Finite Length Scale Research Articles

Ideal gas thermodynamics with an invariant energy scale

A viable approach towards Quantum Gravity is the Doubly Special Relativity (DSR) framework in which an observer-independent finite energy upper bound (or a finite smallest length scale) appears quite naturally. In this work, we have studied the thermodynamic properties of an ideal gas in a specific DSR framework, known as the Magueijo-Smolin (MS) Model. We use the fact that DSR can be considered as nonlinear representation of Lorentz Group. Subsequently, various thermodynamic parameters of ideal gas have been derived in this modified framework to compare the corresponding deviations from the usual scenario due to the presence of the invariant energy (length) scale.

Generalized kinetic equation for tokamak plasma equilibrium distribution function

A generalized kinetic equation for the equilibrium distribution function in a finite beta, arbitrary tokamak plasma is derived. The equation is correct to second order in ρ/L (ρ is the particle Larmor radius and L is the system size). Resolving the finite Larmor radius length scales with no restriction on the ratio of poloidal to total equilibrium magnetic field, Bϑ/B, it generalizes the drift kinetic theory of Hazeltine [Phys. Plasmas 15, 77 (1973)] to the limit of Bϑ/B∼1 (e.g., to ensure validity for spherical tokamaks). Two cases are considered. The first provides the equilibrium distribution function, consistent with the generalized gyrokinetic formalism of Dudkovskaia et al. [Plasma Phys. Controlled Fusion 65, 045010 (2023)], derived specifically to capture neoclassical equilibrium currents in the gyrokinetic stability analyses in strong gradient regions. The second assumes short length scales in the direction perpendicular to the magnetic field, which can occur as a result of small coherent magnetic structures in the plasma, such as neoclassical tearing mode magnetic islands close to threshold. This then extends the drift island equations of Dudkovskaia et al. [Nucl. Fusion 63, 016020 (2023)] for the plasma response to magnetic islands to a spherical tokamak plasma configuration. Resolving ρ∼ρϑ (or Bϑ∼B), where ρϑ is the particle poloidal Larmor radius, is also expected to influence calculations of the magnetic island propagation frequency and the associated contributions to the island onset conditions.

Dynamic Crack-Front Deformations in Cohesive Materials.

Crack fronts deform due to heterogeneities, and inspecting these deformations can reveal local variations of material properties, and help predict out-of-plane damage. Current models neglect the influence of a finite dissipation length scale behind the crack tip, called the process zone size. The latter introduces scale effects in the deformation of the crack front, that are mitigated by the dynamics of the crack. We provide and numerically validate a theoretical framework for dynamic crack-front deformations in heterogeneous cohesive materials, a key step toward identifying the effective properties of a microstructure.

Structural and rheological behavior of β-lactoglobulins influenced by high hydrostatic pressure – From a single molecule to the aggregates

The structures and rheological behavior of high-hydrostatic-pressure treated β-lactoglobulins (HPβlg) after lyophilizing and pulverizing were determined in the reconstituting systems. Both of computational and experimental approaches were applied to examine and understand the structural changes in the β-lactoglobulins (βlg) under high pressure. For the diluted systems the molecular dynamics managed to explain the experimental observations, while such matches failed for the concentrated systems, indicating that both of pressure and concentration exerted effects on the denaturation and aggregation of β-lactoglobulins (βlg) under high hydrostatic pressure (HHP) treatments. It was found that HPβlg obtained from high concentrations and pressures had extensively unfolded structures and aggregated through reaction-limited clustering (RLC) induced by disulphide bond formations. With the increased concentration and high pressure during the treatments the HPβlg RLC aggregates exhibited branched and densely packed structures, giving cold-set gels without any assistance from gelators in the reconstituting dispersions. The gels of the HPβlg exhibited self-similar structures with a finite length scale and a fractal dimension of 2.23–2.25 that was larger than that for a critical gel (2.00), indicating rubber-like networks. Moreover, such fractal dimension also revealed that the linear strand-like structures and ordered aggregations of HPβlg were mainly resulted from the LRC aggregates formed during HHP and lyophilization. However, it was intriguing to find that the cold-set gelation of those HPβlg aggregates was induced by diffusion-limited clustering. According to the current study, βlg powders with desirable characteristics are possible to design and produce through controls over the protein concentrations and pressures during HHP processing, which would be of great practical and industrial interests. • HHP-induced unfolding of β-lactoglobulin was illustrated by computer simulations. • Concentration and pressure affect the denaturation of β-lactoglobulins. • Cold-set gelation of HHP-treated β-lactoglobulins was observed. • HHP-β-lactoglobulins gelled through reaction-limited clustering (LRC) aggregations.

