Scale Separation Research Articles

On the generation of free-stream turbulence at low Reynolds number: A numerical study

We investigate the generation of free-stream perturbations at a relatively low characteristic Reynolds number of 1000 by means of direct numerical simulations using a synthetic turbulence generation method. This approach consists of generating turbulent fluctuations by means of digital filtering and a source term formulation in the Navier–Stokes equations. To assess its validity in the framework of decaying turbulence, we compare the results with those obtained with a physically-based, grid-induced turbulent flow in terms of spatial decay, evolution of characteristic length-scales and energy spectra. Also, we highlight relevant differences such as those in the streamwise development length and the anisotropy of the largest scales. Then, we characterize the generated perturbations when systematically varying the input parameters, namely the initial integral length-scale and turbulence intensity. Here, we notice differences in the streamwise decay of the turbulence intensity and the development length as we vary these parameters. By inspecting the evolution of the characteristic length-scales and the micro-scale Reynolds number, we also identify that the effective scale separation is highly sensitive to these variations.

Process development studies on the recovery of caesium specific calix-crown-6 extractant from actual spent calix solution for efficient spent solvent management

Abstract This paper reports the studies carried out on the development of a process for the recovery of 1,3-dioctyloxycalix[4]arene-18-crown-6 (CC-6) from the spent solvent generated during industrial scale separation of 137Cs from High Level Liquid Waste (HLLW). Initial works involved the validation of a conceptual process design and optimization of the process parameters with a simulated solvent. The optimized process was then tested with actual spent solvent to recover calix-crown-6. Such a process to recover undegraded and potentially re-usable calix-crown-6 from the spent solvent has been attempted for the first time with the aim of value recovery and reduced spent solvent management burden.

Homogenization and continuum limit of mechanical metamaterials

When used in bulk applications, mechanical metamaterials set forth a multiscale problem with many orders of magnitude in scale separation between the micro and macro scales. However, mechanical metamaterials fall outside conventional homogenization theory on account of the flexural, or bending, response of their members, including torsion. We show that homogenization theory, based on calculus of variations and notions of Gamma-convergence, can be extended to account for bending. The resulting homogenized metamaterials exhibit intrinsic generalized elasticity in the continuum limit. We illustrate these properties in specific examples including two-dimensional honeycomb and three-dimensional octet-truss metamaterials.

Coexistence of Defect Morphologies in Three-Dimensional Active Nematics.

We establish how active stress globally affects the morphology of disclination lines of a three-dimensional active nematic liquid crystal under chaotic flow. Thanks to a defect detection algorithm based on the local nematic orientation, we show that activity selects a crossover length scale in between the size of small defect loops and that of long and tangled defect lines of fractal dimension 2. This length scale crossover is consistent with the scaling of the average separation between defects as a function of activity. Moreover, on the basis of numerical simulation in a 3D periodic geometry, we show the presence of a network of regular defect loops, contractible onto the 3-torus, always coexisting with wrapping defect lines. While the length of regular defects scales linearly with the emerging active length scale, it verifies an inverse quadratic dependence for wrapping defects. The shorter the active length scale, the more the defect lines wrap around the periodic boundaries, resulting in extremely long and buckled structures.

A coupling concept for Stokes-Darcy systems: The ICDD method

We present a coupling framework for Stokes-Darcy systems valid for arbitrary flow direction at low Reynolds numbers and for isotropic porous media. The proposed method is based on an overlapping domain decomposition concept to represent the transition region between the free-fluid and the porous-medium regimes. Matching conditions at the interfaces of the decomposition impose the continuity of velocity (on one interface) and pressure (on the other one) and the resulting algorithm can be easily implemented in a non-intrusive way. The numerical approximations of the fluid velocity and pressure obtained by the studied method converge to the corresponding counterparts computed by direct numerical simulation at the microscale, with convergence rates equal to suitable powers of the scale separation parameter ε in agreement with classical results in homogenization.

Energy loss of a heavy fermion in a collisional QED plasma

We compute the energy loss of heavy fermions moving in a plasma, taking into account the modification of the photon collective modes induced by collisions using a Bhatnagar-Gross–Krook collisional kernel. We include contributions from both hard and soft scatterings of the heavy fermion using a collisionally modified hard-thermal-loop resummed propagator. Using this method, one does not need to introduce a separation scale between hard- and soft-momentum exchanges. To place our calculation in context, we review other theoretical approaches to computing the collisional energy loss of fermions and discuss the systematics and results obtained in each approach compared to using a resummed propagator for both hard and soft momentum exchanges. Our final results indicate that self-consistently including the effect of collisions in the self-energies of the resummed propagator results in an increased energy loss compared to using collisionless hard-thermal-loop propagators. The effect becomes larger as the magnitude of the coupling constant and the velocity of the fermion increase. Published by the American Physical Society 2024

Phase diagrams of bone remodeling using a 3D stochastic cellular automaton.

