Hasil untuk "Descriptive and experimental mechanics"

Zhidong Zhang

In this work, we first focus on the mathematical structure of the three-dimensional (3D) Ising model. In the Clifford algebraic representation, many internal factors exist in the transfer matrices of the 3D Ising model, which are ascribed to the topology of the 3D space and the many-body interactions of spins. They result in the nonlocality, the nontrivial topological structure, as well as the long-range entanglement between spins in the 3D Ising model. We review briefly the exact solution of the ferromagnetic 3D Ising model at the zero magnetic field, which was derived in our previous work. Then, the framework of topological quantum statistical mechanics is established, with respect to the mathematical aspects (topology, algebra, and geometry) and physical features (the contribution of topology to physics, Jordan-von Neumann-Wigner framework, time average, ensemble average, and quantum mechanical average). This is accomplished by generalizations of our findings and observations in the 3D Ising models. Finally, the results are generalized to topological quantum field theories, in consideration of relationships between quantum statistical mechanics and quantum field theories. It is found that these theories must be set up within the Jordan-von Neumann-Wigner framework, and the ergodic hypothesis is violated at the finite temperature. It is necessary to account the time average of the ensemble average and the quantum mechanical average in the topological quantum statistical mechanics and to introduce the parameter space of complex time (and complex temperature) in the topological quantum field theories. We find that a topological phase transition occurs near the infinite temperature (or the zero temperature) in models in the topological quantum statistical mechanics and the topological quantum field theories, which visualizes a symmetrical breaking of time inverse symmetry.

Vatsala Goyal, Keith E. Gordon, Theresa Sukal-Moulton

<i>Introduction:</i> Performance in a single step has been suggested to be a sensitive measure of movement quality in pediatric clinical populations. Although there is less information available in children with typical development, researchers have postulated the importance of analyzing the effect of body weight modulation on the initiation of stair ascent, especially during single-limb stance where upright stability is most critical. The purpose of this study was to investigate the effect of load modulation from −20% to +15% of body weight on typical pediatric lower limb joint moments during a step-up task. <i>Methods:</i> Fourteen participants between 5 and 21 years who did not have any neurological or musculoskeletal concerns were recruited to perform multiple step-up trials. Peak extensor support and hip abduction moments were identified during the push-off and pull-up stance phases. Linear regressions were used to determine the relationship between peak moments and load. Mixed-effects models were used to estimate the effect of load on hip, knee, and ankle percent contributions to peak support moments. <i>Results:</i> There was a positive linear relationship between peak support moments and load in both stance phases, where these moments scaled with load. There was no relationship between peak hip abduction moments and load. While the ankle and knee were the primary contributors to the support moments, the hip contributed more than expected in the pull-up phase. <i>Discussion:</i> Clinicians can use these results to contextualize movement differences in pediatric clinical populations, including in those with cerebral palsy, and highlight potential target areas for rehabilitation for populations such as adolescent athletes.

Saïf ed-Dîn Fertahi, Shafiqur Rehman, Khadija Lahrech et al.

This review provides a comprehensive examination of CFD modeling procedures for SCPP, with an emphasis on the detailed methodologies and a case study of the Manzanares prototype in Spain. The introduction delineates the historical context and physical modeling principles of solar chimneys, while highlighting their potential in industrial applications. The governing equations are meticulously discussed, covering assumptions in both 2D and 3D CFD modeling, the continuity and momentum equations, and the selection and accuracy of turbulence models, particularly the k-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ε</mi></semantics></math></inline-formula> equations. The review also delves into heat transfer modeling, encompassing the energy equation and radiation modeling. Analytical evaluations of turbine pressure drop ratios and performance metrics for power generation efficiency are critically analyzed. The establishment of boundary conditions in solar chimney applications, including sky temperature assessments and distinctions between 2D and 3D boundary conditions, is extensively explored. Mesh generation techniques for both 2D and 3D CFD models are presented, supported by case studies. Parametric studies and experimental investigations are scrutinized to elucidate their impact on the performance of solar chimneys. The temperature–entropy diagram for an idealized Brayton cycle is introduced as a conceptual framework for efficiency analysis. Validation of the CFD codes, both 2D and 3D, against experimental data is performed to ensure model accuracy. The review further examines energy balance approaches in modeling solar chimneys, presenting state-of-the-art CFD results and discussing their implications in both 2D and 3D contexts. The synthesis of these findings culminates in a comprehensive conclusion, offering insights into the future directions and potential advancements in the CFD modeling of solar chimneys. This work aims to serve as a definitive reference for researchers and practitioners in the field, providing a robust foundation for the development and optimization of SCPP technology.