Stability of thermoelastic sliding problem with contact pressure-dependent thermal contact resistance

The sliding contact problem of a rigid indenter over an elastic body with constant temperature difference was investigated using finite element method by considering a contact pressure-dependent thermal resistance. The stability boundary was identified by inspecting the transient contact behaviors, which showed a linear relationship between two nondimensional parameters at the log scale. This proportionality resulted in a nondimensional ratio, which depended on temperature, contact resistance, and sliding speed in the case of unit nondimensional material properties, suggesting “critical temperature difference”. Moreover, the inclusion of Poisson ratio prevented the indefinite bifurcation behavior and led to a finite length scale in the steady state.

Edge fluctuations and third-order phase transition in harmonically confined long-range systems

We study the distribution of the position of the rightmost particle x max in a N-particle Riesz gas in one dimension confined in a harmonic trap. The particles interact via long-range repulsive potential, of the form r −k with −2 < k < ∞ where r is the inter-particle distance. In equilibrium at temperature O(1), the gas settles on a finite length scale L N that depends on N and k. We numerically observe that the typical fluctuation of y max = x max/L N around its mean is of . Over this length scale, the distribution of the typical fluctuations has a N independent scaling form. We show that the exponent η k obtained from the Hessian theory predicts the scale of typical fluctuations remarkably well. The distribution of atypical fluctuations to the left and right of the mean ⟨y max⟩ are governed by the left and right large deviation functions (LDFs), respectively. We compute these LDFs explicitly ∀ k > −2. We also find that these LDFs describe a pulled to pushed type phase transition as observed in Dyson’s log-gas (k → 0) and 1d one component plasma (k = −1). Remarkably, we find that the phase transition remains third order for the entire regime. Our results demonstrate the striking universality of the third order transition even in models that fall outside the paradigm of Coulomb systems and the random matrix theory. We numerically verify our analytical expressions of the LDFs via Monte Carlo simulation using an importance sampling algorithm.

Temperature-dependent anomalous energy transport in finite-length quasi-one-dimensional MoS2 : Crossover from phonons to solitons

Anomalous energy transport is a widely investigated character in one-dimensional lattice and both phonons and solitons are candidate energy carriers responsible for the thermal conductivity divergence before their mean-free paths. However, it was long believed the contribution of solitons could be neglected even close to the melting point in a real crystalline solid. In this paper, we show that a crossover of wave-packet dynamics, from a phonon- to a soliton-dominated state, occurs in a quasi-one-dimensional molybdenum disulfide $({\mathrm{MoS}}_{2})$ sheet at high temperatures far below its melting point by nonequilibrium and equilibrium molecular dynamics simulations. Divergent sound speed variation and the corresponding heat capacity peaks are observed in the transition-temperature region that is related to a second-order phase transition. We also find that its anomalous energy transport falls into a universality class with thermal conductivity divergence exponent $\ensuremath{\alpha}=2/5$ at a finite length scale within 2000 nm when solitons are excited above 600 K, and the scaling relations derived from the L\'evy walk of energy carriers is fulfilled as $\ensuremath{\alpha}=2\ensuremath{-}1/\ensuremath{\gamma}=\ensuremath{\beta}\ensuremath{-}1$ in the soliton-dominated state above 1800 K. Our results reveal the peculiar solitonlike contribution to thermal conduction at high temperatures in the low-dimensional crystalline solids.

Field-induced vortex-like textures as a probe of the critical line in reentrant spin glasses

We study the evolution of the low-temperature field-induced magnetic defects observed under an applied magnetic field in a series of frustrated amorphous ferromagnets (Fe_{1-x}Mn_{x})_{75}P_{16}B_{3}Al_{3} (“a-Fe_{1-x}Mn_{x}”). Combining small-angle neutron scattering and Monte Carlo simulations, we show that the morphology of these defects resemble that of quasi-bidimensional spin vortices. They are observed in the so-called “reentrant” spin-glass (RSG) phase, up to the critical concentration x_{mathrm{C}} approx 0.36 which separates the RSG and “true” spin glass (SG) within the low temperature part of the magnetic phase diagram of a-Fe1−xMnx. These textures systematically decrease in size with increasing magnetic field or decreasing the average exchange interaction, and they finally disappear in the SG sample (x = 0.41), being replaced by field-induced correlations over finite length scales. We argue that the study of these nanoscopic defects could be used to probe the critical line between the RSG and SG phases.