We propose a 3D stochastic cellular automaton model, governed by evolutionary game theory, to simulate bone remodeling dynamics. The model includes four voxel states: Formation, Quiescence, Resorption, and Environment. We simulate the Resorption and Formation processes on separate time scales to explore the parameter space and derive a phase diagram that illustrates the sensitivity of these processes to parameter changes. Combining these results, we simulate a full bone remodeling cycle. Furthermore, we show the importance of modeling small neighborhoods for studying local bone microenvironment controls. This model can guide experimental design and, in combination with other models, it could assist to further explore external impacts on bone remodeling. Consequently, this model contributes to an improved understanding of complex dynamics in bone remodeling dynamics and exploring alterations due to disease or drug treatment.

Synergistic Construction of Sub-Nanometer Channel Membranes through MOF–Polymer Composites: Strategies and Nanofiltration Applications

The selective separation of small molecules at the sub-nanometer scale has broad application prospects in the field, such as energy, catalysis, and separation. Conventional polymeric membrane materials (e.g., nanofiltration membranes) for sub-nanometer scale separations face challenges, such as inhomogeneous channel sizes and unstable pore structures. Combining polymers with metal–organic frameworks (MOFs), which possess uniform and intrinsic pore structures, may overcome this limitation. This combination has resulted in three distinct types of membranes: MOF polycrystalline membranes, mixed-matrix membranes (MMMs), and thin-film nanocomposite (TFN) membranes. However, their effectiveness is hindered by the limited regulation of the surface properties and growth of MOFs and their poor interfacial compatibility. The main issues in preparing MOF polycrystalline membranes are the uncontrollable growth of MOFs and the poor adhesion between MOFs and the substrate. Here, polymers could serve as a simple and precise tool for regulating the growth and surface functionalities of MOFs while enhancing their adhesion to the substrate. For MOF mixed-matrix membranes, the primary challenge is the poor interfacial compatibility between polymers and MOFs. Strategies for the mutual modification of MOFs and polymers to enhance their interfacial compatibility are introduced. For TFN membranes, the challenges include the difficulty in controlling the growth of the polymer selective layer and the performance limitations caused by the “trade-off” effect. MOFs can modulate the formation process of the polymer selective layer and establish transport channels within the polymer matrix to overcome the “trade-off” effect limitations. This review focuses on the mechanisms of synergistic construction of polymer–MOF membranes and their structure–nanofiltration performance relationships, which have not been sufficiently addressed in the past.

Effective boundary conditions for second-order homogenization

Using matched asymptotic expansions, we derive an equivalent bar model for a periodic, one-dimensional lattice made up of linear elastic springs connecting both nearest and next-nearest neighbors. We obtain a strain-gradient model with effective boundary conditions accounting for the boundary layers forming at the endpoints. It is accurate to second order in the scale separation parameter ɛ≪1, as shown by a comparison with the solution to the discrete lattice problem. The homogenized modulus associated with the gradient effect (gradient stiffness) is found negative, as is often the case in second-order homogenization. Negative gradient stiffnesses are widely viewed as paradoxical as they can induce short-wavelength oscillations in the homogenized solution. In the one-dimensional lattice, the asymptotically correct boundary conditions are shown to suppress the oscillations, thereby restoring consistency. By contrast, most of the existing work on second-order homogenization makes use of postulated boundary conditions which, we argue, not only ruin the order of the approximation but are also the root cause of the undesirable oscillations.

A positive metric over DGKT vacua

We study the notion of a metric over the space of AdS solution in string theory, leading to an associated distance between them. Such a distance is the idea underlying the AdS distance conjecture. We utilise the previously developed prescription for extracting such a metric: taking an off-shell quadratic variation of the string theory effective action and then evaluating it over the space of on-shell solutions. It was shown that this prescription leads to a well-defined positive metric over M-theory Freund-Rubin vacua. In this work, we use the same prescription to calculate the metric over type IIA DGKT vacua. These are much more involved, they have multiple flux parameters and exhibit scale separation. While it remains an open question whether these vacua exist as fully localised solutions of string theory, they are well-defined within the four-dimensional effective theory, which is all that is required for the calculation. We find that they also have a positive metric over them. Interestingly, this metric turns out to be independent of the many flux parameters in the solution, similarly to what happens for metrics over scalar field spaces. This non-trivial flux cancellation, as well as results from explicit vacua, lead us to propose a Swampland condition: that the metric over the space of vacua in quantum gravity, as defined by the above prescription, is always positive.

