetic energy through scales and find that it can be decomposed into two parts: one increase in effective viscous dissipation and a purely elastic contribution that dominates over the nonlinear flux in the range of k over which the elastic scaling is observed. The multiscale balance between the two fluxes determines the crossover wave number that depends nonmonotically on the Deborah number. Consistently, structure functions also show two scaling ranges, with intermittency present in both of them in equal measure.

Probabilistic local wellposedness of 1D quintic NLS below [formula omitted

We consider the Cauchy problem of the nonlinear Schrödinger equation i∂tu+∂x2u±u5=0 on the real line, which is L2-critical. We prove the local well-posedness of the initial value problem (IVP) for the scaling supercritical regularity regime −110<s<0 in probabilistic manner. One of the main ingredient is to establish the probabilistic bilinear Strichartz estimate.

Random Walk on a Rough Surface: Renormalization Group Analysis of a Simple Model

The field-theoretic renormalization group is applied to a simple model of a random walk on a rough fluctuating surface. We consider the Fokker–Planck equation for a particle in a uniform gravitational field. The surface is modeled by the generalized Edwards–Wilkinson linear stochastic equation for the height field. The full stochastic model is reformulated as a multiplicatively renormalizable field theory, which allows for the application of the standard renormalization theory. The renormalization group equations have several fixed points that correspond to possible scaling regimes in the infrared range (long times and large distances); all the critical dimensions are found exactly. As an example, the spreading law for the particle’s cloud is derived. It has the form R2(t)≃t2/Δω with the exactly known critical dimension of frequency Δω and, in general, differs from the standard expression R2(t)≃t for an ordinary random walk.

Dodecaploid Xenopus longipes provides insight into the emergence of size scaling relationships during development

Genome and cell size are strongly correlated across species1,2,3,4,5,6 and influence physiological traits like developmental rate.7,8,9,10,11,12 Although size scaling features such as the nuclear-cytoplasmic (N/C) ratio are precisely maintained in adult tissues,13 it is unclear when during embryonic development size scaling relationships are established. Frogs of the genus Xenopus provide a model to investigate this question, since 29 extant Xenopus species vary in ploidy from 2 to 12 copies (N)of the ancestral frog genome, ranging from 20 to 108 chromosomes.14,15 The most widely studied species, X.laevis (4N= 36) and X.tropicalis (2N= 20), scale at all levels, from body size to cellular and subcellular levels.16 Paradoxically, the rare, critically endangered dodecaploid (12N= 108) Xenopus longipes (X.longipes) is a small frog.15,17 We observed that despite some morphological differences, X.longipes and X.laevis embryogenesis occurred with similar timing, with genome to cell size scaling emerging at the swimming tadpole stage. Across the three species, cell size was determined primarily by egg size, whereas nuclear size correlated with genome size during embryogenesis, resulting in different N/C ratios in blastulae prior to gastrulation. At the subcellular level, nuclear size correlated more strongly with genome size, whereas mitotic spindle size scaled with cell size. Our cross-species study indicates that scaling of cell size to ploidy is not due to abrupt changes in cell division timing, that different size scaling regimes occur during embryogenesis, and that the developmental program of Xenopus is remarkably consistent across a wide range of genome and egg sizes.

Multilayered Atomic Relaxation in van der Waals Heterostructures

When two-dimensional van der Waals materials are stacked to build heterostructures, moir\'e patterns emerge from twisted interfaces or from mismatch in lattice constant of individual layers. Relaxation of the atomic positions is a direct, generic consequence of the moir\'e pattern, with many implications for the physical properties. Moir\'e driven atomic relaxation may be naively thought to be restricted to the interfacial layers and thus irrelevant for multi-layered heterostructures. However, we provide experimental evidence for the importance of the three dimensional nature of the relaxation in two types of van der Waals heterostructures: First, in multi-layer graphene twisted on graphite at small twist angles ($\theta\approx0.14^\circ$) we observe propagation of relaxation domains even beyond 18 graphene layers. Second, we show how for multi-layer PdTe$_2$ on Bi$_2$Se$_3$ the moir\'e lattice constant depends on the number of PdTe$_2$ layers. Motivated by the experimental findings, we developed a continuum approach to model multi-layered relaxation processes based on the generalized stacking fault energy functional given by ab-initio simulations. Leveraging the continuum property of the approach enables us to access large scale regimes and achieve agreement with our experimental data for both systems. Furthermore it is well known that the electronic structure of graphene sensitively depends on local lattice deformations. Therefore we study the impact of multi-layered relaxation on the local density of states of the twisted graphitic system. We identify measurable implications for the system, experimentally accessible by scanning tunneling microscopy. Our multi-layered relaxation approach is not restricted to the discussed systems, and can be used to uncover the impact of an interfacial defect on various layered systems of interest.

