We present a dynamical model of crystal growth, in which it is possible to reliably achieve asymmetric products, beginning from symmetric initial conditions and growing within an isotropic environment. The asymmetric growth is the result of a positive feedback mechanism that amplifies the effect of thermal fluctuations in the coverage of surfactants on the growing crystalline facets. Within our simple model, we are able to understand the kinetic and thermodynamic factors involved in both the onset of symmetry breaking and the persistence of anisotropic growth. We demonstrate that the mechanism is general by studying models with increasing complexity. We argue that this mechanism of symmetry breaking underpins observations of colloidal, seed-mediated syntheses of single crystalline metal nanorods capped with strongly interacting surfactants. The parameters within our model are related to experimental observables such as the concentration, hydrophobicity, and binding strength of the surfactants, which suggests a potential route to optimize the yield of asymmetric products in colloidal nanoparticle syntheses.
Software development relies heavily on text-based communication, making sentiment analysis a valuable tool for understanding team dynamics and supporting trustworthy AI-driven analytics in requirements engineering. However, existing sentiment analysis tools often perform inconsistently across datasets from different platforms, due to variations in communication style and content. In this study, we analyze linguistic and statistical features of 10 developer communication datasets from five platforms and evaluate the performance of 14 sentiment analysis tools. Based on these results, we propose a mapping approach and questionnaire that recommends suitable sentiment analysis tools for new datasets, using their characteristic features as input. Our results show that dataset characteristics can be leveraged to improve tool selection, as platforms differ substantially in both linguistic and statistical properties. While transformer-based models such as SetFit and RoBERTa consistently achieve strong results, tool effectiveness remains context-dependent. Our approach supports researchers and practitioners in selecting trustworthy tools for sentiment analysis in software engineering, while highlighting the need for ongoing evaluation as communication contexts evolve.
UI automation is a useful technique for UI testing, bug reproduction, and robotic process automation. Recording user actions with an application assists rapid development of UI automation scripts, but existing recording techniques are intrusive, rely on OS or GUI framework accessibility support, or assume specific app implementations. Reverse engineering user actions from screencasts is non-intrusive, but a key reverse-engineering step is currently missing - recognizing human-understandable structured user actions ([command] [widget] [location]) from action screencasts. To fill the gap, we propose a deep learning-based computer vision model that can recognize 11 commands and 11 widgets, and generate location phrases from action screencasts, through joint learning and multi-task learning. We label a large dataset with 7260 video-action pairs, which record user interactions with Word, Zoom, Firefox, Photoshop, and Windows 10 Settings. Through extensive experiments, we confirm the effectiveness and generality of our model, and demonstrate the usefulness of a screencast-to-action-script tool built upon our model for bug reproduction.
The q-deformed statistical mechanics for fermions has been used to investigate the Thomas-Fermi screening length at finite temperature. Considering linear response, the calculations have been made at weakly nondegenerate regime. The results show that q-deformation has significance effects on screening length at higher temperatures. It is also shown that the q-deformation effects vanish at zero temperature limit. One can find that more correction terms of deformation have more effects on screening length. The bahaviour of screening length is different for different values of q.
Natural Language Processing (NLP) is now a cornerstone of requirements automation. One compelling factor behind the growing adoption of NLP in Requirements Engineering (RE) is the prevalent use of natural language (NL) for specifying requirements in industry. NLP techniques are commonly used for automatically classifying requirements, extracting important information, e.g., domain models and glossary terms, and performing quality assurance tasks, such as ambiguity handling and completeness checking. With so many different NLP solution strategies available and the possibility of applying machine learning alongside, it can be challenging to choose the right strategy for a specific RE task and to evaluate the resulting solution in an empirically rigorous manner. In this chapter, we present guidelines for the selection of NLP techniques as well as for their evaluation in the context of RE. In particular, we discuss how to choose among different strategies such as traditional NLP, feature-based machine learning, and language-model-based methods. Our ultimate hope for this chapter is to serve as a stepping stone, assisting newcomers to NLP4RE in quickly initiating themselves into the NLP technologies most pertinent to the RE field.