General framework for quantifying dissipation pathways in open quantum systems. II. Numerical validation and the role of non-Markovianity.

In the previous paper [C. W. Kim and I. Franco, J. Chem. Phys. 160, 214111-1-214111-13 (2024)], we developed a theory called MQME-D, which allows us to decompose the overall energy dissipation process in open quantum system dynamics into contributions by individual components of the bath when the subsystem dynamics is governed by a Markovian quantum master equation (MQME). Here, we contrast the predictions of MQME-D against the numerically exact results obtained by combining hierarchical equations of motion (HEOM) with a recently reported protocol for monitoring the statistics of the bath. Overall, MQME-D accurately captures the contributions of specific bath components to the overall dissipation while greatly reducing the computational cost compared to exact computations using HEOM. The computations show that MQME-D exhibits errors originating from its inherent Markov approximation. We demonstrate that its accuracy can be significantly increased by incorporating non-Markovianity by exploiting time scale separations (TSS) in different components of the bath. Our work demonstrates that MQME-D combined with TSS can be reliably used to understand how energy is dissipated in realistic open quantum system dynamics.

LGBTQ+ Sociopolitical Engagement: Examining the Role of House Ball Community Involvement and LGBTQ+ Community Connection.

Recent events such as the Black Lives Matter movement, COVID-19, and political elections have highlighted the power of a socially and politically engaged society. One under-researched cultural pillar at the core of sociopolitical resistance for lesbian, gay, bisexual, transgender, and queer (LGBTQ+) people of color (POC) has been the House Ball Community, a dynamic subculture made up of intricate social networks. This study uses data collected for the Social Justice Sexuality Project (N = 246) to examine LGBTQ+ community connection and House Ball Community involvement as predictors of LGBTQ+ and intersectional LGBTQ+ sociopolitical engagement. Two continuous variables, community connection and sociopolitical engagement (consisting of separate scales about LGBTQ+ individuals and LGBTQ+ POC), were included in the analysis. Multivariate linear regression analyses were performed to examine the relationships between these variables. While community connection was significantly associated with both scales of sociopolitical engagement, House Ball involvement was only associated with intersectional LGBTQ+ sociopolitical engagement. Relative to community connection, House Ball involvement was more strongly associated with intersectional LGBTQ+ sociopolitical engagement. Findings suggest that House Ball involvement may influence behavior for LGBTQ+ POC. Authors discuss implications for intersectionality in social movements and culturally responsive direct, community, and systems-level social work practice within the current U.S. sociopolitical landscape.

Effects of the wall temperature on separation flowfield of swept shock wave/boundary layer interactions

Swept shock wave/boundary layer interaction (SWBLI) is a complex flow phenomenon commonly observed in three-dimensional hypersonic inlets. Wall temperatures can influence the scale of the separation of the swept SWBLI. It may lead to inlets unstart, resulting in a significant decrease in mass flow rate. This study delves into the flowfield of swept SWBLI under varying wall temperatures, using both experimental and numerical methods to examine the effects of these temperature changes on the separation scaling and the fluctuating velocity within the SWBLI flowfield. The investigation uncovers that modifications in wall temperature significantly impact the boundary layer's subsonic layer thickness, streamwise momentum distribution, and shear stress, which collectively alter the separation scale. To estimate characteristic surface limiting streamline angles under changed wall temperature conditions, a predictive model is proposed that utilizes the boundary layer shape factor H as a metric. Additionally, it is established that wall temperature variations can influence surface friction coefficients, which can, in turn, affect the pressure rise process during separation and alter the spatial angle of the separation shock. The fluctuating velocity characteristic reveals that the wall temperature affects the separated flow mainly on the incoming boundary layer.

