Bibliografie tematiche / Test-First-Ansatz

Letteratura scientifica selezionata sul tema "Test-First-Ansatz"

Autore: Grafiati
Pubblicato: 27 luglio 2024
Ultima modifica: 29 luglio 2024

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Articoli di riviste sul tema "Test-First-Ansatz"

1

Waimann, Johanna, Philipp Junker e Klaus Hackl. "A variational material model for transformation-induced plasticity in polycrystalline steels". Journal of the Mechanical Behavior of Materials 24, n. 5-6 (1 dicembre 2015): 153–59. http://dx.doi.org/10.1515/jmbm-2015-0022.

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AbstractThis work presents a variational material model for transformation-induced plasticity in steels. We will use the principle of the minimum of the dissipation potential to develop a coupled material model for plastic deformations and phase transformations that simultaneously accounts for the hardening effects that play an important role. We will use a polycrystalline approach and introduce a combined Voigt/Reuß bound and a coupled ansatz for the dissipation functional to model the simultaneous effects of plastic deformations and phase transformations. Finally, we will present the first numerical results for a tension/compression test.
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2

Saleh, Mahmoud, Endre Kovács, Imre Ferenc Barna e László Mátyás. "New Analytical Results and Comparison of 14 Numerical Schemes for the Diffusion Equation with Space-Dependent Diffusion Coefficient". Mathematics 10, n. 15 (8 agosto 2022): 2813. http://dx.doi.org/10.3390/math10152813.

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We examine the one-dimensional transient diffusion equation with a space-dependent diffusion coefficient. Such equations can be derived from the Fokker–Planck equation and are essential for understanding the diffusion mechanisms, e.g., in carbon nanotubes. First, we construct new, nontrivial analytical solutions with the classical self-similar Ansatz in one space dimension. Then we apply 14 different explicit numerical time integration methods, most of which are recently introduced unconditionally stable schemes, to reproduce the analytical solution. The test results show that the best algorithms, especially the leapfrog-hopscotch, are very efficient and severely outperform the conventional Runge–Kutta methods. Our results may attract attention in the community who develops multi-physics engineering software.
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3

Frodl, P., F. T. Sommer, K. Hau e F. Wahl. "On the Effective Interaction of two Hydrogen Centres in Niobium". Zeitschrift für Naturforschung A 45, n. 7 (1 luglio 1990): 857–66. http://dx.doi.org/10.1515/zna-1990-0704.

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AbstractWe derive an effective interaction between hydrogen impurities in Niobium using a microscopic theory of hydrogen in metals. Our model consists of an infinite bcc-crystal with two hydrogen centres occupying tetrahedral interstitial sites, neighbouring on the first to the fourth coordination shell. The elastic interactions are assumed to obey the classical harmonic approximation. The electronic interactions due to both the coulomb potentials and the overlap of the impurity induced electron densities in the vicinity of the interstitials also play an important role. These latter interactions are treated as two-body interactions in a zeroth order approximation of the New Tamm-Dancoffmethod. A separation ansatz results in an effective interaction which depends on the distance between the interstitials and upon the spin states of their excess electrons. We propose some improvements on our model, and to test our calculations, we construct the grand partition function of an appropriate lattice gas model.
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4

Askar, Ali Habeeb, Ádám Nagy, Imre Ferenc Barna e Endre Kovács. "Analytical and Numerical Results for the Diffusion-Reaction Equation When the Reaction Coefficient Depends on Simultaneously the Space and Time Coordinates". Computation 11, n. 7 (29 giugno 2023): 127. http://dx.doi.org/10.3390/computation11070127.

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We utilize the travelling-wave Ansatz to obtain novel analytical solutions to the linear diffusion–reaction equation. The reaction term is a function of time and space simultaneously, firstly in a Lorentzian form and secondly in a cosine travelling-wave form. The new solutions contain the Heun functions in the first case and the Mathieu functions for the second case, and therefore are highly nontrivial. We use these solutions to test some non-conventional explicit and stable numerical methods against the standard explicit and implicit methods, where in the latter case the algebraic equation system is solved by the preconditioned conjugate gradient and the GMRES solvers. After this verification, we also calculate the transient temperature of a 2D surface subjected to the cooling effect of the wind, which is a function of space and time again. We obtain that the explicit stable methods can reach the accuracy of the implicit solvers in orders of magnitude shorter time.
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5

Bokulić, Ana, e Ivica Smolić. "Immersing the Schwarzschild Black Hole in Test Nonlinear Electromagnetic Fields". Physical Sciences Forum 2, n. 1 (22 febbraio 2021): 22. http://dx.doi.org/10.3390/ecu2021-09301.

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Killing vector fields can be used as gauge vector potentials since the associated electromagnetic field tensor automatically satisfies the source-free Maxwell’s equations in vacuum spacetimes. This fact enabled Wald to find the form of the electromagnetic tensor corresponding to the Kerr black hole immersed in a uniform test magnetic field. We present the generalisation of this result, which is valid for static black holes surrounded by nonlinear electromagnetic fields. The first obstacle we encountered when dealing with the nonlinear electrodynamics was that the above-described ansatz no longer works. Secondly, finding the exact solution in a closed form proved to be a rather challenging task because it would require solving a highly nonlinear differential equation. The alternative approach is via perturbative expansion around the original Wald’s solution. We obtain the equation which determines the lowest order correction to the gauge vector field 1-form and magnetic scalar potential. With the main focus on the Born–Infeld and Euler–Heisenberg theories on the Schwarzschild background, we calculate the aforementioned correction. Additionally, we show that this perturbative correction does not change electric and magnetic Komar charges or the asymptotic behaviour of the field. Finally, stating physical arguments, we justify the usage of the perturbative approach.
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6

Sim, Fabio M., Eka Budiarto e Rusman Rusyadi. "Comparison and Analysis of Neural Solver Methods for Differential Equations in Physical Systems". ELKHA 13, n. 2 (22 ottobre 2021): 134. http://dx.doi.org/10.26418/elkha.v13i2.49097.

