Energy Minimization Research Articles

Elasticity of Diametrically Compressed Microfabricated Woodpile Lattices

Modulus–porosity relationships are invaluable to rational material design of porous and structured solids. When struts in a lattice are compressed diametrically, the mechanics is rather complex. Herein, the problem of modulus–porosity in the spirit of scaling arguments and analyses based on simple ansatz followed by variational minimization of the elastic potential energy is addressed. Using scaling arguments, a simple power law where the apparent modulus of elasticity scales quadratically with the volume fraction for diametrically compressed elastic lattices is obtained. The modulus–porosity relationship is found to be consistent with computations and laboratory experiments on additively manufactured woodpile lattices with various cross‐sectional shapes and lattice spacing. It is also shown that the persistence length of diametrically pinched elastic rods is small, so that the effect of compressive strain from neighboring sites can be ignored. The decay behavior is surprisingly accurately captured by the variational approach and is consistent with computations. Finally, the range of validity of the quadratic power law presented here, up to relative density ~80%, is identified. On the apparent modulus–porosity plane, the experimental data aligns well with the power law for modulus–porosity predicted from simple analyses and finite element calculations.

Dynamical theory of topological defects II: universal aspects of defect motion

We study the dynamics of topological defects in continuum theories governed by a free energy minimization principle, building on our recently developed framework (Romano et al 2023 J. Stat. Mech. 083211). We show how the equation of motion of point defects, domain walls, disclination lines and any other singularity can be understood with one unifying mathematical framework. For disclination lines, this also allows us to study the interplay between the internal line tension and the interaction with other lines. This interplay is non-trivial, allowing defect loops to expand, instead of contracting, due to external interaction. We also use this framework to obtain an analytical description of two long-lasting problems in point defect motion, namely the scale dependence of the defect mobility and the role of elastic anisotropy in the motion of defects in liquid crystals. For the former, we show that the effective defect mobility is strongly problem-dependent, but it can be computed with high accuracy for a pair of annihilating defects. For the latter, we show that at the first order in perturbation theory, anisotropy causes a non-radial force, making the trajectory of annihilating defects deviate from a straight line. At higher orders, it also induces a correction in the mobility, which becomes non-isotropic for the +1/2 defect. We argue that, due to its generality, our method can help to shed light on the motion of singularities in many different systems, including driven and active non-equilibrium theories.

Markov Blankets and Mirror Symmetries-Free Energy Minimization and Mesocortical Anatomy.

A theoretical account of development in mesocortical anatomy is derived from the free energy principle, operating in a neural field with both Hebbian and anti-Hebbian neural plasticity. An elementary structural unit is proposed, in which synaptic connections at mesoscale are arranged in paired patterns with mirror symmetry. Exchanges of synaptic flux in each pattern form coupled spatial eigenmodes, and the line of mirror reflection between the paired patterns operates as a Markov blanket, so that prediction errors in exchanges between the pairs are minimized. The theoretical analysis is then compared to the outcomes from a biological model of neocortical development, in which neuron precursors are selected by apoptosis for cell body and synaptic connections maximizing synchrony and also minimizing axonal length. It is shown that this model results in patterns of connection with the anticipated mirror symmetries, at micro-, meso- and inter-arial scales, among lateral connections, and in cortical depth. This explains the spatial organization and functional significance of neuron response preferences, and is compatible with the structural form of both columnar and noncolumnar cortex. Multi-way interactions of mirrored representations can provide a preliminary anatomically realistic model of cortical information processing.

A novel technique for minimizing energy functional using neural networks

An energy functional describes the equilibrium state of a system. In this work, we present a novel technique, Functional Optimization using Neural Networks (FONN), for minimizing the system’s energy. FONN utilizes neural networks to process information at discrete grid points, considering their interactions with neighboring grid points, to update the state of the system. The training process involves formulating a loss function based on the system’s energy, and with the help of multiple fine-tuning steps, the method employs a progressive energy reduction technique that decreases the energy in multiple steps. FONN’s effectiveness is demonstrated across various problems, including the minimization of the heat and Lyapunov energy. Moreover, the paper explores the minimization of the elastic bending energy with an area constraint.

