Framework Of Mechanics Research Articles

Quantum versus classical quenches and the broadening of wave packets

The time dependence of one-dimensional quantum mechanical probability densities is presented when the potential in which a particle moves is suddenly changed, called a quench. Quantum quenches are mainly addressed, but a comparison with results for the dynamics in the framework of classical statistical mechanics is useful. Analytical results are presented when the initial and final potentials are harmonic oscillators. When the final potential vanishes, the problem reduces to the broadening of wave packets. A simple introduction to the concept of the Wigner function is presented, which allows a better understanding of the dynamics of general wave packets. It is pointed out how special the broadening of Gaussian wave packets is, the only example usually presented in quantum mechanics textbooks.

Higher-order phase-space moments for off-diagonal rotating Morse oscillators

The present paper proposes an advancement beyond the recent mathematical formulation [Cherroud O and Yahiaoui S-A 2023 Eur. Phys. J. Plus. 138 534], by extending their approach to the evaluation of off-diagonal matrix elements 〈xˆmpˆl〉n,n′J,J′ for the rotation-vibration Morse oscillators. Calculations are conducted within the framework of phase-space quantum mechanics, considering (r → r eq). This methodology facilitates the derivation of analytical expressions for 〈xˆs〉n,n′J,J′ and 〈pˆs〉n,n′J,J′ matrix elements, where s = 1, 2, …. This approach enables the evaluation of both diagonal ( n=n′,J=J′≠0 ) and off-diagonal ( n≠n′,J=J′≠0 ) matrix elements through a more explicit and compact analytic formula, applicable for cases where J≠J′ as well as for scenarios involving non-rotating effects J=J′=0 .

On the experimental determination and prediction of damage evolution in composites via cyclic testing

This study introduces a novel approach to obtaining and predicting damage evolution laws using quasi-static cyclic testing within the framework of continuum damage mechanics. To achieve this, a comprehensive set of characterization and parameter identification tests was performed. Carbon-epoxy specimens were manufactured using the filament-winding technique, and these laminates were tested using a universal testing machine. Digital image correlation was employed in all experiments to capture strain fields, and an alternative method utilizing the combined loading compression device is presented to obtain mechanical properties. Once the material was characterized, cyclic tests were conducted, including [Formula: see text], [Formula: see text], and [Formula: see text] tensile tests, and shear v-notch tests. These aim to determine damage evolution laws for both conditions, pure and coupled stress states. From these tests, values for damage onset and threshold were obtained and used to define four new parameters. These parameters permit the estimation of degradation relationships for any arbitrary orientation without requiring additional tests. This approach was tested as the proof-of-concept within the positive range of transverse tension and in-plane shear stress domain. The obtained results are promising, justifying its extension to other failure mechanisms. While acknowledging its limitations, this new approach holds potential for implementation in the analysis of progressive failure in fiber-reinforced composite materials, possibly in conjunction with established failure criteria and computational tools, mainly in the finite element method domain.

A review on the mechanical behaviour of microcellular and nanocellular polymeric foams: What is the effect of the cell size reduction?

Research on nanocellular foams is motivated in part by the promise of physical properties, in particular mechanical properties, that can go beyond the classical mechanical framework. However, due to the difficulty in obtaining foams of a given density but different cell sizes, determining the effect of cell size on the mechanical properties of polymer foams remains a challenge. To overcome this difficulty, studies on the mechanical behaviour of mesocellular, microcellular and nanocellular polymer foams have been compiled in this review article. After describing the different cellular structures between meso-, micro- and nanocellular foams, the mechanical properties are examined as a function of relative density and cell size. It is shown that for small strains and at low strain rates, nanocellular foams exhibit mechanical behaviour predicted by the Gibson and Ashby model. Relative density remains the first important factor to be taken into account when studying the Young’s modulus and buckling stress of nanocellular foams. The focus then shifts to fracture properties, as microcellular foams have already been shown to be far superior to more conventional foams. As studies are still scarce and different methodologies have been used, no general conclusions can be drawn. However, the fracture and impact properties could be greatly improved by this change in scale. The local confinement of molecular chains in polymeric nanocellular foams or the relaxation of the triaxial stress state in front of the crack tip could explain these observations.