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Differential equations are ubiquitous in many fields of study, yet not all equations, whether ordinary or partial, can be solved analytically. Traditional numerical methods such as time-stepping schemes have been devised to approximate these solutions. With the advent of modern deep learning, neural networks have become a viable alternative to traditional numerical methods. By reformulating the problem as an optimisation task, neural networks can be trained in a semi-supervised learning fashion to approximate nonlinear solutions. In this paper, neural solvers are implemented in TensorFlow for a variety of differential equations, namely: linear and nonlinear ordinary differential equations of the first and second order; Poisson’s equation, the heat equation, and the inviscid Burgers’ equation. Different methods, such as the naive and ansatz formulations, are contrasted, and their overall performance is analysed. Experimental data is also used to validate the neural solutions on test cases, specifically: the spring-mass system and Gauss’s law for electric fields. The errors of the neural solvers against exact solutions are investigated and found to surpass traditional schemes in certain cases. Although neural solvers will not replace the computational speed offered by traditional schemes in the near future, they remain a feasible, easy-to-implement substitute when all else fails.
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7

Berry, Tyrus, e John Harlim. "Linear theory for filtering nonlinear multiscale systems with model error". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, n. 2167 (8 luglio 2014): 20140168. http://dx.doi.org/10.1098/rspa.2014.0168.

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In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online , as part of a filtering procedure, simultaneously produce accurate filtering and equilibrium statistical prediction. In contrast, an offline estimation technique based on a linear regression, which fits the parameters to a training dataset without using the filter, yields filter estimates which are worse than the observations or even divergent when the slow variables are not fully observed. This finding does not imply that all offline methods are inherently inferior to the online method for nonlinear estimation problems, it only suggests that an ideal estimation technique should estimate all parameters simultaneously whether it is online or offline.
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8

Hou, Jue, Yunfeng Jiang e Yuan Miao. "Rational Q-systems at root of unity I. Closed chains". SciPost Physics 16, n. 5 (22 maggio 2024). http://dx.doi.org/10.21468/scipostphys.16.5.129.

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Abstract (sommario):
The solution of Bethe Ansatz equations for XXZ spin chain with the parameter q being a root of unity is infamously subtle. In this work, we develop the rational Q-system for this case, which offers a systematic way to find all physical solutions of the Bethe Ansatz equations at root of unity. The construction contains two parts. In the first part, we impose additional constraints to the rational Q-system. These constraints eliminate the so-called Fabricius-McCoy (FM) string solutions, yielding all primitive solutions. In the second part, we give a simple procedure to construct the descendant tower of any given primitive state. The primitive solutions together with their descendant towers constitute the complete Hilbert space. We test our proposal by extensive numerical checks and apply it to compute the torus partition function of the 6-vertex model at root of unity.
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9

Bargheer, Till, Thiago Fleury e Vasco Gonçalves. "Higher-point integrands in $\mathcal{N} = 4$ super Yang-Mills theory". SciPost Physics 15, n. 2 (10 agosto 2023). http://dx.doi.org/10.21468/scipostphys.15.2.059.

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Abstract (sommario):
We compute the integrands of five-, six-, and seven-point correlation functions of twenty-prime operators with general polarizations at the two-loop order in \mathcal{N}=4𝒩=4 super Yang-Mills theory. In addition, we compute the integrand of the five-point function at three-loop order. Using the operator product expansion, we extract the two-loop four-point function of one Konishi operator and three twenty-prime operators. Two methods were used for computing the integrands. The first method is based on constructing an ansatz, and then numerically fitting for the coefficients using the twistor-space reformulation of \mathcal{N}=4𝒩=4 super Yang-Mills theory. The second method is based on the OPE decomposition. Only very few correlator integrands for more than four points were known before. Our results can be used to test conjectures, and to make progresses on the integrability-based hexagonalization approach for correlation functions.
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10

Haug, Tobias, e Kishor Bharti. "Generalized Quantum Assisted Simulator". Quantum Science and Technology, 25 luglio 2022. http://dx.doi.org/10.1088/2058-9565/ac83e7.

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Abstract (sommario):
Abstract We provide a noisy intermediate-scale quantum framework for simulating the dynamics of open quantum systems, generalized time evolution, non-linear differential equations and Gibbs state preparation. Our algorithm does not require any classical-quantum feedback loop, bypass the barren plateau problem and does not necessitate any complicated measurements such as the Hadamard test. We introduce the notion of the hybrid density matrix, which allows us to disentangle the different steps of our algorithm and delegate classically demanding tasks to the quantum computer. Our algorithm proceeds in three disjoint steps. First, we select the ansatz, followed by measuring overlap matrices on a quantum computer. The final step involves classical post-processing data from the second step. Our algorithm has potential applications in solving the Navier-Stokes equation, plasma hydrodynamics, quantum Boltzmann training, quantum signal processing and linear systems. Our entire framework is compatible with current experiments and can be implemented immediately.
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Libri sul tema "Test-First-Ansatz"

1

Beck, Kent. Test Driven Development: By Example. Pearson Education, Limited, 2022.

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2

Beck, Kent. Test Driven Development: By Example. Pearson Education, Limited, 2022.

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3

Beck, Kent. Test Driven Development: By Example (The Addison-Wesley Signature Series). Addison-Wesley Professional, 2002.

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4

Test-driven development: By Example. Addison-Wesley, 2006.

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5

Test-Driven development by Example. AWP, 2002.

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6

Test-driven development: By example. Boston: Addison-Wesley, 2003.

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