Finite Correlation Research Articles

Inverse identification of in-situ curing shrinkage using a method combining 3D digital image correlation and finite-element simulation

Curing shrinkage of adhesives in the bonding process usually leads to deformation and residual stresses. The measurement of curing shrinkage is valuable in providing fundamental information for better understanding, controlling, and optimizing the curing process. This paper developed an efficient hybrid inverse identification method for in-situ measurement of the volume shrinkage. This method associates the artificial fish swarm algorithm (AFSA) with a finite element method (FEM) and 3D digital image correlation (3D-DIC) technology. A homemade apparatus for experimental characterization of curing shrinkage is prepared and tested. The evolution of the volume shrinkage is inversely identified by matching the 3D-DIC and the FEM results using the AFSA algorithm. The results are further validated by a direct-density measurement and the standard physical property of the adhesive. Those experimental results demonstrated that the proposed method is a viable non-contact, non-destructive, and in-situ technique that can be applied to measure the in-situ curing shrinkage.

Control of stochastic and inverse stochastic resonances in a liquid-crystal electroconvection system using amplitude and phase noises

Stochastic and inverse stochastic resonances are counterintuitive phenomena, where noise plays a pivotal role in the dynamics of various biological and engineering systems. Even though these resonances have been identified in various systems, a transition between them has never been observed before. The present study demonstrates the presence of both resonances in a liquid crystal electroconvection system using combined amplitude and phase noises, which correspond to colored noises with appropriate cutoff frequencies (i.e., finite correlation times). We established the emergence of both resonances and their transition through systematic control of the electroconvection threshold voltage using these two noise sources. Our numerical simulations were experimentally confirmed and revealed how the output performance of the system could be controlled by combining the intensity and cutoff frequency of the two noises. Furthermore, we suggested the crucial contribution of a usually overlooked additional phase noise to the advancements in various noise-related fields.

Chiral chains with two valleys and disorder of finite correlation length

Chiral chains with two valleys and disorder of finite correlation length

Sample canonical correlation coefficients of high-dimensional random vectors with finite rank correlations

Consider two random vectors x˜=Az+C11∕2x∈Rp and y˜=Bz+C21∕2y∈Rq, where x∈Rp, y∈Rq and z∈Rr are independent random vectors with i.i.d. entries of zero mean and unit variance, C1 and C2 are p×p and q×q deterministic population covariance matrices, and A and B are p×r and q×r deterministic factor loading matrices. With n independent observations of x˜ and y˜, we study the sample canonical correlations between them. Under the sharp fourth moment condition on the entries of x, y and z, we prove the BBP transition for the sample canonical correlation coefficients (CCCs). More precisely, if a population CCC is below a threshold, then the corresponding sample CCC converges to the right edge of the bulk eigenvalue spectrum of the sample canonical correlation matrix and satisfies the famous Tracy-Widom law; if a population CCC is above the threshold, then the corresponding sample CCC converges to an outlier that is detached from the bulk eigenvalue spectrum. We prove our results in full generality, in the sense that they also hold for near-degenerate population CCCs and population CCCs that are close to the threshold.

Small-scale dynamo with finite correlation times.

Fluctuation dynamos occur in most turbulent plasmas in astrophysics and are the prime candidates for amplifying and maintaining cosmic magnetic fields. A few analytical models exist to describe their behavior, but they are based on simplifying assumptions. For instance, the well-known Kazantsev model assumes an incompressible flow that is δ-correlated in time. However, these assumptions can break down in the interstellar medium as it is highly compressible and the velocity field has a finite correlation time. Using the renewing flow method developed by Bhat and Subramanian (2014), we aim to extend Kazantsev's results to a more general class of turbulent flows. The cumulative effect of both compressibility and finite correlation time over the Kazantsev spectrum is studied analytically. We derive an equationfor the longitudinal two-point magnetic correlation function in real space to first order in the correlation time τ and for an arbitrary degree of compressibility (DOC). This generalized Kazantsev equationencapsulates the original Kazantsev equation. In the limit of small Strouhal numbers St∝τ we use the Wentzel-Kramers-Brillouin approximation to derive the growth rate and scaling of the magnetic power spectrum. We find the result that the Kazantsev spectrum is preserved, i.e., M_{k}(k)∼k^{3/2}. The growth rate is also negligibly affected by the finite correlation time; however, it is reduced by the finite magnetic diffusivity and the DOC together.