Abstract 2345: Docking and molecular dynamic simulations of mithramycin against Sp1, Sp3, and survivin

Abstract Purpose: Therapeutic targeting of transcription factors, Specificity protein (Sp)1 and Sp3 and their downstream effectors, such as survivin, are studied in various cancers. Due to role in in poorer cancer prognoses in several cancers their downregulation has been investigated as an effective treatment approach. Mithramycin (Mit) showed innate anti-cancer properties by targeting Sp proteins through GC/GT DNA binding interference. Recent studies have given new insights into further mechanisms of action of Mit, however in-depth binding and mechanistic studies are lacking. Our objective is to investigate Mit’s specific binding interactions with Sp1, Sp3, and survivin. Methods: Protein structures and sequences for Sp1, Sp3, and survivin (ID: P08047, Q02447, and O153392, respectively) were retrieved from UniProtKB database. Experimental predicted structures for Sp1 and Sp3 were obtained from AlphaFold. Sequence lengths of Sp1 and Sp3 were 785 and 781 amino acids (aa), domain regions of Sp1 (619-785) and Sp3 (461-781) were note. Survivin structure was obtained from PDB and was comprised of 142 aa. Co-crystallized compounds were removed during analyses using BIOVIA Discovery Studio 4.5 Visualizer. Prediction of binding sites and docking were performed using CASTp, GHECOM, DEPTH tools, glide, and AutoDock 4.2 software. Energy minimization and Molecular dynamics simulations were performed in the Schrödinger suite. Results: Binding sites were identified for Sp1, Sp3, and survivin. Simulated docking demonstrated multiple binding complexes and varying binding energies. The most efficient binding was seen with Sp1 and Sp3. RMSF and RMSD simulations revealed stabilization of Sp1-, Sp3-, and survivin-Mit complexes. This shows Mithramycin can potentially inhibit all three proteins, with slightly more stability with Sp1 and Sp3. Radius of gyration (rGyr), H-bond analysis, and solvent accessible surface area (SASA) support docking findings with Mit-protein complexes remaining stable in the binding pocket, forming new H-bonds, and altering hydrophilic and hydrophobic interaction areas. Conclusion: Our findings warrant further in vitro testing of the ability of Mit to interact with a wider range of oncogenic targets. While we only tested the ability of Mit to interact with Sp1, Sp3 and survivin, similar model can be used to evaluate the interaction with other critical proteins associated with cancer and to further elucidate mechanisms of action. These finding are crucial to understanding base mechanistic abilities and can be useful to test additional agents for their ability to interact with Sp1 or survivin. Citation Format: Christoffer Briggs Lambring, Santosh K. Behera, Riyaz Basha. Docking and molecular dynamic simulations of mithramycin against Sp1, Sp3, and survivin [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 2345.

Enhanced Computational Study with Experimental Correlation on I-V Characteristics of Tantalum Oxide (TaOx) Memristor Devices in a 1T1R Configuration.

Memristors, non-volatile switching memory platform, has recently attracted significant interest, offering unique potential to enable the realization of human brain-like neuromorphic computing efficiency. Memristors also demonstrate excellent temperature tolerance, long-term durability, and high tunability with nanosecond pulses, making them highly attractive for neuromorphic computing applications. To better understand the material processing, microstructure, and property relationship of switching mechanisms in memristor devices, computational methodologies, and tools are developed to predict the I-V characteristics of memristor devices based on tantalum oxide (TaOx) resistive random-access memory (ReRAM) integrated with an n-channel metal-oxide-semiconductor (NMOS) transistor. A multiphysics model based on coupled partial differential equations for electrical and thermal transport phenomena is solved for the high- and low-resistance states during the formation, growth, and destruction of a conducting filament through SET and RESET stages. These stages effectively represent the migration of oxygen vacancies within an oxide exchange layer. A series of parametric studies and energy minimization calculations are conducted to determine probable ranges for key material and model parameters accounting for the experimental data. The computational model successfully predicted the measured I-V curves across various gate voltages applied to the NMOS transistor in the one transistor one resistance (1T1R) configuration.

ბუნებრივი რესურსის ბაზაზე მიღებული სორბენტებით CO2-ის ადსორბციისას შესაძლო პროცესთა თერმოდინამიკური ანალიზი

This research paper examines the potential mechanisms involved in the adsorption of carbon dioxide using sorbents derived from the natural resources found in Georgia (with a primary focus on zeolite-based materials). A succinct characterization of zeolites obtained from the Dzegvi deposit is provided, along with the presentation of the average chemical composition of the collected samples. The study identifies three distinct series of reactions for in-depth investigation. According to the referenced sources, the standard molar values of the thermodynamic properties of the substances involved in the reaction are sought. The Gibbs free energy minimization method is employed to ascertain both the magnitudes and directions of the free energy changes and equilibrium constants for the proposed reactions within the temperature range spanning 400 to 1200 Kelvin. Their temperature dependence is expressed graphically. Reactions are evaluated based on thermodynamic point of view.

