Kristof T. Schütt, M. Gastegger, A. Tkatchenko
et al.
Machine learning advances chemistry and materials science by enabling large-scale exploration of chemical space based on quantum chemical calculations. While these models supply fast and accurate predictions of atomistic chemical properties, they do not explicitly capture the electronic degrees of freedom of a molecule, which limits their applicability for reactive chemistry and chemical analysis. Here we present a deep learning framework for the prediction of the quantum mechanical wavefunction in a local basis of atomic orbitals from which all other ground-state properties can be derived. This approach retains full access to the electronic structure via the wavefunction at force-field-like efficiency and captures quantum mechanics in an analytically differentiable representation. On several examples, we demonstrate that this opens promising avenues to perform inverse design of molecular structures for targeting electronic property optimisation and a clear path towards increased synergy of machine learning and quantum chemistry. Machine learning models can accurately predict atomistic chemical properties but do not provide access to the molecular electronic structure. Here the authors use a deep learning approach to predict the quantum mechanical wavefunction at high efficiency from which other ground-state properties can be derived.
Nanofluidics has firmly established itself as a new field in fluid mechanics, as novel properties have been shown to emerge in fluids at the nanometric scale. Thanks to recent developments in fabrication technology, artificial nanofluidic systems are now being designed at the scale of biological nanopores. This ultimate step in scale reduction has pushed the development of new experimental techniques and new theoretical tools, bridging fluid mechanics, statistical mechanics, and condensed matter physics. This review is intended as a toolbox for fluids at the nanometer scale. After presenting the basic equations that govern fluid behavior in the continuum limit, we show how these equations break down and new properties emerge in molecular-scale confinement. A large number of analytical estimates and physical arguments are given to organize the results and different limits.
MA-semirings form a proper subclass of inverse semirings that properly contains both the class of rings and the class of distributive lattices with the least element. In this paper, we study generalized derivations satisfying certain algebraic identities of MA-semirings with involution. The main objective of this research is to investigate identities involving three, two, one generalized derivation in MA-semirings with involution, ensuring commutativity. Hermitian and skew-Hermitian elements are primarily used to formulate the basic tools for the development of this paper and these notions are the fundamental units of the second kind involution. Involution of the second kind plays a key role not only for proving the main results (see Theorems 1, 3, 5) but also it enables us to observe more results from their proofs (see Theorems 2, 4, 6). Since every derivation is a generalized derivation, the results obtained naturally extend a variety of results on derivations. Moreover, several well-established results on derivations of MA-semirings and rings under the similar environment can be concluded as special cases.
In this paper, we study a class of nonlocal boundary value problems for elliptic-parabolic equations subject to integral-type conditions. Such problems naturally emerge in various physical and engineering contexts, including diffusion processes in composite materials and systems with memory or nonlocal interactions. The model considered involves a mixed-type equation in which the elliptic and parabolic components are coupled through nonlocal boundary terms, while the boundary conditions incorporate integral constraints that generalize the traditional Dirichlet and Neumann formulations. To investigate the solvability of this problem, we employ analytical methods based on the theory of parabolic and elliptic operators in weighted Ho¨lder spaces, which are particularly suitable for handling boundary singularities and ensuring regularity of solutions. We establish the existence, uniqueness, and continuous dependence of solutions on the input data, thereby proving the well-posedness of the problem. Furthermore, we derive coercivity inequalities for solutions of the associated mixed nonlocal boundary problems, which guarantee their stability and provide essential tools for studying related inverse and control problems. The findings extend several classical results and offer a unified approach to the analysis of nonlocal elliptic-parabolic models.
Drop shafts play a vital role in urban drainage and tunnel sewerage systems. To gain an insight into the magnitude of transient flow fluctuations inside a drop shaft attached to a scroll vortex intake, large eddy simulations (LESs) are performed in this study. First, the LES predictions are validated against experimental data from Guo (2012), demonstrating good agreement for both the time-averaged head-discharge relationship and the minimum air-core percentage. Subsequently, the transient fluctuations of the air core inside the drop shaft are investigated, with the worst-case scenario being choking of the air core inside the drop shaft, which might lead to a grave consequence to the system response. The transient fluctuations of the air core are found to have up to 13 % variation in the non-dimensional air-core area due to dynamic contraction and expansion. Additionally, velocity characteristics at different vertical and angular locations within the drop shaft are analysed, offering new insights into vortex structures and challenging assumptions from existing analytical models. The transient simulation results also reveal a global vortex structure together with embedded small-scale vortices using the
$\Omega$
-criterion vortex identification method.
The study of classes of first-order countable language models and their properties is an important direction in model theory. Of particular interest are axiomatizable classes of models (varieties, quasivarieties, finitely axiomatizable classes, Jonssonian classes, etc.). In this paper we present the results obtained on the properties of formula-definable classes of models and formula-definable semigroups of elementary types, namely, we study the properties of semigroups of elementary types of models in a first-order language. We consider products of elementary types which form a commutative semigroup with unit. A two-place relation of absorption of one elementary type by another is introduced, which allows us to distinguish formula-definable semigroups of elementary types and corresponding classes of models. On the basis of the axiomatizability property of formula-definite semigroups of elementary types, their connection with ultraproducts and infinite products is established. Examples of idempotently formula-definite and non-idempotently formuladefinite semigroups are given, and their peculiarities are discussed. The paper demonstrates both the study of semigroups of elementary types and the study of properties of formula-definite classes of models.
