Choice Of Parameters Research Articles

Γ-Convergence for Plane to Wrinkles Transition Problem

We consider a variational problem modeling transition between flat and wrinkled region in a thin elastic sheet and identify the Γ-limit as the sheet thickness goes to 0, thus extending the previous work of the first author (Bella et al. in Arch Ration Mech Anal 218(1):163–217, 2015). The limiting problem is scalar and convex, but constrained and posed for measures. For the Γ-lim inf inequality, we first pass to quadratic variables so that the constraint becomes linear, and then obtain the lower bound using Reshetnyak’s theorem. The construction of the recovery sequence for the Γ-lim sup inequality relies on mollification of quadratic variables and careful choice of multiple construction parameters. Eventually for the limiting problem, we show existence of a minimizer and equipartition of the energy for each frequency.

Mitigating Winner-Take-All Resource Competition through Antithetic Control Mechanism.

Competition among genes for limited transcriptional and translational resources impairs the functionality and modularity of synthetic gene circuits. Traditional control mechanisms, such as feedforward and negative feedback loops, have been proposed to alleviate these challenges, but they often focus on individual modules or inadvertently increase the burden on the system. In this study, we introduce three novel multimodule control strategies─local regulation, global regulation, and negatively competitive regulation (NCR)─that employ an antithetic regulatory mechanism to mitigate resource competition. Our systematic analysis reveals that while all three control mechanisms can alleviate resource competition to some extent, the NCR controller consistently outperforms both the global and local controllers. This superior performance stems from the unique architecture of the NCR controller, which is independent of specific parameter choices. Notably, the NCR controller not only facilitates the activation of less active modules through cross-activation mechanisms but also effectively utilizes the resource consumption within the controller itself. These findings emphasize the critical role of carefully designing the topology of multimodule controllers to ensure robust performance.

Complexity of linearized quadratic penalty for optimization with nonlinear equality constraints

AbstractIn this paper we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints, are locally smooth. For solving this problem, we propose a linearized quadratic penalty method, i.e., we linearize the objective function and the functional constraints in the penalty formulation at the current iterate and add a quadratic regularization, thus yielding a subproblem that is easy to solve, and whose solution is the next iterate. Under a new adaptive regularization parameter choice, we provide convergence guarantees for the iterates of this method to an $$\epsilon $$ ϵ first-order optimal solution in $${\mathcal {O}}({\epsilon ^{-2.5}})$$ O ( ϵ - 2.5 ) iterations. Finally, we show that when the problem data satisfy Kurdyka–Lojasiewicz property, e.g., are semialgebraic, the whole sequence generated by the proposed algorithm converges and we derive improved local convergence rates depending on the KL parameter. We validate the theory and the performance of the proposed algorithm by numerically comparing it with some existing methods from the literature.

An investigation of firm size distributions involving the growth functions

Following the ideas of prospect theory, a class of growth functions is used to characterize deterministic variations of firm size, which portrays the asymmetric efforts of the firm to achieve the desired size. Considering the differences in the ability of different firm size to cope with uncertainties, the Boltzmann equation for the evolution of firm size is constructed. Utilizing a suitable scaling limit, the Fokker–Planck equation is acquired and its explicit steady-state solution is derived. Our results illustrate that different choices of parameters in the growth function lead to various statistical laws for firm size, such as the Amoroso distribution, the lognormal distribution and Zipf’s law. Under certain conditions, inequality for the distribution of firm size decreases as firm size increases. The numerical analyses are presented to illustrate our results.