Resolving uncertainty on the fly: modeling adaptive driving behavior as active inference.

Understanding adaptive human driving behavior, in particular how drivers manage uncertainty, is of key importance for developing simulated human driver models that can be used in the evaluation and development of autonomous vehicles. However, existing traffic psychology models of adaptive driving behavior either lack computational rigor or only address specific scenarios and/or behavioral phenomena. While models developed in the fields of machine learning and robotics can effectively learn adaptive driving behavior from data, due to their black box nature, they offer little or no explanation of the mechanisms underlying the adaptive behavior. Thus, generalizable, interpretable, computational models of adaptive human driving behavior are still rare. This paper proposes such a model based on active inference, a behavioral modeling framework originating in computational neuroscience. The model offers a principled solution to how humans trade progress against caution through policy selection based on the single mandate to minimize expected free energy. This casts goal-seeking and information-seeking (uncertainty-resolving) behavior under a single objective function, allowing the model to seamlessly resolve uncertainty as a means to obtain its goals. We apply the model in two apparently disparate driving scenarios that require managing uncertainty, (1) driving past an occluding object and (2) visual time-sharing between driving and a secondary task, and show how human-like adaptive driving behavior emerges from the single principle of expected free energy minimization.

Numerical investigation of non-local elasticity theory for free vibration of polymer embedded multi-layer graphene sheets

The present study investigates the free vibration behavior of multi-layered graphene sheets with various shapes embedded in a polymer matrix under different boundary conditions based on Eringen non local elasticity. The governing equations are obtained through the minimization of potential energy or Newton’s law which is not only equivalent to Hamilton’s principle and mutually can be derived from each other. Differential Quadrature and pb2 Rayleigh Ritz procedures are applied to Multi-layered Graphene sheets employing Eringen’s elasticity and classical plate theory. Results indicate that the resonant frequencies of the sheets are overestimated up to 60% using the classical elastic model. Depending on the shapes of Graphene sheets, small-scale parameters, boundary conditions, stiffness of polymer matrix, the number of layers and van der Waal’s interaction on the vibrational characteristics of graphene sheets are studied, and the results are tabulated. Conclusions are drawn and recommendations are provided for future work.

Geometrically constrained multifield models with BNRT solutions

In this paper, we investigate multifield models in which the two-field BNRT model is coupled to a third field through mediator functions in the Lagrangian density. To conduct the investigation, we obtain the equations of motion and develop a first-order formalism based on energy minimization. Two possibilities are considered: (i) the third field acting in the mediator functions to modify the BNRT solutions; (ii) the BNRT fields feeding the mediator function to produce effects in the kink solution of the third field. In the case (i), the results show that the solutions may be related to the standard ones with the coordinate redefined in terms of the mediator functions if they are equal. This allows to induce effects similar to geometric constrictions in the core, or to compactify the tail of the BNRT solutions. If the mediator functions differ one from another, we show that the effects are distinct, with the compactification of just one of the two-field solutions. In the case (ii), the orbit parameter of the model plays an important role, modifying the mediator function that induces changes in the profile of the kink associated to the third field.

A minimal physical model for curvotaxis driven by curved protein complexes at the cell’s leading edge

Cells often migrate on curved surfaces inside the body, such as curved tissues, blood vessels, or highly curved protrusions of other cells. Recent in vitro experiments provide clear evidence that motile cells are affected by the curvature of the substrate on which they migrate, preferring certain curvatures to others, termed "curvotaxis." The origin and underlying mechanism that gives rise to this curvature sensitivity are not well understood. Here, we employ a "minimal cell" model which is composed of a vesicle that contains curved membrane protein complexes, that exert protrusive forces on the membrane (representing the pressure due to actin polymerization). This minimal-cell model gives rise to spontaneous emergence of a motile phenotype, driven by a lamellipodia-like leading edge. By systematically screening the behavior of this model on different types of curved substrates (sinusoidal, cylinder, and tube), we show that minimal ingredients and energy terms capture the experimental data. The model recovers the observed migration on the sinusoidal substrate, where cells move along the grooves (minima), while avoiding motion along the ridges. In addition, the model predicts the tendency of cells to migrate circumferentially on convex substrates and axially on concave ones. Both of these predictions are verified experimentally, on several cell types. Altogether, our results identify the minimization of membrane-substrate adhesion energy and binding energy between the membrane protein complexes as key players of curvotaxis in cell migration.