Performance-based engineering for natural hazards facilitates the design and appraisal of structures with rigorous evaluation of their uncertain structural behavior under potentially extreme stochastic loads expressed in terms of failure probabilities against stated criteria. As a result, efficient stochastic simulation schemes are central to computational frameworks that aim to estimate failure probabilities associated with multiple limit states using limited sample sets. In this work, a generalized stratified sampling scheme is proposed in which two phases of sampling are involved: the first is devoted to the generation of strata-wise samples and the estimation of strata probabilities whereas the second aims at the estimation of strata-wise failure probabilities. Phase-I sampling enables the selection of a generalized stratification variable (i.e., not necessarily belonging to the input set of random variables) for which the probability distribution is not known a priori. To improve the efficiency, Markov Chain Monte Carlo Phase-I sampling is proposed when Monte Carlo simulation is deemed infeasible and optimal Phase-II sampling is implemented based on user-specified target coefficients of variation for the limit states of interest. The expressions for these coefficients are derived with due regard to the sample correlations induced by the Markov chains and the uncertainty in the estimated strata probabilities. The proposed stochastic simulation scheme reaps the benefits of near-optimal stratified sampling for a broader choice of stratification variables in high-dimensional reliability problems with a mechanism to approximately control the accuracy of the failure probability estimators. The practicality of the scheme is demonstrated using two examples involving the estimation of failure probabilities associated with highly nonlinear responses induced by wind and seismic excitations.
Extreme mechanical processes such as strong lattice distortion and bond breakage during fracture are ubiquitous in nature and engineering, which often lead to catastrophic failure of structures. However, understanding the nucleation and growth of cracks is challenged by their multiscale characteristics spanning from atomic-level structures at the crack tip to the structural features where the load is applied. Molecular simulations offer an important tool to resolve the progressive microstructural changes at crack fronts and are widely used to explore processes therein, such as mechanical energy dissipation, crack path selection, and dynamic instabilities (e.g., kinking, branching). Empirical force fields developed based on local descriptors based on atomic positions and the bond orders do not yield satisfying predictions of fracture, even for the nonlinear, anisotropic stress-strain relations and the energy densities of edges. High-fidelity force fields thus should include the tensorial nature of strain and the energetics of rare events during fracture, which, unfortunately, have not been taken into account in both the state-of-the-art empirical and machine-learning force fields. Based on data generated by first-principles calculations, we develop a neural network-based force field for fracture, NN-F$^3$, by combining pre-sampling of the space of strain states and active-learning techniques to explore the transition states at critical bonding distances. The capability of NN-F$^3$ is demonstrated by studying the rupture of h-BN and twisted bilayer graphene as model problems. The simulation results confirm recent experimental findings and highlight the necessity to include the knowledge of electronic structures from first-principles calculations in predicting extreme mechanical processes.
Recently, a class of machine learning methods called physics-informed neural networks (PINNs) has been proposed and gained prevalence in solving various scientific computing problems. This approach enables the solution of partial differential equations (PDEs) via embedding physical laws into the loss function. Many inverse problems can be tackled by simply combining the data from real life scenarios with existing PINN algorithms. In this paper, we present a multi-task learning method using uncertainty weighting to improve the training efficiency and accuracy of PINNs for inverse problems in linear elasticity and hyperelasticity. Furthermore, we demonstrate an application of PINNs to a practical inverse problem in structural analysis: prediction of external loads of diverse engineering structures based on limited displacement monitoring points. To this end, we first determine a simplified loading scenario at the offline stage. By setting unknown boundary conditions as learnable parameters, PINNs can predict the external loads with the support of measured data. When it comes to the online stage in real engineering projects, transfer learning is employed to fine-tune the pre-trained model from offline stage. Our results show that, even with noisy gappy data, satisfactory results can still be obtained from the PINN model due to the dual regularization of physics laws and prior knowledge, which exhibits better robustness compared to traditional analysis methods. Our approach is capable of bridging the gap between various structures with geometric scaling and under different loading scenarios, and the convergence of training is also greatly accelerated through not only the layer freezing but also the multi-task weight inheritance from pre-trained models, thus making it possible to be applied as surrogate models in actual engineering projects.