TDS Simulator: A MATLAB App to model temperature-programmed hydrogen desorption

We present TDS Simulator, a new software tool aimed at modelling thermal desorption spectroscopy (TDS) experiments. TDS is a widely used technique for quantifying key characteristics of hydrogen-material interactions, such as diffusivity and trapping. However, interpreting the output of TDS experiments is non-trivial and requires appropriate post-processing tools. This work introduces the first software tool capable of simulating TDS curves for arbitrary choices of material parameters and hydrogen trap characteristics, using the primary hydrogen diffusion and trapping models (Oriani, McNabb-Foster). Moreover, TDS Simulator contains a specific functionality for loading experimental TDS data and conducting the inverse calibration of a selected transport model, providing automatic estimates of the density and binding energy of each hydrogen trap type in the material. In its first version, TDS Simulator is provided as a MATLAB App, which is made freely available to the community and provides a simple graphical user interface (GUI) to make use of TDS Simulator straightforward. As reported in the present manuscript, the outputs of TDS Simulator have been extensively validated against literature data. Demonstrations of automatic determination of trap characteristics from experimental data through the optimisation tool are also provided. The present work enables an efficient and straightforward characterisation of hydrogen-material characteristics relevant to multiple applications, from nuclear fusion to the development of hydrogen-compatible materials for the hydrogen economy. TDS Simulator can be downloaded from https://mechmat.web.ox.ac.uk/codes (To be uploaded immediately after the review process).

Investigation of the aerodynamic performance of the dragonfly-inspired tandem wings considering the coupling between the stroke plane and phase difference

The dragonfly's tandem wings can make full use of the interference of various spatial vortices to obtain efficient flight capability. The complex coupling among multiple motion parameters will have an important influence on the interference between the forewing (FW) and hindwing (HW). In this paper, the aerodynamic performance of the dragonfly-inspired tandem wings is analyzed using the Computational Fluid Dynamics (CFD) method considering the coupling effect of the stroke plane and phase difference. The variation of the force coefficient, vortex structure and aerodynamic efficiency of the tandem wings in forward flight are analyzed, respectively. The results show that the stroke plane angle affects the distribution of the leading edge vortex (LEV) and trailing edge vortex (TEV), which primarily controls the trend of horizontal force variation. The phase difference of tandem wings will change the fluctuation of the horizontal force coefficient curve by affecting the meeting time of the forewing and hindwing. However, with the increase of stroke plane angle, the fluctuation of aerodynamic coefficient caused by phase difference will decrease. The propulsion efficiency(η) and power loading(PL) can be improved through increasing the stroke plane angle and selecting a reasonable phase difference. The conclusion can provide theoretical guidance for the design of the dragonfly-inspired tandem flapping wing aircraft (DTFWA) and the choice of motion parameters.

Influence of the scanning strategy on the microstructure and the tribological behavior of a Ni-based superalloy processed by additive manufacturing

The ABD-900AM is a newly developed nickel-based alloy specifically designed for additive manufacturing, and it can be printed using a wide range of process parameters. This alloy, combined with the L-PBF process, allows for the production of dense parts with reference microstructures that are multi-scale, and facilitates the study of the links between these microstructures and their tribological behaviors. To study the relationships between microstructures and tribological behaviors, the parts are built vertically without interlayer rotation. The plane studied are obtained with three scanning directions : 0°, 45° and 90°. These angles allow to generate different microstructures on the planes on which are conducted the microstructural characterizations and tribological tests, for which the sliding direction is always parallel to the building direction. This choice of parameter enables access to different crystallographic textures (200) and (111), and cellular structures with varying morphologies and homogeneity within the melt pools. Tribological tests were performed on these microstructures in a ball-on-flat configuration with alternating motion, without lubrication, and at room temperature. For the three laser angles (0°, 45°, and 90°), the wear volumes are 0.60 ± 0.12 mm3, 0.81 ± 0.15 mm3, and 1.00 ± 0.09 mm3, respectively. The wear resistance is primarily related to the amount of oxide layers formed on the wear track of the samples.