Martin Zlatić, Felipe Rocha, Laurent Stainier et al.

We present a comparison between two approaches to modelling hyperelastic material behaviour using data. The first approach is a novel approach based on Data-driven Computational Mechanics (DDCM) that completely bypasses the definition of a material model by using only data from simulations or real-life experiments to perform computations. The second is a neural network (NN) based approach, where a neural network is used as a constitutive model. It is trained on data to learn the underlying material behaviour and is implemented in the same way as conventional models. The DDCM approach has been extended to include strategies for recovering isotropic behaviour and local smoothing of data. These have proven to be critical in certain cases and increase accuracy in most cases. The NN approach contains certain elements to enforce principles such as material symmetry, thermodynamic consistency, and convexity. In order to provide a fair comparison between the approaches, they use the same data and solve the same numerical problems with a selection of problems highlighting the advantages and disadvantages of each approach. Both the DDCM and the NNs have shown acceptable performance. The DDCM performed better when applied to cases similar to those from which the data is gathered from, albeit at the expense of generality, whereas NN models were more advantageous when applied to wider range of applications.

Arash Ghahraman, Gyula Bene

Viscous linear surface waves are studied at arbitrary wavelength, layer thickness, viscosity, and surface tension. We find that in shallow enough fluids no surface waves can propagate. This layer thickness is determined for some fluids, water, glycerin, and mercury. Even in any thicker fluid layers, propagation of very short and very long waves is forbidden. When wave propagation is possible, only a single propagating mode exists for a given horizontal wave number. In contrast, there are two types of non-propagating modes. One kind of them exists at all wavelength and material parameters, and there are infinitely many such modes for a given wave number, distinguished by their decay rates. The other kind of non-propagating mode that is less attenuated may appear in zero, one, or two specimens. We notice the presence of two length scales as material parameters, one related to viscosity and the other to surface tension. We consider possible modes for a given material on the parameter plane layer thickness versus wave number and discuss bifurcations among different mode types. Motion of surface particles and time evolution of surface elevation is also studied at various parameters in glycerin, and a great variety of behaviour is found, including counterclockwise surface particle motion and negative group velocity in wave propagation.

Alberto Carpinteri, Gianni Niccolini, Federico Accornero

By using complex potentials, some light is shed on the analogy between the singularity problems arising in fluid and fracture mechanics—in particular, those concerning plane irrotational flows around sharp obstacles and plane elasticity in cracked bodies. Applications to two equivalent geometries are shown: a thin plate transversally immersed in a uniform flow and a crack subjected to uniform out-of-plane shearing stress at infinity (Mode III). The matching between the fluid velocity field and the shearing stress field is consistent with the hydrodynamic analogy. Aside from the Reynolds criterion for the natural laminar-to-turbulent transition, a velocity-intensity factor criterion is defined to predict the forced turbulent-to-vortex-shedding fluid-flow transition (forced transitional flow) generated by a transversal plate obstacle. It is interesting to remark that the velocity-intensity factor presents physical dimensions intermediate between those of a velocity and a kinematic viscosity. In addition, it will be demonstrated that size affects the occurrence of natural-to-forced transitional phenomena in fluids, in a strict analogy to the scale-dependent ductile-to-brittle failure transitions in solids.