Theory of melting of glasses

ABSTRACT Glassy matter like crystals resists change in shape. Therefore a theory for their continuous melting should show how the shear elastic constant μ goes to zero. Since viscosity is the long wave-length low frequency limit of shear correlations, the same theory should give phenomena like the Volger-Fulcher dependence of the viscosity on temperature near the transition. A continuum model interrupted randomly by asymmetric rigid defects with orientational degrees of freedom is considered. Such defects are orthogonal to the continuum excitations, and are required to be imprisoned by rotational motion of the nearby atoms of the continuum. The defects interact with an angle dependent potential. A renormalisation group for the elastic constants, and the fugacity of the defects in 3D is constructed. The principal results are that there is a scale-invariant reduction of μ as a function of length at any temperature , above which it is 0 macrosopically but has a finite correlation length which diverges as . Viscosity is shown to be proportional to and has the Vogel-Fulcher form. The specific heat is . As , the Kauzman temperature from above, the configuration entropy of the liquid is exhausted. The theory also gives the ‘fragility’ of glasses in terms of their .

Spontaneous dimerization, spin-nematic order, and deconfined quantum critical point in a spin-1 Kitaev chain with tunable single-ion anisotropy

Kitaev-type spin chains have been demonstrated to be fertile playgrounds in which exotic phases and unconventional phase transitions are ready to appear. In this work, we use the density-matrix renormalization-group method to study the quantum phase diagram of a spin-1 Kitaev chain with a tunable negative single-ion anisotropy (SIA). When the strength of the SIA is small, the ground state is revealed to be a spin-nematic phase, which escapes conventional magnetic order but is characterized by a finite spin-nematic correlation because of the breaking spin-rotational symmetry. As the SIA increases, the spin-nematic phase is taken over by either a dimerized phase or an antiferromagnetic phase through an Ising-type phase transition, depending on the direction of the easy axis. For large enough SIA, the dimerized phase and the antiferromagnetic phase undergo a ``Landau-forbidden'' continuous phase transition, suggesting new platform of deconfined quantum critical point in spin-1 Kitaev chain.

Monitoring structural scale composite specimens in a post‐buckling regime: The integrated finite element stereo digital image correlation approach with geometrically non‐linear regularization

AbstractEven though the simulations used to describe the failure of laminates are becoming more and more predictive, complex testing under multiaxial loadings is still required to validate the design of structural parts in a wide range of industrial domains. It is thus essential to assess the actual boundary conditions to allow for an objective comparison between testing and calculations, in particular since the structural tests are complex and often leads to buckling. Therefore, accurate estimation of force and moment fluxes applied to the specimen is critical. In this context, stereo digital image correlation (SDIC) has proven to be an important measurement tool and provides very well‐resolved surface displacement fields, but the exploitation of such measurements to calculate fluxes remains problematic when testing composites. The first objective of this study is both to reduce the uncertainty associated with fluxes determination on a complex test and to simplify the extraction process with respect to existing procedures. The second objective is to make this methodology robust to geometrically non‐linear deformations. In this paper, we propose a new methodology that extracts minimal boundary conditions in the form of 3D mechanically admissible displacements fields. The approach developed uses a finite element SDIC (FE‐SDIC) method regularized by means of mechanical behaviour admissibility equations. Results show that the new methodology outputs much more accurate fluxes than classical data generated from multiple differentiations of the displacement fields. Excellent noise robustness is obtained and quantified. Numerical predictions have been satisfactorily compared with experimental data from one structural‐scale composite specimen under complex testing.