Thermodynamics of Modified Chaplygin-Jacobi Gas and Modified Chaplygin-Abel Gas: Stability Analysis and Observational Constraints

This paper explores the thermodynamic properties and stability of two newly introduced gas models, namely the Modified Chaplygin-Jacobi gas and the Modified Chaplygin-Abel gas. To achieve this, we examine the behavior of relevant physical parameters to gain in depth information about the evolution of the universe. The specific heat formalism is employed to verify the applicability of the third law of thermodynamics. Furthermore, the equation of state for the thermal system is obtained by applying thermodynamic variables. The stability of the gas models is investigated within the framework of classical thermodynamics, focusing on adiabatic processes, specific heat capacities, and isothermal conditions. It is inferred that the proposed fluid configurations exhibit thermodynamic stability and undergo adiabatic expansion for suitable parameter choices. We then perform observational analysis using CC+BAO and Pantheon+SH0ES datasets to impose constraints on our model parameters using the Markov Chain Monte Carlo (MCMC) process.

Morphology and Properties of the Laser-Irradiated Composition “Chrome Coating — Copper Substrate”

Introduction. During pulsed laser processing and modification of the surface of non-ferrous alloys and coatings based on them, several still unresolved issues arise. In particular, the extreme thermal deformation conditions of laser processing are not linked to the peculiarities of structure formation and formation of properties in irradiated “coating — copper substrate” compositions. A metal physical analysis of the possibility and reasons for increasing the adhesion strength of coatings to a metal (copper) substrate during high-speed laser processing is insufficiently substantiated and evidence-based. To make a reasonable choice of technological parameters for the surface hardening mode of non-ferrous alloy products, as well as for obtaining high-quality workable composite layers on their surface, it is necessary to solve the above issues and tasks. The aim of this article is to determine the possibility and conditions for increasing the adhesion strength of a chrome coating to a copper substrate under laser irradiation of the composition.Materials and Methods. Metal physical studies in the work were carried out on samples of non-ferrous alloys of the Cu–Zn system with a chrome electrochemical coating with a thickness of 20 μm. The “copper substrate — chrome coating” composition was irradiated at a Kvant-16 installation with a radiation power density of 70–250 MW/m2. Metallographic structural analysis, scanning probe microscopy, and durometric studies were used in the work.Results. It has been calculated that the dynamic and thermal stresses arising in the laser-irradiated compositions “chrome coating — copper substrate” were about 320 MPa. Metal physical studies revealed that, in extreme thermal deformation conditions of laser treatment, the effect of contact melting was manifested at the boundary of the coating with the copper base. Dynamic recrystallization occurred in the surface layers of the irradiated L62 copper alloy, resulting in the formation of grains with a size of 4.5–5.0 μm on the surface of the alloy with an initial grain size of 25 μm.Discussion and Conclusion. It has been found that the adhesion strength of a chrome coating to a copper alloy substrate increased laser irradiation at a radiation power density of 150 MW/m2. This was due to the formation of a transition region 2–4 μm deep in the contact zone with a structure consisting of sections of mutually insoluble solid solutions based on chromium and copper. Based on the analysis of the copper —chromium state diagram and the model of the temperature field under laser irradiation of the chromium coating, it was suggested that contact melting occurred in the transition zone from the coating to the copper substrate. It was shown that thermostrictive stresses, the calculated quantitative values of which were about 320 MPa, had an initiating effect on the observed processes of structure formation in the laser irradiation zones. It was found that such a level of stresses arising in copper alloys under laser irradiation was sufficient for plastic deformation and dynamic recrystallization of the metal and contributed to the formation of a fine-grained structure (4.5–5.0 μm) with an initial grain size of 25 μm. An analysis of the results of studies of irradiated compositions "coating — copper substrate" allowed us to conclude that they expanded the technological capabilities of the laser method of hardening materials and ensure guaranteed high performance of irradiated products with coatings

On time-periodic solutions to an interaction problem between compressible viscous fluids and viscoelastic beams