Energy Minimization Partial Task Offloading With Joint Dynamic Voltage Scaling and Transmission Power Control in Fog Computing

Energy Minimization Partial Task Offloading With Joint Dynamic Voltage Scaling and Transmission Power Control in Fog Computing

Energy Minimization for Cellular-Connected Aerial Edge Computing System With Binary Offloading

Energy Minimization for Cellular-Connected Aerial Edge Computing System With Binary Offloading

Anisotropic Characterization of the Chukchi Boardland Based on Ocean-Bottom Seismic Experiment during N11-CHINARE

Abstract The current research focus at Chukchi Boardland (CB) revolves around sediment stratification and crustal structure, but investigations into deep stress fields and mantle dynamics are limited. This article presents a study on the anisotropic characteristics of the CB. Shear-wave splitting measurements were conducted using the transverse energy minimization at six stations recovered from the 11th Chinese National Arctic Research Expedition. The observation period for these six stations ranged from 2 August 2020 to 8 September 2020. The results demonstrate significant anisotropy within the CB, with the fast shear-wave polarization direction ranging from N60°E to N70°E. The time delays between fast and slow shear waves were found to be ∼0.7 s. By comparing the anisotropy observed at the CB with that at land stations in Arctic Alaska, this study suggested that the genesis of anisotropy beneath the CB was related to the formation of the Amerasian basin. The tectonic processes of rifting during basin evolution and midocean ridge spreading led to the development of anisotropy in the lithosphere beneath the CB during expansion.

Quantifying the impact of geological and construction factors on hydraulic fracture dynamics in heterogeneous rock layers using the phase field method

Hydraulic fracturing, a pivotal practice for optimizing development in tight oil reservoirs, encounters challenges in accurately predicting propagation paths within heterogeneous rock formations. Existing phase models often overlook the influence of complex formations, especially in porous media with heterogeneous characteristics. Addressing this gap, we present a novel phase field method aligned with on-site practices. This innovative approach considers cracks, bedding planes, and faults as heterogeneous structures, integrating directional physical and mechanical properties. The key innovation lies in constructing assignment functions to characterize mechanical and seepage parameters of the rock matrix. Anchored in pore elasticity theory and the principle of energy minimization, we establish and validate a hydraulic coupled phase field model through plaster experiments. This model not only corrects the oversight of formation heterogeneity but also provides a comprehensive analysis of the impact of physical and construction parameters on crack propagation. The study extends to numerical simulation studies on three typical heterogeneous rock layers—natural fractures, bedding planes, and faults. Utilizing indicators like fracture pressure, crack extension length, and damage area, a random forest algorithm quantifies the degree of influence of each factor on fracturing. Our results underscore varying impacts from geological factors (natural fractures, bedding angle, stress difference, elastic modulus, matrix porosity, and permeability) and construction factors (cluster spacing, perforation length, fracturing fluid viscosity, displacement, well spacing, and perforation opening) on the fracturing effect of heterogeneous rock layers. In conclusion, our proposed phase field framework demonstrates predictive capability across diverse heterogeneous situations. This innovative model not only rectifies past oversights but also offers insights unattainable through traditional experimental testing, significantly advancing our understanding of hydraulic fracture dynamics.

Density-based topology optimization for minimizing von Mises stress using the modified optimality criteria method and demonstration by tensile testing

The authors propose a modified optimality criteria (OC) method that incorporates the concept of Newton's method for the OC method. The modified OC method has fewer arbitrary parameters set by the engineer. In this study, density-based topology optimization for minimizing von Mises stress (VMS) using a modified OC method is performed. In this problem, the value of the second-order derivative is not always positive semidefinite. Thus, the concept of the modified Newton's method is incorporated into the modified OC method. In conclusion, the performance function descends more quickly and with less dependence on parameter settings than when using the OC method. A mathematical proof of the convergence properties of the modified OC method, based on the Newton's method proof, is also presented. To encourage manufacturing, optimal designs obtained by strain energy or VMS minimization were fabricated and evaluated by tensile testing.

