Physically motivated models of polymer networks with dynamic cross-links: comparative study and future outlook

Polymer networks consisting of a mixture of chemical and physical cross-links are known to exhibit complex time-dependent behaviour due to the kinetics of bond association and dissociation. In this article, we highlight and compare two recent physically based constitutive models that describe the nonlinear viscoelastic behaviour of such transient networks. These two models are developed independently by two groups of researchers using different mathematical formulations. Here, we show that this difference can be attributed to different viewpoints: Lagrangian versus Eulerian. We establish the equivalence of the two models under the special situation where chains obey Gaussian statistics and steady-state bond dynamics. We provide experimental data demonstrating that both models can accurately predict the time-dependent uniaxial behaviour of a poly(vinylalcohol) dual cross-link hydrogel. We review the advantages and disadvantages of both approaches in applications and close by discussing a list of open challenges and questions regarding the mathematical modelling of soft, viscoelastic networks.

New Analytical Model for Swellable Materials

As discussed in Chapter 6, numerical prediction of swelling can be attempted using existing hyperelastic material models available in commercial finite element (FE) packages. However, none of these models can accurately represent the behavior of swelling elastomers. The major shortcoming of currently available swelling models is that they consider Gaussian statistics for mechanical contribution of configuration entropy, which is based on chains having limited extensibility. Some later models (not yet incorporated into commercial FE packages) can give a reasonable account of certain behavior patterns in swelling elastomers, but do not explain other aspects well. One of the new approaches is to treat swelling elastomers as gels. As described earlier, gels are mostly liquid, yet they behave like solids due to a three-dimensional cross-linked network within the liquid. Many authors consider gel as poro-elastic or porous and use Darcy’s law to model the amount of fluid influx. However, a swollen elastomer mostly consists of the solvent. When an external load is applied, maximum resistance comes from the solvent molecules as in diffusion. Also, most of the new models are quite complex in concept and formulation, and there is a serious need for a scientifically simpler model.

Tsallis statistics and generalized uncertainty principle

It has been argued that non-Gaussian statistics provide a natural framework to investigate semiclassical effects in the context of Planck-scale deformations of the Heisenberg uncertainty relation. Here we substantiate this point by considering the Unruh effect as a specific playground. By working in the realm of quantum field theory, we reformulate the derivation of the modified Unruh effect from the generalized uncertainty principle (GUP) in the language of the nonextensive Tsallis thermostatistics. We find a nontrivial monotonic relation between the nonextensivity index q and the GUP deformation parameter $$\beta $$ β , which generalizes an earlier result obtained in quantum mechanics. We then extend our analysis to black hole thermodynamics. We preliminarily discuss our outcome in the broader context of an effective description of Planck-scale gravitational physics based on Tsallis theory.

On the choice of the collapse operator in cosmological Continuous Spontaneous Localisation (CSL) theories

The Continuous Spontaneous Localisation (CSL) theory in the cosmological context is subject to uncertainties related to the choice of the collapse operator. In this paper, we constrain its form based on generic arguments. We show that, if the collapse operator is even in the field variables, it is unable to induce the collapse of the wavefunction. Instead, if it is odd, we find that only linear operators are such that the outcomes are distributed according to Gaussian statistics, as required by measurements of the cosmic microwave background. We discuss implications of these results for previously proposed collapse operators. We conclude that the cosmological CSL collapse operator should be linear in the field variables.

Extreme vertical drafts in the polar summer mesosphere: A super mesospheric bore?

<p>The polar summer mesosphere is the Earth’s coldest region, allowing the formation of mesospheric ice clouds, potentially linked to climate change. These clouds produce strong radar echoes that are used as tracers of mesospheric dynamics. Here we report the first observations of extreme vertical drafts in the mesosphere, characterized by velocities larger than 40 m/s, i.e., more than five standard deviations larger than the observed wind variability. The morphology seems to resemble mesospheric bores, however the scales observed are much larger. Powerful vertical drafts, intermittent in space and time, emerge also in direct numerical simulations of stratified flows, predicting non-Gaussian statistics of vertical velocities. This evidence suggests that mesospheric bores might result from the interplay of gravity waves and turbulent motions. Our extreme event is interpreted as a mesospheric "super-bore", impacting mesospheric mixing and ice-formation, and would potentially impact planning of sub-orbital flights, and the investigation of biological material in the near space.</p>

Sparse balance: excitatory-inhibitory networks with small bias currents and broadly distributed synaptic weights

Cortical circuits generate excitatory currents that must be cancelled by strong inhibition to assure stability. The resulting excitatory-inhibitory (E-I) balance can generate spontaneous irregular activity but, in standard balanced E-I models, this requires that an extremely strong feedforward bias current be included along with the recurrent excitation and inhibition. The absence of experimental evidence for such large bias currents inspired us to examine an alternative regime that exhibits asynchronous activity without requiring unrealistically large feedforward input. In these networks, irregular spontaneous activity is supported by a continually changing sparse set of neurons. To support this activity, synaptic strengths must be drawn from high-variance distributions. Unlike standard balanced networks, these sparse balance networks exhibit robust nonlinear responses to uniform inputs and non-Gaussian statistics. In addition to simulations, we present a mean-field analysis to illustrate the properties of these networks.

Independently Controlling Stochastic Field Realization Magnitude and Phase Statistics for the Construction of Novel Partially Coherent Sources

In this paper, we present a method to independently control the field and irradiance statistics of a partially coherent beam. Prior techniques focus on generating optical field realizations whose ensemble-averaged autocorrelation matches a specified second-order field moment known as the cross-spectral density (CSD) function. Since optical field realizations are assumed to obey Gaussian statistics, these methods do not consider the irradiance moments, as they, by the Gaussian moment theorem, are completely determined by the field’s first and second moments. Our work, by including control over the irradiance statistics (in addition to the CSD function), expands existing synthesis approaches and allows for the design, modeling, and simulation of new partially coherent beams, whose underlying field realizations are not Gaussian distributed. We start with our model for a random optical field realization and then derive expressions relating the ensemble moments of our fields to those of the desired partially coherent beam. We describe in detail how to generate random optical field realizations with the proper statistics. We lastly generate two example partially coherent beams using our method and compare the simulated field and irradiance moments theory to validate our technique.

Common Information Components Analysis

Wyner’s common information is a measure that quantifies and assesses the commonality between two random variables. Based on this, we introduce a novel two-step procedure to construct features from data, referred to as Common Information Components Analysis (CICA). The first step can be interpreted as an extraction of Wyner’s common information. The second step is a form of back-projection of the common information onto the original variables, leading to the extracted features. A free parameter γ controls the complexity of the extracted features. We establish that, in the case of Gaussian statistics, CICA precisely reduces to Canonical Correlation Analysis (CCA), where the parameter γ determines the number of CCA components that are extracted. In this sense, we establish a novel rigorous connection between information measures and CCA, and CICA is a strict generalization of the latter. It is shown that CICA has several desirable features, including a natural extension to beyond just two data sets.