Abstract In this paper, we study a nonlinear fluid-structure interaction problem between a ‘square-root’ viscoelastic beam and a compressible viscous fluid. The beam is immersed in the fluid which fills a two-dimensional rectangular domain with periodic boundary conditions in both directions, while both the beam and the fluid are under the effect of time-periodic forces. By using a decoupling approach, at least one time-periodic weak solution to this problem is constructed which has a bounded energy and a fixed prescribed mass. The lack of a priori energy bounds is overcome by a series of estimates based on a careful choice of parameters. The most challenging one is the pressure estimate, which is obtained by utilizing the specific periodic geometry and the Bogovskiǐ operator on a fixed domain that has a uniform constant. With uniform estimates and improved regularity of the beam as in (Muha and Schwarzacher 2023 Ann. Inst. Henri Poin. Anal. Non Lineaire 39 1369–412), the time-periodic solution is constructed by a series of limit procedures, following the finite-dimensional time-space construction from (Feireisl et al 2012 Arch. Rational Mech. Anal. 204 74586).

Efficient relaxation scheme for the SIR and related compartmental models

In this paper, we introduce a novel numerical approach for approximating the Susceptible–Infectious–Recovered (SIR) model in epidemiology. Our method enhances the existing linearization procedure by incorporating a suitable relaxation term to tackle the transcendental equation of nonlinear type. Developed within the continuous framework, our relaxation method is explicit and easy to implement, relying on a sequence of linear differential equations. This approach yields accurate approximations in both discrete and analytical forms. Through rigorous analysis, we prove that, with an appropriate choice of the relaxation parameter, our numerical scheme is non-negativity-preserving; moreover, it is strongly convergent to the true solution. We also extend the applicability of our relaxation method to handle some variations of the traditional SIR model. Finally, we present numerical examples using simulated data to demonstrate the effectiveness of our proposed method.

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Low-frequency spectral graph convolution networks with one-hop connections information for personalized tag recommendation

Graph neural networks (GNNs) have gained prominence as an effective technique for representation learning and have found wide application in tag recommendation tasks. Existing approaches aim to encode the hidden collaborative information among entities into embedding representations by propagating node information between connected nodes. However, in sparse observable graph structures, a significant number of connections are missing, leading to incomplete and biased propagation. To address these issues, we propose a novel model called Low-frequency Spectral Graph Convolution Networks with one-hop connections information for Personalized Tag Recommendation (LSGCNT). This model utilizes graph convolution in the spectral domain and incorporates a graph structure comprising two bipartite graphs, the user–tag interaction graph and the item–tag interaction graph. Our model aims to reduce information loss caused by propagation by utilizing graph convolution networks with trainable convolution kernels to recover preference information. In order to preserve useful low-frequency signals, we couple graph convolution with low-pass filters in the frequency domain. Through reconstructing the true rating tensor and ranking the tag scores within the tensor, we can achieve top-N recommendations. Furthermore, to preserve the one-hop connection information of the bipartite graphs, we treat the observed two bipartite graphs as two homogeneous graphs, where both users and tags contribute to the convolution of a node in the user–tag graph, and both items and tags contribute to the convolution of a node in the item–tag graph. Lastly, we analyze the impact of different internal components, pooling methods, parameter choices, and prediction approaches of LSGCNT on recommendation performance. Experimental results on two real-world datasets demonstrate that LSGCNT achieves superior recommendation performance compared with eight other state-of-the-art recommendation models.

Simulating the LOcal Web (SLOW) III. Synchrotron emission from the local cosmic web

Detecting diffuse synchrotron emission from the cosmic web is still a challenge for current radio telescopes. We aim to make predictions about the detectability of cosmic web filaments from simulations. We present the first cosmological magnetohydrodynamic simulation of a 500 $h^ c$Mpc volume with an on-the-fly spectral cosmic ray (CR) model. This allows us to follow the evolution of populations of CR electrons and protons within every resolution element of the simulation. We modeled CR injection at shocks, while accounting for adiabatic changes to the CR population and high-energy-loss processes of electrons. The synchrotron emission was then calculated from the aged electron population, using the simulated magnetic field, as well as different models for the origin and amplification of magnetic fields. We used constrained initial conditions, which closely resemble the local Universe, and compared the results of the cosmological volume to a zoom-in simulation of the Coma cluster, to study the impact of resolution and turbulent reacceleration of CRs on the results. We find a consistent injection of CRs at accretion shocks onto cosmic web filaments and galaxy clusters. This leads to diffuse emission from filaments of the order $S_ $ for a potential LOFAR observation at 144 MHz, when assuming the most optimistic magnetic field model. The flux can be increased by up to two orders of magnitude for different choices of CR injection parameters. This can bring the flux within a factor of ten of the current limits for direct detection. We find a spectral index of the simulated synchrotron emission from filaments of $ -1.0 -- -1.5 in the LOFAR band.