Controlled formation of three-dimensional cavities during lateral epitaxial growth

Epitaxial growth is a fundamental step required to create devices for the semiconductor industry, enabling different materials to be combined in layers with precise control of strain and defect structure. Patterning the growth substrate with a mask before performing epitaxial growth offers additional degrees of freedom to engineer the structure and hence function of the semiconductor device. Here, we demonstrate that conditions exist where such epitaxial lateral overgrowth can produce complex, three-dimensional structures that incorporate cavities of deterministic size. We grow germanium on silicon substrates patterned with a dielectric mask and show that fully-enclosed cavities can be created through an unexpected self-assembly process that is controlled by surface diffusion and surface energy minimization. The result is confined cavities enclosed by single crystalline Ge, with size and position tunable through the initial mask pattern. We present a model to account for the observed cavity symmetry, pinch-off and subsequent evolution, reflecting the dominant role of surface energy. Since dielectric mask patterning and epitaxial growth are compatible with conventional device processing steps, we suggest that this mechanism provides a strategy for developing electronic and photonic functionalities.

Frank-Read Mechanism in Nematic Liquid Crystals

In a crystalline solid under mechanical stress, a Frank-Read source is a pinned dislocation segment that repeatedly bows and detaches, generating concentric dislocation loops. We demonstrate that, in nematic liquid crystals, an analogous Frank-Read mechanism can generate concentric disclination loops. Using experiment, simulation, and theory, we study a disclination segment pinned between surface defects on one substrate in a nematic cell. Under applied twist of the nematic director, the pinned segment bows and emits a new disclination loop which expands, leaving the original segment intact; loop emission repeats for each additional 180° of applied twist. We present experimental micrographs showing loop expansion and snap-off, numerical simulations of loop emission under both quasistatic and dynamic loading, and theoretical analysis considering both free energy minimization and the balance of competing forces. We find that the critical stress for disclination loop emission scales as the inverse of segment length and changes as a function of strain rate and temperature, in close analogy to the Frank-Read source mechanism in crystals. Lastly, we discuss how Frank-Read sources could be used to modify microstructural evolution in both passive and active nematics. Published by the American Physical Society 2024

A New Multi-Objective Optimization Strategy for Improved C3MR Liquefaction Process

In the traditional C3MR process (T-C3MR), the boiling gas (BOG) output from the last stage of the gas–liquid separator is directly discharged, in which the excellent low-temperature capability is not utilized, and the system efficiency is decreased. In liquefied natural gas (LNG), single-objective optimization methods are commonly used to optimize system parameters, which may result in incomplete system analysis. To solve the above problems, this paper proposes a multi-objective optimization strategy for the improved C3MR process(I-C3MR) based on a new multi-objective optimization algorithm called EHR-GWO-GA. Firstly, the main work proposes an I-C3MR structure. Secondly, an optimization strategy of the I-C3MR with the maximization of liquefaction amount, minimization of unit energy consumption and minimization of exergy loss as objective functions are proposed. Based on the optimization results, the influence of decision variables on liquefaction amount, unit energy consumption and exergy loss are analyzed, and the results show that the decision variables have good adaptability. Finally, a detailed exergy analysis of the equipment used is made, and the results show that the main exergy losses come from the water coolers and compressors, accounting for 32% and 34%, respectively. Compared to the T-C3MR, the improved C3MR based on EHR-GWO-GA(E-C3MR) has an approximate 8% increase in liquefaction amount—a roughly 23% decrease in unit energy consumption and a decrease of nearly 24% in exergy loss.

Adaptive Equivalent Factor-Based Energy Management Strategy for Plug-In Hybrid Electric Buses Considering Passenger Load Variations

Energy management strategies (EMSs) are one of the key technologies for the development of plug-in hybrid electric buses (PHEBs). This paper addresses the issue of optimal energy distribution for PHEBs under significant variations in passenger load at different bus stations, which cannot be solved by a single equivalent factor equivalent fuel consumption minimization energy management strategy (ECMS). An adaptive equivalent factor equivalent fuel consumption minimization energy management strategy (A-ECMS) considering passenger load is proposed. First, the powertrain system of the PHEB is modeled, and the accuracy of the model is verified in a simulation environment. Then, the reference SOC descent trajectory of the battery is obtained using a dynamic programming (DP) algorithm, the recursive least squares (RLS) method is employed to identify the passenger load, and the influence of different loads on the state of charge (SOC) trajectory under a single equivalent factor is analyzed. Finally, a genetic algorithm (GA) is used to establish the correspondence between passenger load, bus station, and equivalent factor, enabling the actual SOC to follow the reference SOC descent trajectory, thereby achieving optimal energy distribution. Simulation results demonstrate that the A-ECMS reduces fuel consumption of the PHEB per 100 km by 2.59% and 10.10% compared to the ECMS and rule-based EMS, respectively, validating the effectiveness of the proposed strategy.