Mechanics of materials is a classic course of engineering presenting the fundamentals of strain and stress analysis to junior undergraduate students in several engineering majors. So far, material deformation and strain have been only analyzed using theoretical and numerical approaches, and they have been experimentally validated by expensive machines and tools. This paper presents a novel approach for strain and deformation analysis by using quadcopters. We propose to treat quadcopters as finite number of particles of a deformable body and apply the principles of continuum mechanics to illustrate the concept of axial and shear deformation by using quadcopter hardware in a $3$-D motion space. The outcome of this work can have significant impact on undergraduate education by filling the gap between in-class learning and hardware realization and experiments, where we introduce new roles for drones as "teachers" providing a great opportunity for practicing theoretical concepts of mechanics in a fruitful and understandable way.
In this paper, a simple case of Bayesian mechanics under the free energy principle is formulated in axiomatic terms. We argue that any dynamical system with constraints on its dynamics necessarily looks as though it is performing inference against these constraints, and that in a non-isolated system, such constraints imply external environmental variables embedding the system. Using aspects of classical dynamical systems theory in statistical mechanics, we show that this inference is equivalent to a gradient ascent on the Shannon entropy functional, recovering an approximate Bayesian inference under a locally ergodic probability measure on the state space. We also use some geometric notions from dynamical systems theory$\unicode{x2014}$namely, that the constraints constitute a gauge degree of freedom$\unicode{x2014}$to elaborate on how the desire to stay self-organised can be read as a gauge force acting on the system. In doing so, a number of results of independent interest are given. Overall, we provide a related, but alternative, formalism to those driven purely by descriptions of random dynamical systems, and take a further step towards a comprehensive statement of the physics of self-organisation in formal mathematical language.
Tensor networks (TNs) have become one of the most essential building blocks for various fields of theoretical physics such as condensed matter theory, statistical mechanics, quantum information, and quantum gravity. This review provides a unified description of a series of developments in the TN from the statistical mechanics side. In particular, we begin with the variational principle for the transfer matrix of the 2D Ising model, which naturally leads us to the matrix product state (MPS) and the corner transfer matrix (CTM). We then explain how the CTM can be evolved to such MPS-based approaches as density matrix renormalization group (DMRG) and infinite time-evolved block decimation. We also elucidate that the finite-size DMRG played an intrinsic role for incorporating various quantum information concepts in subsequent developments in the TN. After surveying higher-dimensional generalizations like tensor product states or projected entangled pair states, we describe tensor renormalization groups (TRGs), which are a fusion of TNs and Kadanoff-Wilson type real-space renormalization groups, focusing on their fixed point structures. We then discuss how the difficulty in TRGs for critical systems can be overcome in the tensor network renormalization and the multi-scale entanglement renormalization ansatz.
Carter L. Johnson, Timothy J. Lewis, Robert D. Guy
Understanding principles of neurolocomotion requires the synthesis of neural activity, sensory feedback, and biomechanics. The nematode \textit{C. elegans} is an ideal model organism for studying locomotion in an integrated neuromechanical setting because its neural circuit has a well-characterized modular structure and its undulatory forward swimming gait adapts to the surrounding fluid with a shorter wavelength in higher viscosity environments. This adaptive behavior emerges from the neural modules interacting through a combination of mechanical forces, neuronal coupling, and sensory feedback mechanisms. However, the relative contributions of these coupling modes to gait adaptation are not understood. The model consists of repeated neuromechanical modules that are coupled through the mechanics of the body, short-range proprioception, and gap-junctions. The model captures the experimentally observed gait adaptation over a wide range of mechanical parameters, provided that the muscle response to input from the nervous system is faster than the body response to changes in internal and external forces. The modularity of the model allows the use of the theory of weakly coupled oscillators to identify the relative roles of body mechanics, gap-junctional coupling, and proprioceptive coupling in coordinating the undulatory gait. The analysis shows that the wavelength of body undulations is set by the relative strengths of these three coupling forms. In a low-viscosity fluid environment, the competition between gap-junctions and proprioception produces a long wavelength undulation, which is only achieved in the model with sufficiently strong gap-junctional coupling.The experimentally observed decrease in wavelength in response to increasing fluid viscosity is the result of an increase in the relative strength of mechanical coupling, which promotes a short wavelength.