Identification of Thermal Response of Mesoscopic Liquids under Mechanical Excitation: From Harmonic to Nonharmonic Thermal Wave

In the conventional picture, the temperature of a liquid bath in the quiescent state is uniform down to thermal fluctuation length scales. Here we examine the impact of a low-frequency shear mechanical field (hertz) on the thermal equilibrium of polypropylene glycol and liquid water away from any phase transition confined between high-energy surfaces. We show the emergence of both cooling and heating shear waves of several tens of micrometers widths varying synchronously with the applied shear strain wave. The thermal wave is stable at low strain amplitude and low frequency while thermal harmonics develop by increasing the frequency or the strain amplitude. The liquid layer behaves as a dynamic thermoelastic medium challenging the extension of the fluctuation-dissipation theorem to nonequilibrium fluids. This view is in agreement with recent theoretical models predicting that liquids support shear elastic waves up to a finite propagation length scale of the order the thermal wave.

Vanishing Thermal Equilibration for Hole-Conjugate Fractional Quantum Hall States in Graphene

Transport through edge channels is responsible for conduction in quantum Hall (QH) phases. Robust quantized values of charge and thermal conductances dictated by bulk topology appear when equilibration processes become dominant. We report on measurements of electrical and thermal conductances of integer and fractional QH phases, realized in hexagonal boron nitride encapsulated graphite-gated bilayer graphene devices for both electron and hole doped sides with different valley and orbital symmetries. Remarkably, for complex edges at filling factors ν=5/3 and 8/3, closely related to the paradigmatic hole-conjugate ν=2/3 phase, we find quantized thermal conductance whose values (3κ_{0}T and 4κ_{0}T, respectively where κ_{0}T is the thermal conductance quantum) are markedly inconsistent with the values dictated by topology (1κ_{0}T and 2κ_{0}T, respectively). The measured thermal conductance values remain insensitive to different symmetries, suggesting its universal nature. Our findings are supported by a theoretical analysis, which indicates that, whereas electrical equilibration at the edge is established over a finite length scale, the thermal equilibration length diverges for strong electrostatic interaction. Our results elucidate the subtle nature of crossover from coherent, mesoscopic to topology-dominated transport.

Emergence of linear isotropic elasticity in amorphous and polycrystalline materials.

We investigate the emergence of isotropic linear elasticity in amorphous and polycrystalline solids via extensive numerical simulations. We show that the elastic properties are correlated over a finite length scale ξ_{E}, so that the central limit theorem dictates the emergence of continuum linear isotropic elasticity on increasing the specimen size. The stiffness matrix of systems of finite size L>ξ_{E} is obtained, adding to that predicted by linear isotropic elasticity a random one of spectral norm (L/ξ_{E})^{-3/2} in three spatial dimensions. We further demonstrate that the elastic length scale corresponds to that of structural correlations, which in polycrystals reflect the typical size of the grain boundaries and length scales characterizing correlations in the stress field. We finally demonstrate that the elastic length scale affects the decay of the anisotropic long-range correlations of locally defined shear modulus and shear stress.

A multifidelity method for a nonlocal diffusion model

Nonlocal models feature a finite length scale, referred to as the horizon, such that points separated by a distance smaller than the horizon interact with each other. Such models have proven to be useful in a variety of settings. However, due to the reduced sparsity of discretizations, they are also generally computationally more expensive compared to their local differential equation counterparts. We introduce a multifidelity Monte Carlo method that combines the high-fidelity nonlocal model of interest with surrogate models that use coarser grids and/or smaller horizons and thus have lower fidelities and lower costs. Using the multifidelity method, the overall computational cost of uncertainty quantification is reduced without compromising accuracy. It is shown for a one-dimensional nonlocal diffusion example that speedups of up to two orders of magnitude can be achieved using the multifidelity method to estimate the expectation of an output of interest.