Inferring to cooperate: Evolutionary games with Bayesian inferential strategies

Abstract Strategies for sustaining cooperation and preventing exploitation by selfish agents in repeated games have mostly been restricted to Markovian strategies where the response of an agent depends on the actions in the previous round. Such strategies are characterized by lack of learning. However, learning from accumulated evidence over time and using the evidence to dynamically update our response is a key feature of living organisms. Bayesian inference provides a framework for such evidence-based learning mechanisms. It is therefore imperative to understand how strategies based on Bayesian learning fare in repeated games with Markovian strategies. Here, we consider a scenario where the Bayesian player uses the accumulated evidence of the opponent’s actions over several rounds to continuously update her belief about the reactive opponent’s strategy. The Bayesian player can then act on her inferred belief in different ways. By studying repeated Prisoner’s dilemma games with such Bayesian inferential strategies, both in infinite and finite populations, we identify the conditions under which such strategies can be evolutionarily stable. We find that a Bayesian strategy that is less altruistic than the inferred belief about the opponent’s strategy can outperform a larger set of reactive strategies, whereas one that is more generous than the inferred belief is more successful when the benefit-to-cost ratio of mutual cooperation is high. Our analysis reveals how learning the opponent’s strategy through Bayesian inference, as opposed to utility maximization, can be beneficial in the long run, in preventing exploitation and eventual invasion by reactive strategies.

Scn1a haploinsufficiency in the prefrontal cortex engages to cognitive impairment and depressive phenotype.

Altered development and function of the prefrontal cortex (PFC) during adolescence is implicated in the origin of mental disorders. Deficits in the GABAergic system prominently contribute to these alterations. Nav1.1 is a voltage-gated Na+ channel critical for normal GABAergic activity. Here, we studied the role of Nav1.1 in PFC function and its potential relationship with the aetiology of mental disorders. Dysfunction of Nav1.1 activity in the medial PFC (mPFC) of adolescent mice enhanced the local excitation/inhibition ratio, resulting in epileptic activity, cognitive deficits and depressive-like behaviour in adulthood, along with a gene expression profile linked to major depressive disorder (MDD). Additionally, it reduced extracellular serotonin concentration in the dorsal raphe nucleus and brain-derived neurotrophic factor expression in the hippocampus, two MDD-related brain areas beyond the PFC. We also observed alterations in oscillatory activity and impaired hippocampal-mPFC coherence during sleep. Finally, we found reduced expression levels of SCN1A, the gene encoding Nav1.1, in post-mortem PFC samples from human MDD subjects. Collectively, our results provide a novel mechanistic framework linking adolescence-specific alterations in Nav1.1 function in the PFC to the pathogenesis of epilepsy and comorbidities such as cognitive impairment and depressive disorders.

Upregulation of the AMPK-FOXO1-PDK4 pathway is a primary mechanism of pyruvate dehydrogenase activity reduction in tafazzin-deficient cells

Barth syndrome (BTHS) is a rare disorder caused by mutations in the TAFAZZIN gene. Previous studies from both patients and model systems have established metabolic dysregulation as a core component of BTHS pathology. In particular, features such as lactic acidosis, pyruvate dehydrogenase (PDH) deficiency, and aberrant fatty acid and glucose oxidation have been identified. However, the lack of a mechanistic understanding of what causes these conditions in the context of BTHS remains a significant knowledge gap, and this has hindered the development of effective therapeutic strategies for treating the associated metabolic problems. In the current study, we utilized tafazzin-knockout C2C12 mouse myoblasts (TAZ-KO) and cardiac and skeletal muscle tissue from tafazzin-knockout mice to identify an upstream mechanism underlying impaired PDH activity in BTHS. This mechanism centers around robust upregulation of pyruvate dehydrogenase kinase 4 (PDK4), resulting from hyperactivation of AMP-activated protein kinase (AMPK) and subsequent transcriptional upregulation by forkhead box protein O1 (FOXO1). Upregulation of PDK4 in tafazzin-deficient cells causes direct phospho-inhibition of PDH activity accompanied by increased glucose uptake and elevated intracellular glucose concentration. Collectively, our findings provide a novel mechanistic framework whereby impaired tafazzin function ultimately results in robust PDK4 upregulation, leading to impaired PDH activity and likely linked to dysregulated metabolic substrate utilization. This mechanism may underlie previously reported findings of BTHS-associated metabolic dysregulation.

Preferential Solvation Phenomena as Solute-Induced Structure-Making/Breaking Processes: Linking Thermodynamic Preferential Interaction Parameters to Fundamental Structure Making/Breaking Functions.