Julien Gibelin

We present a collection of simple derivations for the neutron-induced resonance cross-sections. These formulae are commonly used to experimentally describe the fundamental properties of resonances for neutron-rich nuclei far from stability and to describe unbound nuclei. The main goal of this article is to illustrate their dependencies with basic observables in order to discuss the pertinence of experimental approaches in the derivation of their properties, especially for "N-body" resonances.

Masahiro Ishigaki, Yoshiyasu Hirose, Satoshi Abe et al.

For estimating thermal flow in a nuclear reactor during an accident accurately, it is important to improve the accuracy of computational fluid dynamics simulations. The temperature and flow velocity are not homogeneous and have large variations in a reactor containment vessel because of its very large volume. In addition, Kelm’s work pointed out that the influence of variations of initial and boundary conditions was important. Therefore, it is necessary to set the initial and boundary conditions taking into account the variations of these physical quantities. However, it is a difficult subject to set such complicated initial and boundary conditions. Then, we can obtain realistic initial and boundary conditions and an accurate flow field by data assimilation, and we can improve the accuracy of the simulation result. In this study, we applied data assimilation by a local ensemble transform Kalman filter to a simulation of natural convection behavior in density stratification, and we performed a twin model experiment. We succeeded in estimating the flow fields and improving the simulation accuracy by the data assimilation, even if we applied the boundary condition with error for the true condition.

P. Lovreglio, K. A. Buist, J. A. M. Kuipers et al.

Dispersion is the spreading of a solute while it is moved by a flowing medium. The study of dispersion in catalytic chemical reactors is fundamental to their design, since dispersion influences the reactant and product transport within the bed. In this paper, longitudinal and transverse dispersion of an inert tracer in slender packed beds of spheres and spherocylinders is studied using Computational Fluid Dynamics simulations. The focus is on the analysis of dispersion from full field data. The purpose is to develop a methodology that can later also be used to characterize dispersion from full field experimental data such as MRI measurements. Results obtained by means of particle-resolved CFD simulations are discussed. Spatial distributions and residence times are analyzed and the results are interpreted by comparison to results obtained from 1D and 2D convection-diffusion equations.

Ivette Rodriguez, Oriol Lehmkuhl

The flow topology of the wake behind a circular cylinder at the super-critical Reynolds number of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi><mo>=</mo><mn>7.2</mn><mo>×</mo><msup><mn>10</mn><mn>5</mn></msup></mrow></semantics></math></inline-formula> is investigated by means of large eddy simulations. In spite of the many research works on circular cylinders, there are no studies concerning the main characteristics and topology of the near wake in the super-critical regime. Thus, the present work attempts to fill the gap in the literature and contribute to the analysis of both the unsteady wake and the turbulent statistics of the flow. It is found that although the wake is symmetric and preserves similar traits to those observed in the sub-critical regime, such as the typical two-lobed configuration in the vortex formation zone, important differences are also observed. Owing to the delayed separation of the flow and the transition to turbulence in the attached boundary layer, Reynolds stresses peak in the detached shear layers close to the separation point. The unsteady mean flow is also investigated, and topological critical points are identified in the vortex formation zone and the near wake. Finally, time-frequency analysis is performed by means of wavelets. The study shows that in addition to the vortex shedding frequency, the inception of instabilities that trigger transition to turbulence occurs intermittently in the attached boundary layer and is registered as a phenomenon of variable intensity in time.

Patrick Foltyn, Ferdinand Restle, Markus Wissmann et al.

The measurement of the apparent contact angle on structured surfaces is much more difficult to obtain than on smooth surfaces because the pinning of liquid to the roughness has a tremendous influence on the three phase contact line. The results presented here clearly show an apparent contact angle variation along the three phase contact line. Accordingly, not only one value for the apparent contact angle can be provided, but a contact angle distribution or an interval has to be given to characterize the wetting behavior. For measuring the apparent contact angle distribution on regularly structured surfaces, namely micrometric pillars and grooves, an experimental approach is presented and the results are provided. A short introduction into the manufacturing process of such structured surfaces, which is a combination of Direct LASER Writing (DLW) lithography, electroforming and hot embossing shows the high quality standard of the used surfaces.