Spatial extent of a single lipid's influence on bilayer mechanics.

To what spatial extent does a single lipid affect the mechanical properties of the membrane that surrounds it? The lipid composition of a membrane determines its mechanical properties. The shapes available to the membrane depend on its compositional material properties, and therefore, the lipid environment. Because each individual lipid species' chemistry is different, it is important to know its range of influence on membrane mechanical properties. This is defined herein as the lipid's mechanical extent. Here, a lipid's mechanical extent is determined by quantifying lipid redistribution and the average curvature that lipid species experience on fluctuating membrane surfaces. A surprising finding is that, unlike unsaturated lipids, saturated lipids have a complicated, nonlocal effect on the surrounding surface, with the interaction strength maximal at a finite length-scale. The methodology provides the means to substantially enrich curvature-energy models of membrane structures, quantifying what was previously only conjecture.

Hyperuniformity in cyclically driven glasses

We present a numerical investigation of the density fluctuations in a model glass under cyclic shear deformation conditions. We demonstrate that in our model glass, the compressibility is suppressed in inherently minimally energetic structures, showing a hyperuniform trend at a density which is below the critical jamming density. At low shear amplitudes, i.e. below the yield amplitude, the system reaches an absorbent steady state in which density fluctuations are suppressed, revealing the clear fingerprint of hyperuniformity up to a finite length scale. The opposite scenario is observed above the yield amplitude, where density fluctuations are strongly enhanced. We demonstrate that the transition to this state is accompanied by a spatial phase separation into two distinct hyperuniform regions, as a consequence of shear band formation at amplitudes greater than the yield amplitude.

Bandlimited entanglement harvesting

There are many reasons to believe that there is a fundamental minimum length scale below which distances cannot be reliably resolved. One method of constructing a quantum field with a finite minimum length scale is to use bandlimited quantum field theory, where the spacetime is mathematically both continuous and discrete. This is a modification to the field, which has been shown to have many consequences at the level of the field. We consider an operational approach and use a pair of particle detectors (two-level qubits) as a local probe of the field, which are coupled to the vacuum of the bandlimited massless scalar field in a time-dependent way through a switching function. We show that, mathematically, the bandlimit modifies the spatial profile of the detectors so that they are only quasilocal. We explore two different types of switching functions, Gaussian and Dirac delta. We find that, with Gaussian switching, the bandlimit exponentially suppresses the deexcitation of the detectors when the energy gap between the two levels is larger than the bandlimit. If the detectors are prepared in ground state, in certain regions of the parameter space they are able to extract more entanglement from the field than if there was no bandlimit. When the detectors couple with Dirac-delta switching, we show that a particle detector is most sensitive to the bandlimit when it couples to a small but finite region of spacetime. We find that the effects of a bandlimit are detectable using local probes. This work is important because it illustrates the possible observable consequences of a fundamental bandlimit in a quantum field.

Entropy production in model colloidal suspensions under shear via the fluctuation theorem.

Dissipative systems often exhibit novel and unexpected properties. This is, for instance, the case of simple liquids, which, when subjected to shear and after reaching a steady state, can exhibit a negative entropy production over finite length scales and timescales. This result, among others, is captured by nonequilibrium relations known as fluctuation theorems. Using nonequilibrium molecular dynamics simulations, we examine how, by fine-tuning the properties of the components of a complex fluid, we can steer the nonequilibrium response of the fluid. More specifically, we show how we control the nonequilibrium probability distribution for the shear stress and, in turn, how often states with a negative entropy production can occur. To achieve this, we start by characterizing how the size for the liquid matrix impacts the probability of observing negative entropy states, as well as the timescale over which these can be observed. We then measure how the addition of larger particles to this liquid matrix, i.e., simulating a model colloidal suspension, results in an increase in the occurrence of such states. This suggests how modifications in the composition of the mixture and in the properties of its components lead to an increase in the probability of observing states of negative entropy production and, thus, for the system to run in reverse.