In this work, we identify the explicit macroscopic-to-microscopic rigorous links between existing thermodynamic preferential interaction parameters and microstructural descriptors based on total correlation function integrals, leading to their unambiguous characterization in terms of fundamental structure making/breaking functions . First, we provide the statistics mechanical framework to identify a universal molecular-based signature for the preferential solvation phenomenon involving solutes at infinite dilution in mixed-solvent environments and discuss its fundamental properties. Then, we characterize the functions relevant to the process, identify the microscopic markers for the existing preferential interaction parameters in terms of the functions, and test their compliance with a pair of essential microstructural constraints linked to the properties of the universal signature. Moreover, we illustrate the analysis by probing the behavior of a representative ternary system comprising the solubility of methane in aqueous 1,4-dioxane mixed-solvent environments under ambient conditions. Finally, we discuss some relevant issues surrounding the statistical mechanical (microstructural) interpretation of the thermodynamic (macroscopic) preferential interaction parameters, review some pitfalls in their evaluation from molecular simulation, and provide an outlook.

Mixing of a cylindrical gravity current in a stratified ambient

Simulation results from direct numerical simulations (DNSs) of cylindrical gravity currents propagating into a linearly stratified ambient with stratification strengths ranging from 0 to 0.8, at a moderate Reynolds number of Re=3450 are presented. The simulations are based on the incompressible Navier–Stokes equations, assuming small density differences such that the Boussinesq approximation is valid. The density of the ambient fluid increases linearly from the top (ρ0) to the bottom (ρb) of the domain. A comparative analysis is conducted between the stratified cases and the unstratified case to investigate the impact of ambient stratification strength on the mixing behaviour of cylindrical gravity currents. The energy conversion processes are analysed using the mechanical framework proposed by Winters et al. (1995). The energy budget is formulated by considering gravitational available potential energy, and the evolution of potential energy due to reversible stirring and irreversible diapycnal mixing in the system. The findings reveal a decrease in available potential energy and kinetic energy with increasing stratification strength, indicating lower energy exchange for gravity currents propagating in the stratified environment. Instantaneous and cumulative mixing efficiency calculations during the slumping phase indicate that Kelvin–Helmholtz billow play an important role in stirring the heavy fluid and causing irreversible mixing with the ambient fluid.

Mesoscopic simulation of uniaxial compression fracture of concrete via the nonlocal macro–meso-scale consistent damage model

To capture the uniaxial compression fracture of concrete composite is still a great challenging problem. To this end, the newly proposed nonlocal macro–meso-scale consistent damage (NMMD) model is extended to simulate uniaxial compression fracture of concrete composites. In the NMMD model, a mesoscopic structure composed of material point pairs is attached to each material point. A decomposition scheme suitable for masonry-like materials is adopted to decompose the elongation quantity of point pairs. The topologic damage is defined as the weighted summation of mesoscopic damage in neighboring material point pairs driven by the decomposed elongation quantity. The physically-based energetic degradation function is employed to bridge the geometric discontinuity in solids and the energy dissipation, and thus the topologic damage is integrated into the framework of continuum damage mechanics. The Monte-Carlo method and two-phase random field model are employed to generate stochastic circular and irregular aggregates representing the meso structure of concrete, respectively. The interface transition zone is prescribed by reducing the critical value of interface point pairs. Numerical results indicate that both the crack patterns and stress–strain curves of the uniaxial compression experiments on concrete panels can be well captured by the proposed NMMD model without mesh size sensitivity. The influence of horizontal constraints on the top and bottom surfaces is investigated and shown to have an effect on the crack patterns, strength and deformation capability of the specimen. The necessity of decomposition is also illustrated.

New exact free vibration solution of two-dimensional decagonal quasicrystal cylindrical shells in the symplectic framework

An accurate free vibration analysis of two-dimensional decagonal quasicrystal (QC) cylindrical shells is performed under the framework of symplectic mechanics. Unlike the classical Lagrangain system, the governing equations are reduced into a set of lower order ordinary differential equations, and therefore exact solutions of displacements, rotation angles, internal forces and bending moments in the phonon and phason fields are simultaneously obtained and expressed in terms of symplectic vectors. The present results are compared with existing literature and finite element solutions, and excellent agreements are observed. Furthermore, the effects of key influencing factors on the free vibration characteristics are revealed also.