Lingxiao Wang, Yin Jiang, Kai Zhou

We propose a general framework to extract microscopic interactions from raw configurations with deep neural networks. The approach replaces the modeling Hamiltonian by the neural networks, in which the interaction is encoded. It can be trained with data collected from Ab initio computations or experiments. The well-trained neural networks give an accurate estimation of the possibility distribution of the configurations at fixed external parameters. It can be spontaneously extrapolated to detect the phase structures since classical statistical mechanics as prior knowledge here. We apply the approach to a 2D spin system, training at a fixed temperature, and reproducing the phase structure. Scaling the configuration on lattice exhibits the interaction changes with the degree of freedom, which can be naturally applied to the experimental measurements. Our approach bridges the gap between the real configurations and the microscopic dynamics with an autoregressive neural network.

Hoang Van Tung, Pham Thanh Hieu

The natural frequencies or related resonant frequencies have been widely used for crack detection in structures by the vibration-based technique. However, antiresonant frequencies, the zeros of frequency response function, are less involved to use for the problem because they have not been thoroughly studied. The present paper addresses analysis of antiresonant frequencies of multiple cracked bar in comparison with the resonant ones. First, exact characteristic equations for the resonant and antiresonant frequencies of bar with arbitrary number of cracks are conducted in a new form that is explicitly expressed in term of crack severities. Then, the conducted equations are employed for analysis of variation of resonant and antiresonant frequencies versus crack position and depth. Numerical results show that antiresonant frequencies are indeed useful indicators for crack detection in bar mutually with the resonant ones.

Francesco Mangraviti, Luca Motto Ros

Answering one of the main questions of [FHK14, Chapter 7], we show that there is a tight connection between the depth of a classifiable shallow theory $T$ and the Borel rank of the isomorphism relation $\cong^κ_T$ on its models of size $κ$, for $κ$ any cardinal satisfying $κ^{< κ} = κ> 2^{\aleph_0}$. This is achieved by establishing a link between said rank and the $\mathcal{L}_{\infty κ}$-Scott height of the $κ$-sized models of $T$, and yields to the following descriptive set-theoretical analogue of Shelah's Main Gap Theorem: Given a countable complete first-order theory $T$, either $\cong^κ_T$ is Borel with a countable Borel rank (i.e. very simple, given that the length of the relevant Borel hierarchy is $κ^+ > \aleph_1$), or it is not Borel at all. The dividing line between the two situations is the same as in Shelah's theorem, namely that of classifiable shallow theories. We also provide a Borel reducibility version of the above theorem, discuss some limitations to the possible (Borel) complexities of $\cong^κ_T$, and provide a characterization of categoricity of $T$ in terms of the descriptive set-theoretical complexity of $\cong^κ_T$.

Jonathan Dunn

This paper uses the Minimum Description Length paradigm to model the complexity of CxGs (operationalized as the encoding size of a grammar) alongside their descriptive adequacy (operationalized as the encoding size of a corpus given a grammar). These two quantities are combined to measure the quality of potential CxGs against unannotated corpora, supporting discovery-device CxGs for English, Spanish, French, German, and Italian. The results show (i) that these grammars provide significant generalizations as measured using compression and (ii) that more complex CxGs with access to multiple levels of representation provide greater generalizations than single-representation CxGs.

Mustafa Gökhan Benli, Burak Kaya

In this paper, we determine the descriptive complexity of subsets of the Polish space of marked groups defined by various group theoretic properties. In particular, using Grigorchuk groups, we establish that the sets of solvable groups, groups of exponential growth and groups with decidable word problem are $\mathbfΣ^0_2$-complete and that the sets of periodic groups and groups of intermediate growth are $\mathbfΠ^0_2$-complete. We also provide bounds for the descriptive complexity of simplicity, amenability, residually finiteness, Hopficity and co-Hopficity. This paper is intended to serve as a compilation of results on this theme.

F. Y. AYANT

F. A. Hendi, M. M. Al-Qarni

Hassanali Aghajani, Masoumeh Ebadattalab, Hossein Jafar et al.