Large-scale simulations of particle-hole-symmetric Pfaffian trial wave functions

We introduce a family of paired-composite-fermion trial wave functions for any odd Cooper-pair angular momentum. These wave functions are parameter-free and can be efficiently projected into the lowest Landau level. We use large-scale Monte Carlo simulations to study three cases: Firstly, the Moore-Read phase, which serves us as a benchmark. Secondly, we explore the pairing associated with the anti-Pfaffian and the particle-hole-symmetric Pfaffian. Specifically, we assess whether their trial states feature exponentially decaying correlations and thus represent gapped phases of matter. For Moore-Read and anti-Pfaffian we find decay lengths of $\xi_\text{Moore-Read}=1.30(5)$ and $\xi_\text{anti-Pfaffian}=1.38(14)$, in units of the magnetic length. By contrast, for the case of PH-Pfaffian, we find no evidence of a finite length scale for up to $56$ particles.

Microscopic and long-wave instabilities in 3D fiber composites with non-Gaussian hyperelastic phases

We investigate the microscopic and long-wave (or macroscopic) instabilities in fiber composites (FCs) with hyperelastic phases. To study the influence of the phase stiffening behavior, we employ the phase constitutive models that are developed based on the non-Gaussian statistics of polymeric molecular chains. These non-Gaussian models accurately predict the non-linear behavior of soft materials. Moreover, they can capture the essential soft material stiffening behavior arising due to the finite extensibility of the polymer chains. In turn, the non-linear behavior of the composite phases significantly influences the elastic instabilities and the buckling patterns. Here, we illustrate the phenomenon by the example of FCs with Gent phases. We derive an explicit closed-form expression – in terms of the phase properties and composition – for the onset of long-wave instabilities. To predict the onset of finite length scale (or microscopic) instabilities, we employ the Bloch-Floquet analysis superimposed on finite deformations. We find that the matrix stiffening behavior stabilizes the composites, and can even result in an absolutely stable scenario. Remarkably, Gent FCs with identical phase stiffening characteristics are found to be more stable than their neo-Hookean counterparts for morphologies at which the microscopic instabilities are to develop first. The stiffening behavior of the phases dictates the interplay between the long-wave and microscopic instabilities, and defines the wavelength of the buckling patterns. Thus, the pre-designed phase properties can be used in tailoring the instability-induced patterns in soft fiber composites.

Growth of mutual information in a quenched one-dimensional open quantum many-body system

We study the temporal evolution of the mutual information (MI) in a one-dimensional Kitaev chain, coupled to a fermionic Markovian bath, subsequent to a global quench of the chemical potential. In the unitary case, the MI (or equivalently the bipartite entanglement entropy) saturates to a steady-state value (obeying a volume law) following a ballistic growth. On the contrary, we establish that in the dissipative case the MI is exponentially damped both during the initial ballistic growth as well as in the approach to the steady state. We observe that even in a dissipative system, postquench information propagates solely through entangled pairs of quasiparticles having a finite lifetime; this quasiparticle picture is further corroborated by the out-of-equilibrium analysis of two-point fermionic correlations. Remarkably, in spite of the finite lifetime of the quasiparticles, a finite steady-state value of the MI survives in asymptotic times which is an artifact of nonvanishing two-point correlations. Further, the finite lifetime of quasiparticles renders to a finite length scale in these steady-state correlations.

A model for the investigation of the second-order structure of caustic formations in dispersed flows

The formation of caustics by inertial particles is distinctive of dispersed flows. Their pressureless nature allows crossing trajectories resulting in singularities that cannot be captured accurately by standard Lagrangian approaches due to their fine spatial scale. A promising method for the investigation of caustics is the Osiptsov method or fully Lagrangian approach (FLA). The FLA has the advantage of identifying caustics, but its applicability is hindered by the occurrence of singularities. We present an original robust framework based on the FLA that provides an explicit expression of the dispersed phase structure that does not degenerate in the vicinity of caustics, using a single representative particle. The FLA is extended to account for the Hessian of the dispersed continuum (DC). It demonstrates the integrability of the FLA number density and allows for the calculation of the number density on a given length scale, retaining the functionality of the FLA. Number density models based on the second-order representation of the DC and on the one-dimensional structure of the particle distribution, that account for the anisotropy of the DC on caustics, are derived and applied for analytical flows. The number density is linked to a finite length scale, needed for the introduction of the FLA to spatially filtered flow fields. Finally, the method is used for the calculation of the interparticle separation on caustics. The identification of the structure of caustics presented in this work paves the way to a robust understanding of the mechanisms of particle accumulation.