Convergence of the integral fluctuation theorem estimator for nonequilibrium Markov systems

The integral fluctuation theorem (IFT) for entropy production is among the few equalities that are known to be valid for physical systems arbitrarily driven far from equilibrium. Microscopically, it can be understood as an inherent symmetry for the fluctuating entropy production rate implying the second law of thermodynamics. Here, we examine an IFT statistical estimator based on regular sampling and discuss its limitations for nonequilibrium systems, when sampling rare events becomes pivotal. Furthermore, via a large deviation study, we discuss a method to carefully setup an experiment in the parameter region where the IFT estimator safely converges and also show how to improve the convergence region for Markov chains with finite correlation time. We corroborate our arguments with two illustrative examples.

DMRG analysis of magnetic order in the zigzag edges of hexagonal CrN nanoribbons

We investigate the finite-temperature magnetic order at the edges of hexagonal CrN nanoribbons by using density functional theory combined with the density matrix renormalization group (DMRG) method. Moreover, the spin-dependent transport in nanoribbons is calculated within the semiclassical Boltzmann transport theory. We find that the zigzag edges have lower energy with respect to armchair edges. The zigzag edges of CrN nanoribbon show half-metallic electronic character, which is the same as for the two-dimensional (2D) monolayer. The localized electronic states on the zigzag edges reduce the electronic band gap energy for spin-down electrons. The ab initio electronic results are mapped into an effective 1D Heisenberg spin model up to the next-nearest-neighbor exchange interaction term. For zigzag ribbons, the nearest-neighbor and next-nearest-neighbor magnetic exchange are around 10--12 and $\ensuremath{-}2$ to 0 $\text{meV}/\text{Cr}\phantom{\rule{4.pt}{0ex}}\text{atom}$, respectively. The finite spin correlation length in 1D nanoribbons drops sharply to zero with temperature. The absence of long-range spin correlations at the edges is a practical drawback for future room temperature 2D spintronic devices. The maximally localized Wannier functions are used for band interpolation and spin-dependent transport calculations by using the semiclassical Boltzmann equation. We show that the zigzag edges of CrN are a perfect spin filter under both electron and hole doping.

Collective migration of cells in geometric spaces: Intrinsic correlation length racing against extrinsic confinement size

Many experiments showed that cell groups can exhibit various impressive motion modes (e.g., global rotation and local swirling) in different-sized geometrical spaces, with the underlying mechanisms still unclear. However, recent experiments showed that different types of cells perform distinct motion modes (i.e., global rotation and coherent oscillation) in the same constraint conditions, which brings further puzzles on the movements of collective cells. Here, by comprehensively considering the social interactions between adjacent cells and internal mechanical processes of the cell itself, we propose an active vertex model to bring physical insights into collective cell migration in geometrical constraints. Using this model, we can reproduce all reported motion modes of cells in circular constraints observed in existing experiments. Specifically, as the confinement size decreases, local swirling and global rotation modes successively appear in cell groups with finite correlation length, while eccentric rotation and coherent oscillation modes successively emerge in cell groups with scale-free correlations. We demonstrate that these distinct modes are subtly coded by the intrinsic correlation length of cell groups and the extrinsic confinement size. Unexpectedly, we discover that, in small-size confinements, cell groups with scale-free correlations can spontaneously transition from eccentric rotation into coherent oscillation modes, because the strong social interactions reconcile the movements of all cells. In addition, we propose a velocity indicator that can directly distinguish migration modes emerging in small-scale confinements. These findings are in broad agreement with many experiments, and shed light on the spatiotemporal dynamics of active matter.

Robust charge-density-wave correlations in the electron-doped single-band Hubbard model

There is growing evidence that the hole-doped single-band Hubbard and t − J models do not have a superconducting ground state reflective of the high-temperature cuprate superconductors but instead have striped spin- and charge-ordered ground states. Nevertheless, it is proposed that these models may still provide an effective low-energy model for electron-doped materials. Here we study the finite temperature spin and charge correlations in the electron-doped Hubbard model using quantum Monte Carlo dynamical cluster approximation calculations and contrast their behavior with those found on the hole-doped side of the phase diagram. We find evidence for a charge modulation with both checkerboard and unidirectional components decoupled from any spin-density modulations. These correlations are inconsistent with a weak-coupling description based on Fermi surface nesting, and their doping dependence agrees qualitatively with resonant inelastic x-ray scattering measurements. Our results provide evidence that the single-band Hubbard model describes the electron-doped cuprates.