Large times existence for thin vibrating rods

We consider the dynamical evolution of a thin rod described by an appropriately scaled wave equation of nonlinear elasticity. Under the assumption of well-prepared initial data and external forces, we prove that a solution exists for arbitrarily large times, if the diameter of the cross section is chosen sufficiently small. The scaling regime is such that the limiting equations are linear.

Performance Bounds for Group Testing With Doubly-Regular Designs

In the group testing problem, the goal is to identify a subset of defective items within a larger set of items based on tests whose outcomes indicate whether any defective item is present. This problem is relevant in areas such as medical testing, DNA sequencing, and communications. In this paper, we study a doubly-regular design in which the number of tests-per-item and the number of items-per-test are fixed. We analyze the performance of this test design alongside the Definite Defectives (DD) decoding algorithm in several settings, namely, (i) the sub-linear regime <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k=o(n)$ </tex-math></inline-formula> with exact recovery, (ii) the linear regime <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k=\Theta (n)$ </tex-math></inline-formula> with approximate recovery, and (iii) the size-constrained setting, where the number of items per test is constrained. Under setting (i), we show that our design together with the DD algorithm, matches an existing achievability result for the DD algorithm with the near-constant tests-per-item design, which is known to be asymptotically optimal in broad scaling regimes. Under setting (ii), we provide novel approximate recovery bounds that complement a hardness result regarding exact recovery. Lastly, under setting (iii), we improve on the best known upper and lower bounds in scaling regimes where the maximum test size grows with the total number of items.

Scale dependence of fractal dimension in deterministic and stochastic Lorenz-63 systems.

Many natural systems show emergent phenomena at different scales, leading to scaling regimes with signatures of deterministic chaos at large scales and an apparently random behavior at small scales. These features are usually investigated quantitatively by studying the properties of the underlying attractor, the compact object asymptotically hosting the trajectories of the system with their invariant density in the phase space. This multi-scale nature of natural systems makes it practically impossible to get a clear picture of the attracting set. Indeed, it spans over a wide range of spatial scales and may even change in time due to non-stationary forcing. Here, we combine an adaptive decomposition method with extreme value theory to study the properties of the instantaneous scale-dependent dimension, which has been recently introduced to characterize such temporal and spatial scale-dependent attractors in turbulence and astrophysics. To provide a quantitative analysis of the properties of this metric, we test it on the well-known low-dimensional deterministic Lorenz-63 system perturbed with additive or multiplicative noise. We demonstrate that the properties of the invariant set depend on the scale we are focusing on and that the scale-dependent dimensions can discriminate between additive and multiplicative noise despite the fact that the two cases have exactly the same stationary invariant measure at large scales. The proposed formalism can be generally helpful to investigate the role of multi-scale fluctuations within complex systems, allowing us to deal with the problem of characterizing the role of stochastic fluctuations across a wide range of physical systems.

Causal modifications of gravity and their observational bounds

Since general relativity is the unique theory of massless spin 2 particles at large distances, the most reasonable way to have significant modifications is to introduce one or more light scalars that mediate a new long-range force. Most existing studies of such scalars invoke models that exhibit some kind of "screening" at short distances to hide the force from solar system tests. However, as is well known, such modifications also exhibit superluminality, which can be interpreted as a form of acausality. In this work we explore explicitly subluminal and causal scalar field models. In particular, we study a conformally coupled scalar $\phi$, with a small coupling to matter to obey solar system bounds, and a non-canonical kinetic term $K(X)$ ($X=(\partial\phi)^2/2$) that obeys all subluminality constraints and is hyperbolic. We consider $K(X)$ that is canonical for small $X$, but beyond some nonlinear scale enters a new scaling regime of power $p$, with $1/2<p<1$ (the DBI kinetic term is the limit $p=1/2$ and a canonical scalar is $p=1$). As opposed to screening (and superluminality), this new force becomes more and more important in the regime of high densities (and subluminality). We then turn to the densest environments to put bounds on this new interaction. We compute constraints from precession in binary systems such as Hulse-Taylor, we compute corrections to neutron star hydrostatic equilibrium, and we compute power in radiation, both tensor mode corrections and the new scalar mode, which can be important during mergers.