A brief description of the relations between the factorization method in quantum mechanics, self-similar potentials, integrable systems and the theory of special functions is given. New coherent states of the harmonic oscillator related to the Fourier transformation are constructed.
Starting from the quantum mechanics for $N$ particles, we show that we can directly derive the microcanonical ensemble average of the physical quantity $A$ by using only the long time average and the equal probability assumption for the equal energy states. The system is considered to be embedded in the outer world and we describe them in terms of the density matrix method.
Daddy Balondo Iyela, Jan Govaerts, M. Norbert Hounkonnou
Within the context of Supersymmetric Quantum Mechanics and its related hierarchies of integrable quantum Hamiltonians and potentials, a general programme is outlined and applied to its first two simplest illustrations. Going beyond the usual restriction of shape invariance for intertwined potentials, it is suggested to require a similar relation for Hamiltonians in the hierarchy separated by an arbitrary number of levels, N. By requiring further that these two Hamiltonians be in fact identical up to an overall shift in energy, a periodic structure is installed in the hierarchy of quantum systems which should allow for its solution. Specific classes of orthogonal polynomials characteristic of such periodic hierarchies are thereby generated, while the methods of Supersymmetric Quantum Mechanics then lead to generalised Rodrigues formulae and recursion relations for such polynomials. The approach also offers the practical prospect of quantum modelling through the engineering of quantum potentials from experimental energy spectra. In this paper these ideas are presented and solved explicitly for the cases N=1 and N=2. The latter case is related to the generalised Laguerre polynomials, for which indeed new results are thereby obtained. At the same time new classes of integrable quantum potentials which generalise that of the harmonic oscillator and which are characterised by two arbitrary energy gaps are identified, for which a complete solution is achieved algebraically.
We present a statistical mechanics description to study the ground state of quantum systems. In this approach, averages for the complete system are calculated over the non-interacting energy levels. Taking different interaction parameter, the particles of the system fall into non-interacting microstates, corresponding to different occupation probabilities for these energy levels. Using this novel thermodynamic interpretation we study the Hubbard model for the case of two electrons in two sites and for the half-filled band on a one-dimensional lattice. We show that the form of the entropy depends on the specific system considered.
The relaxation of magnetically confined plasmas in a toroidal geometry is analyzed. From the equations for the Hermitian moments, we show how the system relaxes towards the mechanical equilibrium. In the space of the parallel generalized frictions, after fast transients, the evolution of collisional magnetically confined plasmas is such that the projections of the evolution equations for the parallel generalized frictions and the shortest path on the Hermitian moments coincide. For spatially-extended systems, a similar result is valid for the evolution of the {\it thermodynamic mode} (i.e., the mode with wave-number k = 0). The expression for the affine connection of the space covered by the generalized frictions, close to mechanical equilibria, is also obtained. The knowledge of the components of the affine connection is a fundamental prerequisite for the construction of the (nonlinear) closure theory on transport processes.
We discuss recent results of the replica approach to statistical mechanics of a single classical particle placed in a random N(>>1)-dimensional Gaussian landscape. The particular attention is paid to the case of landscapes with logarithmically growing correlations and to its recent generalisations. Those landscapes give rise to a rich multifractal spatial structure of the associated Boltzmann-Gibbs measure. We also briefly mention related results on counting stationary points of random Gaussian surfaces, as well as ongoing research on statistical mechanics in a random landscape constructed locally by adding many squared Gaussian-distributed terms.