On Clustering of Floating Tracers in Random Velocity Fields

AbstractIn this paper, we investigate the aggregation of a floating tracer into clusters. Motivated by observations of dense patches of buoyant material in the real ocean (e.g., microplastic pollutants, plankton, and sargassum), we develop an idealized model that can reproduce the clustering process. A stochastic, kinematic 2D velocity field is chosen to represent turbulent oceanic surface currents, with a weakly divergent component. Lagrangian particles are introduced and we track their concentrations. We differ from delta‐correlated fields used in previous studies by including finite time correlations. Clustering in these fields can be compared to the traditional setting, through global measures and cluster detection algorithms. The enhanced velocity fields can be deformed using various interpolation methods. We can then investigate the sensitivity of clustering to the representation of temporal/spatial velocity structure to inform future studies of this phenomenon. We find coherency of time‐correlated velocities leads to significantly faster rates of clustering, causing a larger number of longer lived/more populated clusters to form. Clustering is likely relevant to a host of biogeochemical processes of urgent interest, such as phytoplankton blooms and the ecological risk of microplastic pollutants. This work aims to establish an accurate basis for clustering simulations, to enable further exploration.

Entanglement entropy in internal spaces and Ryu-Takayanagi surfaces

We study minimum area surfaces associated with a region, R, of an internal space. For example, for a warped product involving an asymptotically AdS space and an internal space K, the region R lies in K and the surface ends on ∂R. We find that the result of Graham and Karch can be avoided in the presence of warping, and such surfaces can sometimes exist for a general region R. When such a warped product geometry arises in the IR from a higher dimensional asymptotic AdS, we argue that the area of the surface can be related to the entropy arising from entanglement of internal degrees of freedom of the boundary theory. We study several examples, including warped or direct products involving AdS2, or higher dimensional AdS spaces, with the internal space, K = Rm, Sm; Dp brane geometries and their near horizon limits; and several geometries with a UV cut-off. We find that such RT surfaces often exist and can be useful probes of the system, revealing information about finite length correlations, thermodynamics and entanglement. We also make some preliminary observations about the role such surfaces can play in bulk reconstruction, and their relation to subalgebras of observables in the boundary theory.

Noise-induced transitions in gene circuits: A perturbative approach for slow noise.

We consider a generic class of gene circuits affected by nonlinear extrinsic noise. To address this nonlinearity we introduce a general perturbative methodology based on assuming timescale separation between noise and gene dynamics, with fluctuations exhibiting a large but finite correlation time. We apply this methodology to the case of the toggle switch, and by considering biologically relevant log-normal fluctuations, we find that the system exhibits noise-induced transitions. The system becomes bimodal in regions of the parameter space where it would be deterministically monostable. We show that by including higher order corrections our methodology allows one to obtain correct predictions for the occurrence of transitions even for not so large correlation time of the fluctuations, thereby overcoming limitations of previous theoretical approaches. Interestingly we find that at intermediate noise intensities the noise-induced transition in the toggle switch affects one of the genes involved, but not the other one.

Influence of turbulence on Ly α scattering

ABSTRACT We develop a Monte Carlo radiative transfer code to study the effect of turbulence with a finite correlation length on scattering of Ly α photons propagating through neutral atomic hydrogen gas. We investigate how the effective mean free path, the emergent spectrum, and the average number of scatterings that Ly α photons experience change in the presence of turbulence. We find that the correlation length is an important and sensitive parameter that has an influence on physically relevant properties of Ly α radiative transfer. In particular, it can significantly, by orders of magnitude, reduce the number of scattering events that the average Ly α photon undergoes before it escapes the turbulent cloud.