Asymmetric 1,2‐Migration on Vicinal Tetrasubstituted Stereocenters Constructed from α‐Keto Imines

A carbonyl‐assisted asymmetric 1,2‐migratory allylation through in situ generation of vicinal tetrasubstituted stereocenters is reported to access enantiopure α‐amino ketones, and amino‐alcohols with excellent yields and diastereoselectivities. In a remarkable divergence, despite having higher steric hindrance, the allylation exclusively occurs on ketones over imines in the first step, followed by a face‐selective 1,2‐allyl transfer, thus highlighting an exciting interplay between two distinct electrophiles. The methodology distinguishes itself through its adaptability to gram‐scale synthesis, showcasing broad functional group tolerance, and stereodivergence. The density functional theory (DFT) analysis elucidates a deeper understanding of its selectivity and mechanistic framework. Highlighting its transformative potential, the total synthesis of hapalindole alkaloids were adeptly achieved.

Asymmetric 1,2‐Migration on Vicinal Tetrasubstituted Stereocenters Constructed from α‐Keto Imines

A carbonyl‐assisted asymmetric 1,2‐migratory allylation through in situ generation of vicinal tetrasubstituted stereocenters is reported to access enantiopure α‐amino ketones, and amino‐alcohols with excellent yields and diastereoselectivities. In a remarkable divergence, despite having higher steric hindrance, the allylation exclusively occurs on ketones over imines in the first step, followed by a face‐selective 1,2‐allyl transfer, thus highlighting an exciting interplay between two distinct electrophiles. The methodology distinguishes itself through its adaptability to gram‐scale synthesis, showcasing broad functional group tolerance, and stereodivergence. The density functional theory (DFT) analysis elucidates a deeper understanding of its selectivity and mechanistic framework. Highlighting its transformative potential, the total synthesis of hapalindole alkaloids were adeptly achieved.

Fracture mechanics approach to minimum reinforcement design of fibre-reinforced and hybrid-reinforced concrete beams

Fracture mechanics approach to minimum reinforcement design of fibre-reinforced and hybrid-reinforced concrete beams

A tensorial energy-release-rate based anisotropic damage-plasticity model for concrete

This paper proposes an anisotropic damage model for concrete to capture its plasticity and damage behavior effectively. Utilizing the framework of continuum damage mechanics, the model considers the influence of plastic Helmholtz free energy on damage evolution. This approach explicitly deduces damage-related thermodynamic forces without resorting to assumptions such as strain equivalence or energy equivalence. The proposed model employs tensile and compressive damage tensors to describe the development of anisotropic damage in concrete. The solution for plastic strain utilizes the empirical plasticity model. Furthermore, a unified evolutionary criterion for isotropic and anisotropic damage is also established, incorporating damage yield functions and orthogonal flow laws. Numerical simulations are conducted to validate the model’s ability to reproduce typical nonlinear behaviors of concrete structures under various load conditions.

Visual social information use in collective foraging.

Collective dynamics emerge from individual-level decisions, yet we still poorly understand the link between individual-level decision-making processes and collective outcomes in realistic physical systems. Using collective foraging to study the key trade-off between personal and social information use, we present a mechanistic, spatially-explicit agent-based model that combines individual-level evidence accumulation of personal and (visual) social cues with particle-based movement. Under idealized conditions without physical constraints, our mechanistic framework reproduces findings from established probabilistic models, but explains how individual-level decision processes generate collective outcomes in a bottom-up way. In clustered environments, groups performed best if agents reacted strongly to social information, while in uniform environments, individualistic search was most beneficial. Incorporating different real-world physical and perceptual constraints profoundly shaped collective performance, and could even buffer maladaptive herding by facilitating self-organized exploration. Our study uncovers the mechanisms linking individual cognition to collective outcomes in human and animal foraging and paves the way for decentralized robotic applications.

A human neural crest model reveals the developmental impact of neuroblastoma-associated chromosomal aberrations

Early childhood tumours arise from transformed embryonic cells, which often carry large copy number alterations (CNA). However, it remains unclear how CNAs contribute to embryonic tumourigenesis due to a lack of suitable models. Here we employ female human embryonic stem cell (hESC) differentiation and single-cell transcriptome and epigenome analysis to assess the effects of chromosome 17q/1q gains, which are prevalent in the embryonal tumour neuroblastoma (NB). We show that CNAs impair the specification of trunk neural crest (NC) cells and their sympathoadrenal derivatives, the putative cells-of-origin of NB. This effect is exacerbated upon overexpression of MYCN, whose amplification co-occurs with CNAs in NB. Moreover, CNAs potentiate the pro-tumourigenic effects of MYCN and mutant NC cells resemble NB cells in tumours. These changes correlate with a stepwise aberration of developmental transcription factor networks. Together, our results sketch a mechanistic framework for the CNA-driven initiation of embryonal tumours.