Regimes of optical propagation through turbulence: theory and direct numerical simulations

Classical work provides an analytical framework to predict distortions of an electromagnetic wave as it interacts with turbulence. However, there seems to be virtually no systematic validation of these predictions and assessment of the assumptions behind the theory. In this work, we present numerical results of optical distortions based on highly-resolved direct numerical simulations of turbulence at a range of conditions, and new theory which accounts for more realistic representations of turbulent fluctuations. This leads to a number of new results. First, we discover two new scaling regimes for the variance of phase and log-amplitude at propagations comparable to Kolmogorov scales. Second, our theory highlights and overcomes limitations of classical work including the effects of finite outer-scale, non-Kolmogorov intermittency corrections, and a more general representation of small scales. Third, we propose a new universal refractive-index structure parameter in terms of three non-dimensional parameters involving turbulence and optical scales. This yields a universal presentation of all scaling regimes in a new phase space. Finally, high-fidelity direct numerical simulations which resolve all turbulent scales are used to perform the first systematic assessment of classical and new scaling regimes. Excellent agreement is found between simulations and theoretical findings.

The Random Phase Approximation for Interacting Fermi Gases in the Mean-Field Regime

Abstract We present a general approach to justify the random phase approximation for the homogeneous Fermi gas in three dimensions in the mean-field scaling regime. We consider a system of N fermions on a torus, interacting via a two-body repulsive potential proportional to $N^{-\frac {1}{3}}$ . In the limit $N\rightarrow \infty $ , we derive the exact leading order of the correlation energy and the bosonic elementary excitations of the system, which are consistent with the prediction of the random phase approximation in the physics literature.

Cylindrical brushes with ionized side chains: Scaling theory revisited.

We revisit the classic scaling model of a cylindrical polyelectrolyte (PE) brush focusing on molecular brushes with stiff backbones and dispersions of polymer-decorated nanorods. Based on the blob representation we demonstrate that similarly to the case of planar PE brushes, separation of intra- and intermolecular repulsions between charges leads to novel scaling regimes for cylindrical PE brushes in salt-added solution and a sharper decrease in its thickness versus salt concentration dependence. These theoretical predictions may inspire further comprehensive experimental research and computer simulations of synthetic and biopolyelectrolyte cylindrical brushes.

Isobaric heat capacity of carbon dioxide at critical pressure: Singular thermodynamic functions as multiply broken power laws

The isobaric CO2 heat capacity at critical pressure is regressed in an extended temperature interval from the melting point at 216.6 K up to 2000 K. In the vicinity of the critical temperature Tc=304.13K, the calculated critical scaling exponent of the heat capacity is used to extrapolate the empirical data range into the power-law scaling regime. Closed-form representations of the high- and low-temperature branches of the isobaric CO2 heat capacity are obtained by nonlinear least-squares fits of multiply broken power-law distributions, in which the calculated universal scaling exponent is implemented. The regressed broken power laws cover the temperature range from the melting point up to Tc and from Tc to CO2 dissociation temperatures. Index functions representing the Log–Log slope of the heat capacity are used to quantify the crossover from the high- and low-temperature regimes to the critical power-law scaling regime. Even though the focus is on the isobaric heat capacity of a specific one-component fluid, the formalism is kept sufficiently general to be applicable to other thermodynamic functions with critical singularities and to multi-component mixtures.

Stochastic simulation of reference rainfall scenarios for hydrological applications using a universal multi-fractal approach