Gray level residual field: an effective metric for pixelwise matching quality evaluation in local digital image correlation

Gray level residual (GLR), also known as correlation residual field or image difference, reflects the intensity differences between reference and deformed images. In finite element-based global digital image correlation (DIC), GLR field can be readily computed and has been successfully used for crack or damage detection. The computation of pixelwise GLR field requires dense displacement results, which can be obtained using mesh interpolation in global DIC. To obtain the GLR field in subset-based local DIC, in which results are obtained at discrete calculation points, a simple, efficient and practical computation method for GLR field is presented, which accounts for the influence of illumination variations unavoidably occurred in real DIC tests. The proposed method can be easily implemented on both central process unit and graphics process unit to realize real-time visualization. Experiments showed that the GLR field can quantitatively and intuitively evaluate the pixelwise matching quality and provide clearer and finer locations for new components or textures (e.g. cracks) presented in deformed images. By fully leveraging the pixelwise matching quality information provided by the GLR field, the capability and robustness of local DIC is expected to be further enhanced.

Wire-width and electron-density dependence of the crossover in the peak of the static structure factor from 2kF → 4kF in one-dimensional paramagnetic electron gases

We use the variational quantum Monte Carlo (VMC) method to study the wire-width $(b)$ and electron-density $({r}_{\text{s}})$ dependences of the ground-state properties of quasi-one-dimensional paramagnetic electron fluids. The onset of a quasi-Wigner crystal phase is known to depend on electron density and the crossover occurs in the low density regime. We study the effect of wire width on the crossover of the dominant peak in the static structure factor from $k=2{k}_{\text{F}}$ to $k=4{k}_{\text{F}}$. It is found that, for a fixed electron density, in the charge structure factor the crossover from the dominant peak occurring at $2{k}_{\text{F}}$ to $4{k}_{\text{F}}$ occurs as the wire width decreases. Our study suggests that the crossover is due to the interplay of both ${r}_{\text{s}}$ and $b<{r}_{\text{s}}$. The finite wire-width correlation effect is reflected in the peak height of the charge and spin structure factors. We fit the dominant peaks of the charge and spin structure factors assuming fit functions based on our finite wire-width theory and clues from bosonization, resulting in a good fit of the VMC data. The pronounced peaks in the charge and spin structure factors at $4{k}_{\text{F}}$ and $2{k}_{\text{F}}$, respectively, indicate the complete decoupling of the charge and spin degrees of freedom. Furthermore, the wire-width dependence of the electron correlation energy and the Tomonaga-Luttinger parameter ${K}_{\ensuremath{\rho}}$ is found to be significant.

Synergistic strengthening in interlocking metasurfaces

Interlocking metasurfaces (ILMs) are a new class of structural metamaterials consisting of autogenous latching features. ILMs offer non-permanent joints that are an alternative to fasteners, welds, or adhesives. The mechanical properties of ILMs, including strength and stiffness, are governed by both the shape of the individual latching unit cells and the interaction between unit cells. These cross-cell interactions provide a synergistic effect that distinguish ILMs from ordinary isolated latching features: specifically, as the number of interacting unit cells increase, the strength of the ILM also increases. Remarkably, in the present study, ILMs demonstrated interfacial tensile strengths that were as much as four times stronger, and stiffer, than the equivalent isolated latching components. Computational analysis and experimental measurements confirmed the cross-cell interactions associated with ILMs. Both finite element analysis and digital image correlation strain field mapping reveal that unit cells near the edge of the ILM have different load-limiting deformation and failure mechanisms than those away from the edge: unconstrained edge unit cells bend out of the way, thus allowing the interlocking features to move past one another whereas interior unit cells do not. Due to their synergistic strengthening, ILMs show promise as a novel joining technology.

Narrow Pore Crossing of Active Particles under Stochastic Resetting

We propose a two-dimensional model of biochemical activation process, whereby self-propelling particles of finite correlation times are injected at the center of a circular cavity with constant rate equal to the inverse of their lifetime; activation is triggered when one such particle hits a receptor on the cavity boundary, modeled as a narrow pore. We numerically investigated this process by computing the particle mean-first exit times through the cavity pore as a function of the correlation and injection time constants. Due to the breach of the circular symmetry associated with the positioning of the receptor, the exit times may depend on the orientation of the self-propelling velocity at injection. Stochastic resetting appears to favor activation for large particle correlation times, where most of the underlying diffusion process occurs at the cavity boundary.