Atomistic to continuum mechanics description of crystal defects with dislocation density fields: Application to dislocations and grain boundaries

The atomic structure of crystal defects such as dislocations, grain or phase boundaries, control these defects’ properties: their mobility, ability to cross-slip, or solute segregation. These crystal defects can be conveniently studied by atomistic simulations and one then needs to transfer relevant information at the upper scale to model microstructures containing a large number of defects, e.g., a polycrystal. Here, we propose an atomistic to continuum mechanics crossover method that (i) represents the atomic structure of dislocations cores by an appropriate Nye dislocation density tensor field and (ii), captures quantitatively the short and long range mechanical fields of defects. For (i), we propose a modified and improved interpolation method based on the original work by Hartley and Mishin. For (ii), we use a field dislocation mechanics framework that rigorously calculates/evaluates the mechanical fields associated with any Nye dislocation density distribution. The transfer method relies on molecular static calculations using two energetic models — ab-initio for screw dislocation core simulations in tungsten, and EAM potential for low and large angle grain boundaries in copper. Our findings demonstrate the effectiveness of the proposed approach in reconstructing the Burgers vector, and continuous strain and rotation fields. The framework is further applied to analyze the elastic interactions between extrinsic edge dislocations and a low angle grain boundary in copper.

Where is my attention? An explainable AI exploration in water detection from SAR imagery

Attention mechanisms have found extensive application in Deep Neural Networks (DNNs), with numerous experiments over time showcasing their efficacy in improving the overall performance of DNNs. Considering the black-box nature of DNNs, it is unclear how attention mechanisms affect model decision-making processes. Therefore, it is of great significance to explore the internal relationship between the focused area of attention mechanisms and the prediction results. For the first time, an explainable framework for the attention mechanism of Synthetic Aperture Radar (SAR) image analytics is proposed, integrating DNN and eXplainable Artificial Intelligence (XAI), which realizes the effective explanation for attention mechanisms across different locations. The framework consists of three parts: the water extraction network which contains the attention mechanism at different locations; the proposed Attention- Gradient Class Activation Mapping (A-GCAM) method for attribution analysis of attention mechanisms; and we invent Category-specific channel Score of Confidence Mapping (CSCM) to perform geo-visualization for the output features of attention mechanisms. Experiments are conducted with the widely used Sentinel-1 system for water detection, in which three attention mechanisms with different characteristics are added to the encoder and decoder in DNNs. The results show that the framework can make the decision-making process of attention mechanisms transparent, thus improving their comprehensiveness and trustworthiness in various tasks and providing a reliable approach to selecting suitable attention mechanisms for the given task.

Anisotropic Breakage Mechanics for cemented granular materials

The anisotropy of granular geomaterials is sensitive to their fabric, which exhibits anisotropic mechanical properties as a function of deposition history, microscopic fabric, and loading paths. Here, a new fabric-enriched continuum breakage model is proposed to examine the relation between elastic and inelastic anisotropy in granular materials and cemented granular materials. A microstructure model is first implemented in the framework of fabric-enriched continuum breakage mechanics (F-CBM), where the anisotropic behaviour prior to yielding is introduced through a symmetric second-order fabric tensor embedded in the expression of the elastic energy potential. The anisotropic strain energy storage prior to grain crushing leads to the rotation and distortion of the yield surface of cemented granular materials. Parametric analyses are performed to assess the overall capability of the model to characterize the anisotropic inelastic processes in cemented granular. It is shown that the proposed model can accurately predict the strong correlation between anisotropic elasticity and breakage-damage processes in cemented granular materials. When damage involving the skeleton is the dominant inelastic process, the size of the elastic domain contracts and the material exhibits augmented brittleness with the disintegration of cement. While breakage processes are predicted to dominate the response of lightly cemented granular materials resulting in hardening behaviour. This work can be further extended to dynamically capture the anisotropic response of cemented granular materials with water-sensitive mineral constituents by accounting for the evolution of microstructural anisotropy.