Experimental and numerical investigation of two blended blade and endwall configurations

The Blended Blade and Endwall (BBEW) technique has proven to be effective in controlling the intersection of boundary layer in corner region of the compressor endwall. In this study, the experiment and analysis of two different BBEW designs are emphasized. First, based on a linear cascade with 0.7 Mach number inflow, two different configurations, BBEW 1 and BBEW 2, are well conducted. Then, according to the experimental result, control effects of these two BBEW configurations are validated and compared subsequently under various working conditions. The results demonstrate a reduction in total pressure loss of 12.8% and 29% at the design point for BBEW 1 and BBEW 2, respectively. Consequently, the BBEW technique proves effective in suppressing the development of the boundary layer and preventing corner separation. Followed by detailed numerical analysis, improvements around the corner region, especially for the boundary layer, are extracted to show the mechanisms and distinctions between the two configurations. The results indicate that BBEW 1 significantly restrains the development of boundary layer before separation occurs, while BBEW 2 directly controls the strength and scale of the corner separation.

Multiscale interaction analysis of Landfall Typhoon Lekima (2019) based on vorticity equation diagnosis

To investigate the multiscale interaction characteristics of Landfall Typhoon Lekima (2019), this study analyzed the characteristics of the different scale vortex structure and interactions among different scales based on vorticity equation diagnosis. The analysis is based on the simulation results of the WRF model which has been thoroughly verified. The main results are as follows: the original vorticity dominated by the meso-α scale vorticity increases with height and then decreases, with maximum vorticity distributed at 900 hPa. The meso-β scale vorticity varies significantly with altitude, while the meso-γ scale vorticity field exhibits obvious positive vorticity below 850 hPa. The meso-α scale vorticity tendency primarily maintains negative, contributing significantly to the overall reduction in the original vorticity field over time. The increase in mid-to-upper-level (above 550 hPa) original vorticity is mainly related to the variations in the meso-β and meso-γ scale vorticity fields. The original vorticity dominated by the meso-α scale vorticity increases with height and then decreases, and the whole layer vorticity decreases over time. The meso-β scale vorticity varies significantly with altitude and time, while the meso-γ scale vorticity field consistently exhibits significant positive vorticity below 850 hPa. The vorticity equation diagnosis revealed that the primary source terms of the vorticity tendencies are the twisting and stretching terms, and the main sink terms being horizontal and vertical vorticity transport terms below 900 hPa. The source terms and sink terms exchange above 850 hPa. Scale separation results show that the primary contributions of all impact factors originate from the meso-α and meso-γ scale fields (accounting for over 80% of the total), with the contribution of the meso-α scale being less than that of the meso-γ scale and a notable contribution over 35.5% of the interactions between different scales.

On inherent hyperelastic crease

We present analyses of the inherent hyperelastic crease that entails an unstable degenerative singular perturbation field over a uniformly compressed hyperelastic half-space. The analyses reveal asymptotic far-field characteristics of the singular field that bring out admissible incremental elastic deformation mechanisms of the inherent creasing instability typically observed at a compressive strain of ∼0.354 in neo-Hookean solids. The admissible singular perturbation field has an asymptotic leading-order incremental-stress singularity decaying 1/r2 as the distance from the crease tip r→∞. In general, asymptotic incremental-deformation fields of 1/r2 stress singularity can be introduced by surface flaws. We found that the singular field creates a far-field eigenmode of three energy-release angular sectors separated by two energy-elevating sectors of incremental deformation. The far-field eigenmode braces the near-tip energy-release field of the surface flaw against the transition to an unstable self-similar expansion field of creasing. Two asymptotic far-field parameters can characterize the braced-incremental-deformation (bid) and crease fields. One is the Burgers vector of a projected subsurface dislocation of the asymptotically singular far field. The other is a dimensionless shape factor representing the ratio of the subsurface depth of the dislocation to the Burgers vector. Our analyses show that the shape factor gauges the transition from the stable bid field to the unstable inherent crease field at the crease limit point as the compression increases. Two tangential-manifold conservation integrals are revealed to identify the two parameters. At the crease-limit point, matched asymptotes lead to the ratio between the two separate scaling parameters of the asymptotic solutions of the crease-tip folding field and the leading-order far field. To this end, we introduced a novel finite element method (FEM) for simulating the crease field nearly in a hyperelastic half-space with a finite-size simulation domain. Furthermore, we uncovered with the Gent model (1996) that strain-stiffening in hyperelasticity alters the dependence of the shape factor on the compressive strain, raising crease resistance. The new findings in hyperelastic crease mechanisms will help study ruga mechanics of self-organization and design soft-material structures and skin conditions for high crease resistance.