Abstract. Hydrological applications such as storm-water management usually deal with region-specific reference rainfall regulations based on intensity–duration–frequency (IDF) curves. Such curves are usually obtained via frequency analysis of rainfall and exceedance probability estimation of rain intensity for different durations. It is also common for reference rainfall to be expressed in terms of precipitation P, accumulated in a duration D, with a return period T. Meteorological modules of hydro-meteorological models used for the aforementioned applications therefore need to be capable of simulating such reference rainfall scenarios. This paper aims to address three research gaps: (i) the discrepancy between standard methods for defining reference precipitation and the strong multi-scale intermittency of precipitation, (ii) a lack of procedures to adapt multi-fractal precipitation modelling to specified partial statistical references, and (iii) scarcity of proper multi-scale tools to quantitatively estimate the effectiveness of such simulation procedures. Therefore, it proposes (i) a procedure based on extreme non-Gaussian statistics in two scaling regimes due to earth's finite size to tackle multi-scale intermittency head on, (ii) a renormalization technique to make simulations comply with the aforementioned partial statistical references, and (iii) multi-scale metrics to compare simulated rainfall time series with those observed. While the first two proposals are utilized to simulate reference rainfall scenarios for three regions (Paris, Nantes, and Aix-en-Provence) in France that are characterized by different climates, the last one is used to validate them. The scope of this paper is that the baseline precipitation scenarios simulated here can be used as realistic inputs into hydrological models for applications such as the optimal design of storm-water management infrastructure, especially green roofs. Although only purely temporal simulations are considered, this approach could possibly be generalized to space–time as well.

Implications of Seiberg–Witten map on Type-I superconductors

Guided by Pippard superconductivity, we incorporate the Seiberg–Witten map in the classical London theory of Type-I superconductors when an external magnetic field is applied. After defining the noncommutative Maxwell potentials, we derive the London equation for the supercurrent as a function of the noncommutative parameter, up to second order in gauge fields expansions. Keeping track of the effects of noncommutative gauge fields, we argue that noncommutative magnetic field effects can be cast in the London penetration length similar to nonlocal Pippard superconductivity. Also, we show that the flux quantization remains consistent relative to the commutative case. Our effective London penetration length reduces to the standard one in the commutative limit. These results allow us to argue that the framework of noncommutative electrodynamics can give some insights into the anisotropic and nonlocal structure of superconductivity and Condensed Matter Systems, perhaps out of the ultra-microscopic scale regime.

The Glauber-Ising chain under low-temperature protocols

This work is devoted to an in-depth analysis of arbitrary temperature protocols applied to the ferromagnetic Glauber-Ising chain launched from a disordered initial state and evolving in the low-temperature scaling regime. We focus our study on the density of domain walls and the reduced susceptibility. Both the inverse of the former observable and the latter one provide two independent measures of the typical size of the growing ferromagnetic domains. Their product is thus a dimensionless form factor characterising the pattern of growing ordered domains and providing a measure of the distance of the system to thermal equilibrium. We apply this framework to a variety of protocols: everlasting slow quenches, where temperature decreases continuously to zero in the limit of infinitely long times, slow quenches of finite duration, where temperature reaches zero at some long but finite quenching time, time-periodic protocols with weak and strong modulations, and the two-temperature protocol leading to the memory effect found by Kovacs.

Asymptotic optimality of the binomial-exhaustive policy for polling systems with large switchover times

We study an optimal-control problem of polling systems with large switchover times, when a holding cost is incurred on the queues. In particular, we consider a stochastic network with a single server that switches between several buffers (queues) according to a pre-specified order, assuming that the switchover times between the queues are large relative to the processing times of individual jobs. Due to its complexity, computing an optimal control for such a system is prohibitive, and so we instead search for an asymptotically optimal control. To this end, we first solve an optimal control problem for a deterministic relaxation (namely, for a fluid model), that is represented as a hybrid dynamical system. We then “translate” the solution to that fluid problem to a binomial-exhaustive policy for the underlying stochastic system, and prove that this policy is asymptotically optimal in a large-switchover-time scaling regime, provided a certain uniform integrability (UI) condition holds. Finally, we demonstrate that the aforementioned UI condition holds in the following cases: (i) the holding cost has (at most) linear growth, and all service times have finite second moments; (ii) the holding cost grows at most at a polynomial rate (of any degree), and the service-time distributions possess finite moment generating functions.

The microstructure of stochastic volatility models with self-exciting jump dynamics

We provide a general probabilistic framework within which we establish scaling limits for a class of continuous-time stochastic volatility models with self-exciting jump dynamics. In the scaling limit, the joint dynamics of asset returns and volatility is driven by independent Gaussian white noises and two independent Poisson random measures that capture the arrival of exogenous shocks and the arrival of self-excited shocks, respectively. Various well-studied stochastic volatility models with and without self-exciting price/volatility co-jumps are obtained as special cases under different scaling regimes. We analyze the impact of external shocks on the market dynamics, especially their impact on jump cascades and show in a mathematically rigorous manner that many small external shocks may trigger endogenous jump cascades in asset returns and stock price volatility.