Previously, boundary control problems for the second order parabolic type equation in the bounded domain were studied. In this paper, a boundary control problem associated with a fourth-order parabolic equation in a bounded two-dimensional domain was considered. On the part of the considered domain’s boundary, the value of the solution with control function is given. Restrictions on the control are given in such a way that the average value of the solution in the considered domain gets a given value. By the method of separation of variables the given problem is reduced to a Volterra integral equation of the first kind. The existence of the control function was proved by the Laplace transform method and an estimate was found for the minimal time at which the given average temperature in the domain is reached.
Singularly perturbed integro-differential equations with degenerate kernels are considered. It is shown that in the linear case these problems are always uniquely solvable with continuous coefficients, while nonlinear problems either have no real solutions at all or have several of them. For linear problems, the results of Bobojanova are refined; in particular, necessary and sufficient conditions are given for the existence of a finite limit of their solutions as the small parameter tends to zero and sufficient conditions under which the passage to the limit to the solution of the degenerate equation is possible.
This paper presents a novel approach to developing a work roll prediction model that takes into account both the mechanism and condition influences on work roll wear. This was accomplished by conducting an analytic calculation of work roll mechanism influence, constructing a work roll wear model, and combining the wear mechanism with actual wear data. The resulting model is applicable to both symmetric and asymmetric wear of the work roll, and experimental results showed that the relative error between measured and predicted values was less than 5%, with a maximum error of below 15%. This level of accuracy is sufficient for predicting roll wear and lays the foundation for improved strip shape control and roll design. Furthermore, this approach has the potential to generate significant economic benefits and has wide-ranging applications.
A.Zh. Seitmuratov, N.K. Medeubaev, T.T. Kozhoshov
et al.
When solving integrodifferential equations under boundary conditions, taking into account physical nonlinearity, a broad class of boundary-value problems of oscillations arises associated with various boundary conditions at the edges of a flat element. When taking into account non-stationary external influences, the main parameters is the frequency of natural vibrations of a flat component, taking into account temperature, prestressing, and other factors. The study of such problems, taking into account complicating factors, reduces to solving rather complex problems. The difficulty of solving these problems is due to both the type of equations and the variety. We analyze the results of previous works on the boundary problems of vibrations of plane elements. Possible boundary conditions at the edges of a flat element and the necessary initial conditions for solving particular problems of self-oscillation and forced vibrations, and other problems are considered. The set of equations, boundaries, and initial conditions make it possible to formulate and solve various boundary value problems of vibrations for a flat element. The oscillation equations for a flat element in the form of a plate given in this paper contain viscoelastic operators that describe the viscous behavior of the materials of a flat component. In studying oscillations and wave processes, it is advisable to take the kernels of viscoelastic operators regularly, since only such operators describe instantaneous elasticity and then viscous flow.
Ghazala Akram, Maasoomah Sadaf, Iqra Zainab
et al.
The time-fractional nonlinear Drinfeld–Sokolov–Wilson system, which has significance in the study of traveling waves, shallow water waves, water dispersion, and fluid mechanics, is examined in the presented work. Analytic exact solutions of the system are produced using the modified auxiliary equation method. The fractional implications on the model are examined under <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-fractional derivative and a new fractional local derivative. Extracted solutions include rational, trigonometric, and hyperbolic functions with dark, periodic, and kink solitons. Additionally, by specifying values for fractional parameters, graphs are utilized to comprehend the fractional effects on the obtained solutions.
Abstract We compute the first-order α ′ corrections to a family of 4-dimensional, 4-charge, non-extremal black hole solutions of Heterotic Supergravity in the case with 3 independent charges. The solutions are fully analytic, reproduce the extremal limit previously found in the literature and, applying T-duality, they transform as expected. If we reduce to the case with a single independent charge we obtain the corrections to four embeddings of the Reissner-Nordström black hole in string theory. We completely characterize the black hole thermodynamics computing the Hawking temperature, Wald entropy, mass, gauge charges and their dual thermodynamic potentials. We verify that all these quantities are related by the first law of extended black hole mechanics and the Smarr formula once we include a potential associated to the dimensionful parameter α ′ and the scalar charges. We found that the latter are not identified with the poles at infinity of the scalar fields because they receive α ′ corrections.
Nuclear and particle physics. Atomic energy. Radioactivity
The paper considers Morrey-type local spaces from LMpθw The main work is the proof of the commutator compactness theorem for the Riesz potential [b,Iα] in local Morrey-type spaces from LMpθw1 to LMpθw2. We also give new sufficient conditions for the commutator to be bounded for the Riesz potential [b,Iα] in local Morrey-type spaces from LMpθw1 to LMpθw2. In the proof of the commutator compactness theorem for the Riesz potential, we essentially use the boundedness condition for the commutator for the Riesz potential [b,Iα] in local Morrey-type spaces LMpθw, and use the sufficient conditions from the theorem of precompactness of sets in local spaces of Morrey type LMpθw. In the course of proving the commutator compactness theorem for the Riesz potential, we prove lemmas for the commutator ball for the Riesz potential [b,Iα]. Similar results were obtained for global Morrey-type spaces GMpθw and for generalized Morrey spaces Mpw.