Blind source separation algorithm for noisy hydroacoustic signals based on decoupled convolutional neural networks

Wireless communication technology has been widely used in marine engineering, marine ranching and Marine environmental monitoring. However, structural redundancy and functional confusion exist in applying neural networks in signal separation technology in underwater communication environments, which can result in a slower rate of signal separation and lead to confusion of parameters during transfer learning. Based on this, an end-to-end, internal functionally structured decoupled neural network (D-CNN) blind source separation (BSS) model is proposed in this paper, which can realize a neural network BSS algorithm with a well-defined structure and function. The one-dimensional convolutional neural network layer is used in algorithm to automatically extract observed signal's features, based on the features, and there are two generation modules of separation matrix and scaling coefficients. Then the two modules can be used to separate the observed signal and adjust the signal coefficients to obtain the separated signal. Finally the transfer learning technique is used to generalize the model, which reduces the transfer cost of the model in different application scenarios. Experimental results show that when the communication distance is set to 0.02 km–2 km, the MSE of independent signal and related signal can be reduced by 14.24% and 14.95% respectively compared with the nearest Neural FCA algorithm. The results prove that the proposed algorithm can accurately estimate the source signal and improve the signal reception quality.

Effects of coordination and stiffness scale separation in disordered elastic networks.

Many fibrous materials are modeled as elastic networks featuring a substantial separation between the stiffness scales that characterize different microscopic deformation modes of the network's constituents. This scale separation has been shown to give rise to emergent complexity in these systems' linear and nonlinear mechanical response. Here we study numerically a simple model featuring said stiffness scale separation in two-dimensions and show that its mechanical response is governed by the competition between the characteristic stiffness of collective nonphononic soft modes of the stiff subsystem, and the characteristic stiffness of the soft interactions. We present and rationalize the behavior of the shear modulus of our complex networks across the unjamming transition at which the stiff subsystem alone loses its macroscopic mechanical rigidity. We further establish a relation in the soft-interaction-dominated regime between the shear modulus, the characteristic frequency of nonphononic vibrational modes, and the mesoscopic correlation length that marks the crossover from a disorder-dominated response to local mechanical perturbations in the near field, to a linear, continuumlike response in the far field. The effects of spatial dimension on the observed scaling behavior are discussed, in addition to the interplay between stiffness scales in strain-stiffened networks, which is relevant to understanding the nonlinear mechanics of non-Brownian fibrous biomatter.

Evolutionarily stable payoff matrix in hawk–dove games

BackgroundClassical matrix game models aim to find the endpoint of behavioural evolution for a set of fixed possible interaction outcomes. Here, we introduce an evolutionary model in which not only the players’ strategies but also the payoff matrix evolves according to natural selection.ResultsWe start out from the hawk–dove matrix game and, in a way that is consistent with the monomorphic model setup of Maynard Smith and Price, introduce an evolving phenotypic trait that quantifies fighting ability and determines the probability of winning and the cost of losing escalated hawk–hawk fights. We define evolutionarily stable phenotypes as consisting of an evolutionarily stable strategy and an evolutionarily stable trait, which in turn describes a corresponding evolutionarily stable payoff matrix.ConclusionsWe find that the maximal possible cost of escalating fights remains constant during evolution assuming a separation in the time scales of fast behavioural and slow trait selection, despite the fact that the final evolutionarily stable phenotype maximizes the payoff of hawk–hawk fights. Our results mirror the dual nature of Darwinian evolution whereby the criteria of evolutionary success, as well as the successful phenotypes themselves, are a product of natural selection.

Simulation of permeable surfaces using the pressure–velocity jump approach: A lamellar screen upstream of a ground-mounted obstacle

Permeable surfaces are nowadays widely adopted in the construction industry, with applications ranging from wind shields for bridge decks to the external layer of permeable double skin facades. However, due to the large scale separation between the overall structure dimension and the size of the pores, their modelling in CFD simulations is still extremely challenging and over-simplified homogenized models are often used in practice. Inspired by previous studies, the authors recently proposed a generalization of the well-known pressure-jump approach which accounts for flow deflections, denoted as pressure–velocity jump, PVJ. In this study, the derivation of the PVJ approach is briefly recalled and contextualized in the existing literature. Then, we use PVJ to study the influence of a lamellar screen positioned upstream of a ground-mounted obstacle using 2D URANS. In particular, simulations are performed using the proposed PVJ approach and Explicit Models, EM, in which lamellae are explicitly modelled, for square and a rectangular obstacles. Results show a good agreement between EM and PVJ based models, confirming the high potential of the proposed technique.