Convergence rates for a source identification problem with time-integral observation

This paper is concerned with a source identification problem from time-integral observation associated with a bi-parabolic equation. The problem is transformed as solving a linear operator equation, where the operator involved is a compact operator of infinite rank, which implies that the problem is ill-posed. The stable approximations are obtained by employing the Tikhonov regularization method. The main contribution of this paper is about the Hölder rate of convergence for both apriori and aposteriori parameter choice strategies by considering source sets as subsets of the Sobolev spaces. Moreover, we show that in certain cases, the rates obtained for the apriori and aposteriori choices are order optimal in the sense of worst-case error.

Using muscle-tendon load limits to assess unphysiological musculoskeletal model deformation and Hill-type muscle parameter choice.

Musculoskeletal simulations are a useful tool for improving our understanding of the human body. However, the physiological validity of predicted kinematics and forces is highly dependent upon the correct calibration of muscle parameters and the structural integrity of a model's internal skeletal structure. In this study, we show how ill-tuned muscle parameters and unphysiological deformations of a model's skeletal structure can be detected by using muscle elements as sensors with which modelling and parameterization inconsistencies can be identified through muscle and tendon strain injury assessment. To illustrate our approach, two modelling issues were recreated. First, a model repositioning simulation using the THUMS AM50 occupant model version 5.03 was performed to show how internal model deformations can occur during a change of model posture. Second, the muscle material parameters of the OpenSim gait2354 model were varied to illustrate how unphysiological muscle forces can arise if material parameters are inadequately calibrated. The simulations were assessed for muscle and tendon strain injuries using previously published injury criteria and a newly developed method to determine tendon strain injury threshold values. Muscle strain injuries in the left and right musculus pronator teres were detected during the model repositioning. This straining was caused by an unphysiologically large gap (12.92 mm) that had formed in the elbow joint. Similarly, muscle and tendon strain injuries were detected in the modified right-hand musculus gastrocnemius medialis of the gait2354 model where an unphysiological reduction of the tendon slack length introduced large pre-strain of the muscle-tendon unit. The results of this work show that the proposed method can quantify the internal distortion behaviour of musculoskeletal human body models and the plausibility of Hill-type muscle parameter choice via strain injury assessment. Furthermore, we highlight possible actions to avoid the presented issues and inconsistencies in literature data concerning the material characteristics of human tendons.

On the Peculiarities of Wire-Feed Electron Beam Additive Manufacturing (WEBAM) of Nickel Alloy–Copper Bimetal Nozzle Samples

In order to gain insight into the unique characteristics of manufacturing large-scale products with intricate geometries, experimental nozzle-shaped samples were created using wire-feed electron beam additive technology. Bimetal samples were fabricated from nickel-based alloy and copper. Two distinct approaches were employed, utilizing varying substrate thicknesses and differing fabrication parameters. The two approaches were the subject of analysis and comparison through the examination of the surface morphology of the samples using optical microscopy, scanning electron microscopy, and X-ray diffraction analysis. It has been demonstrated that the variation in heat flux distributions resulting from varying the substrate thicknesses gives rise to the development of disparate angles of grain boundary orientation relative to the substrate. Furthermore, it is demonstrated that suboptimal choice of the fabrication parameters results in large disparities in the crystallization times, both at the level of sample as a whole and within the same material volume. For example, for the sample manufacturing by Mode I, the macrostructure of the layers is distinguished by the presence of non-uniformity in their geometric dimensions and the presence of unmelted wire fragments. In order to characterize the experimental nozzle-shaped samples, microhardness was measured, uniaxial tensile tests were performed, and thermal diffusivity was determined. The microhardness profiles and the mechanical properties exhibit a higher degree of strength than those observed in pure copper samples and a lower degree of strength than those observed in Inconel 625 samples obtained through the same methodology. The thermal diffusivity values of the samples are sufficiently close to one another and align with the properties of the corresponding materials in their state after casting or rolling. The data discussed above indicate that Mode II yields the optimal mechanical properties of the sample due to the high cooling rate, which influences the structural and phase state of the resulting products. It was thus concluded that the experimental samples grown by Mode II on a thinner substrate exhibited the best formability.

