Parametric synthesis of stabilizing neurocular control of a technological module

The article proposes a new approach to combined parametric synthesis (synthesis in real or accelerated time) of neuroregulators of multidimensional and multi-connected physical systems and technological processes based on the application of the velocity gradient method in differential form and the theory of sliding modes.

Hereditary low-mode dynamo model

В данной статье рассматривается модель динамо в виде двумерной динамической системы в интегро-дифференциальной форме. В модели реализован стабилизирующий генерацию поля механизм обратной связи в виде подавления α-эффекта функционалом сверточного типа от актуальных и предыдущих значений спиральности и энергии. Наличие этого механизма подавления вводит в модель эредитарность (память). Для модели была построена численная схема ввиде совмещение разностных схем для дифференциальной и интегральной части, двухступенчатый неявный методы Рунге-Кутты и метод трапеций соотвественно. Так же были рассмотрены и графически представлены динамические режимы нашей модели. This article discusses a dynamo model in the form of a two-dimensional dynamical system in integro-differential form. The model implements a stabilizing polarization generator in the form of suppression of the a effect of convolutional type functional from current and previous helicity and energy values. The presence of this suppression mechanism introduces hereditarity (memory) into the model. For modeling, a digital scheme was constructed in the form of a combination of difference schemes for the differential and integral parts, a twostep implicit Runge-Kutta method and a trapezium method, respectively. We also reviewed and graphically presented the dynamic modes of our model.

Nearly constant Q dissipative models and wave equations for general viscoelastic anisotropy

The quality factor ( Q ) links seismic wave energy dissipation to physical properties of the Earth’s interior, such as temperature, stress and composition. Frequency independence of Q , also called constant Q for brevity, is a common assumption in practice for seismic Q inversions. Although exactly and nearly constant Q dissipative models are proposed in the literature, it is inconvenient to obtain constant Q wave equations in differential form, which explicitly involve a specified Q parameter. In our recent research paper, we proposed a novel weighting function method to build the first- and second-order nearly constant Q dissipative models. Of importance is the fact that the wave equations in differential form for these two models explicitly involve a specified Q parameter. This behaviour is beneficial for time-domain seismic waveform inversion for Q , which requires the first derivative of wavefields with respect to Q parameters. In this paper, we extend the first- and second-order nearly constant Q models to the general viscoelastic anisotropic case. We also present a few formulations of the nearly constant Q viscoelastic anisotropic wave equations in differential form.

Time-Independent Plasticity Formulated by Inelastic Differential of Free Energy Function

The authors presented a time-independent plasticity approach, where a typical plastic-loading process is viewed as an infinitesimal state change of two neighboring equilibrium states, and the yield and consistency conditions are formulated based on the conjugate forces of the internal variables. In this paper, a stability condition is proposed, and the yield, consistency, and stability conditions are reformatted by the inelastic differential form of the Gibbs free energy. The Gibbs equation in thermodynamics with internal variables is a representation to the differential form of the Gibbs free energy by a single Gibbs free energy function. In this paper, we propose the so-called extended Gibbs equation, where the differential form may be represented by multiple potential functions. Various associated and nonassociated plasticity with a single or multiple yield functions can be derived from various representations based on the reformulated approach, where yield and plastic potential functions are in the form of inelastic differentials of the potential functions. The generalized Drucker inequality can only be derived from the one-potential representation as a stability condition. For a multiple-potential representation, the stability condition can be ensured if the multiple potentials are concave functions and possess the same stationary point.

Polynomial duality-symmetric lagrangians for free p-forms

We explore the properties of polynomial Lagrangians for chiral p-forms previously proposed by the last named author, and in particular, provide a self-contained treatment of the symmetries and equations of motion that shows a great economy and simplicity of this formalism. We further use analogous techniques to construct polynomial democratic Lagrangians for general p-forms where electric and magnetic potentials appear on equal footing as explicit dynamical variables. Due to our reliance on the differential form notation, the construction is compact and universally valid for forms of all ranks, in any number of dimensions.

Retraction Note: Proofs to one inequality conjecture for the non-integer part of a nonlinear differential form

This article has been retracted. Please see the Retraction Notice for more detail: https://doi.org/10.1186/s13660-021-02555-5

GenChem v1.0 – a chemical pre-processing and testing system for atmospheric modelling

This paper outlines the structure and usage of the GenChem system, which includes a chemical pre-processor GenChem.py) and a simple box model (boxChem). GenChem provides scripts and input files for converting chemical equations into differential form for use in atmospheric chemical transport models (CTMs) and/or the boxChem system. Although GenChem is primarily intended for users of the Meteorological Synthesizing Centre – West of the European Monitoring and Evaluation Programme (EMEP MSC-W) CTM and related systems, boxChem can be run as a stand-alone chemical solver, enabling for example easy testing of chemical mechanisms against each other. This paper presents an outline of the usage of the GenChem system, explaining input and output files, and presents some examples of usage. The code needed to run GenChem is released as open-source code under the GNU license.

Extending the global-direction stencil with “face-area-weighted centroid” to unstructured finite volume discretization from integral form

Accuracy of unstructured finite volume discretization is greatly influenced by the gradient reconstruction. For the commonly used k-exact reconstruction method, the cell centroid is always chosen as the reference point to formulate the reconstructed function. But in some practical problems, such as the boundary layer, cells in this area are always set with high aspect ratio to improve the local field resolution, and if geometric centroid is still utilized for the spatial discretization, the severe grid skewness cannot be avoided, which is adverse to the numerical performance of unstructured finite volume solver. In previous work [Kong, et al. Chin Phys B 29(10):100203, 2020], we explored a novel global-direction stencil and combined it with the face-area-weighted centroid on unstructured finite volume methods from differential form to realize the skewness reduction and a better reflection of flow anisotropy. Greatly inspired by the differential form, in this research, we demonstrate that it is also feasible to extend this novel method to the unstructured finite volume discretization from integral form on both second and third-order finite volume solver. Numerical examples governed by linear convective, Euler and Laplacian equations are utilized to examine the correctness as well as effectiveness of this extension. Compared with traditional vertex-neighbor and face-neighbor stencils based on the geometric centroid, the grid skewness is almost eliminated and computational accuracy as well as convergence rate is greatly improved by the global-direction stencil with face-area-weighted centroid. As a result, on unstructured finite volume discretization from integral form, the method also has superiorities on both computational accuracy and convergence rate.

The method of the compact video frames representation, which are presented in a differential form in computer systems

The most preferable method for constructing the compact representation technology of the binary masks of frames represented in a differential form is the approach. This is based on the identification and description of the lengths of one–dimensional binary series. A binary series is a consecutive binary elements sequence with the same value. In this case, sequences of identical binary elements are replaced by their lengths. And since the elements of the binary masks of the frames represented in the differential form take only two possible values 0 or 1, it is suggested to form the lengths of the binary series without indicating their level.