Empirically exploring the space of monostationarity in dual phosphorylation

AbstractThe dual phosphorylation network provides an essential component of intracellular signaling, affecting the expression of phenotypes and cell metabolism. For particular choices of kinetic parameters, this system exhibits multistationarity, a property that is relevant in the decision-making of cells. Determining which reaction rate constants correspond to monostationarity and which produce multistationarity is an open problem. The system’s monostationarity is linked to the nonnegativity of a specific polynomial. A previous study by Feliu et al. provides a sufficient condition for monostationarity via a decomposition of this polynomial into nonnegative circuit polynomials. However, this decomposition is not unique. We extend their work by a systematic approach to classifying such decompositions in the dual phosphorylation network. Using this classification, we provide a qualitative comparison of the decompositions into nonnegative circuit polynomials via empirical experiments and improve on previous conditions for the region of monostationarity.

Theoretically grounded approaches to account for polarization effects in fixed-charge force fields.

Non-polarizable, or fixed-charge, force fields are the workhorses of most molecular simulation studies. They attempt to describe the potential energy surface (PES) of the system by including polarization effects in an implicit way. This has historically been done in a rather empirical and ad hoc manner. Recent theoretical treatments of polarization, however, offer promise for getting the most out of fixed-charge force fields by judicious choice of parameters (most significantly the net charge or dipole moment of the model) and application of post facto polarization corrections. This Perspective describes these polarization theories, namely the "halfway-charge" theory and the molecular dynamics in electronic continuum theory, and shows that they lead to qualitatively (and often, quantitatively) similar predictions. Moreover, they can be reconciled into a unified approach to construct a force field development workflow that can yield non-polarizable models with charge/dipole values that provide an optimal description of the PES. Several applications of this approach are reviewed, and avenues for future research are proposed.

Transfer learning for accurate description of atomic transport in Al-Cu melts.

Machine learning interatomic potentials (MLIPs) provide an optimal balance between accuracy and computational efficiency and allow studying problems that are hardly solvable by traditional methods. For metallic alloys, MLIPs are typically developed based on density functional theory with generalized gradient approximation (GGA) for the exchange-correlation functional. However, recent studies have shown that this standard protocol can be inaccurate for calculating the transport properties or phase diagrams of some metallic alloys. Thus, optimization of the choice of exchange-correlation functional and specific calculation parameters is needed. In this study, we address this issue for Al-Cu alloys, in which standard Perdew-Burke-Ernzerhof (PBE)-based MLIPs cannot accurately calculate the viscosity and melting temperatures at Cu-rich compositions. We have built MLIPs based on different exchange-correlation functionals, including meta-GGA, using a transfer learning strategy, which allows us to reduce the amount of training data by an order of magnitude compared to a standard approach. We show that r2SCAN- and PBEsol-based MLIPs provide much better accuracy in describing thermodynamic and transport properties of Al-Cu alloys. In particular, r2SCAN-based deep machine learning potential allows us to quantitatively reproduce the concentration dependence of dynamic viscosity. Our findings contribute to the development of MLIPs that provide quantum chemical accuracy, which is one of the most challenging problems in modern computational materials science.