Hadamard’s variational formula in terms of stress and strain tensors

Starting from a Lagrangian action functional for two scalar fields we construct, by variational methods, the Laplacian Green function for a bounded domain and an appropriate stress tensor. By a further variation, imposed by a given vector field, we arrive at an interior version of the Hadamard variational formula, previously considered by P. Garabedian. It gives the variation of the Green function in terms of a pairing between the stress tensor and a strain tensor in the interior of the domain, this contrasting the classical Hadamard formula which is expressed as a pure boundary variation.

An Action Principle for Biological Systems

In the analysis of physical systems, the forces and mechanics of all system changes as codified in the Newtonian laws can be redefined by the methods of Lagrange and Hamilton through an identification of the governing action principle as a more general framework for dynamics. For the living system, it is the dimensional and relational structure of its biologic continuum (both internal and external to the organism) that creates the signature informational metrics and course configurations for the action dynamics associated with any natural systems phenomena. From this dynamic information theoretic framework, an action functional can be also derived in accordance with the methods of Lagrange. The experiential process of acquiring information and translating it into actionable meaning for adaptive responses is the driving force for changes in the living system. The core axiomatic procedure of this adaptive process should include an innate action principle that can determine the system’s directional changes. This procedure for adaptive system reconciliation of divergences from steady state within the biocontinuum can be described by an information metric formulation of the process for actionable knowledge acquisition that incorporates the axiomatic inference of the Kullback’s Principle of Minimum Discrimination Information powered by the mechanics of survival replicator dynamics. This entropic driven trajectory naturally minimizes the biocontinuum information gradient differences like a least action principle and is an inference procedure for directional change. If the mathematical expression of this process is the Lagrangian integrand for adaptive changes within the biocontinuum, then it is also considered as an action functional for the living system.

Simulation of Rare Events in Stochastic Systems

The paper presents algorithms for simulation rare events in stochastic systems based on the theory of large deviations. Here, this approach is used in conjunction with the tools of optimal control theory to estimate the probability that some observed states in a stochastic system will exceed a given threshold by some upcoming time instant. Algorithms for obtaining controlled extremal trajectory (A-profile) of the system, along which the transition to a rare event (threshold) occurs most likely under the influence of disturbances that minimize the action functional, are presented. It is also shown how this minimization can be efficiently performed using numerical-analytical methods of optimal control for linear and nonlinear systems. These results are illustrated by an example for a precipitation-measured monsoon intraseasonal oscillation (MISO) described by a low-order nonlinear stochastic model.

icepack: a new glacier flow modeling package in Python, version 1.0

We introduce a new software package called “icepack” for modeling the flow of glaciers and ice sheets. The icepack package is built on the finite element modeling library Firedrake, which uses the Unified Form Language (UFL), a domain-specific language embedded into Python for describing weak forms of partial differential equations. The diagnostic models in icepack are formulated through action principles that are specified in UFL. The components of each action functional can be substituted for different forms of the user's choosing, which makes it easy to experiment with the model physics. The action functional itself can be used to define a solver convergence criterion that is independent of the mesh and requires little tuning on the part of the user. The icepack package includes the 2D shallow ice and shallow stream models. We have also defined a 3D hybrid model based on spectral semi-discretization of the Blatter–Pattyn equations. Finally, icepack includes a Gauss–Newton solver for inverse problems that runs substantially faster than the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method often used in the glaciological literature. The overall design philosophy of icepack is to be as usable as possible for a wide a swath of the glaciological community, including both experts and novices in computational science.

Poly-symplectic geometry and the AKSZ formalism

In this paper, we extend the AKSZ formulation of the Poisson sigma model to more general target spaces, and we develop the general theory of graded geometry for poly-symplectic and poly-Poisson structures. In particular, we prove a Schwarz-type theorem and transgression for graded poly-symplectic structures, recovering the action functional and the poly-symplectic structure of the reduced phase space of the poly-Poisson sigma model, from the AKSZ construction.

ANALYSIS OF METHODOLOGICAL APPROACHES TO MODERNIZATION OF EDUCATION

The article states that the modernization of education must meet two challenges, as the historical actions taken since the independence of our country have not yet been completed; The importance of the scientific basis for the analysis of methodological approaches to the modernization of education, the content analysis of methodological approaches to the modernization of education without showing that the scientific approach is based on pedagogical theory; As a result of content analysis, guided by the most common definition of educational modernization, it is proved that complex, systematic, action, functional, dynamic approaches can be used for its study, and the potential of other approaches should not be ignored.

Strengthening the Reporting of Nutritional Genomics Research to Inform Knowledge Translation in Personalized Nutrition

The ultimate goal of researching nutrigenetic interactions is to be able to provide individuals with genetically-tailored nutrition advice (when evidence is sufficient) in an effort to optimize health outcomes. Accordingly, original research often discusses the potential for the results to inform genetically-tailored nutrition advice. Despite this, many studies do not report their methods, results, and discussion in a manner that is conducive to knowledge translation. With several consumer nutritional genomics companies now offering genetic testing for personalized nutrition, proper reporting of nutritional genomics research for knowledge translation is of vital importance. Common reporting errors relate to SNP and genotype reporting, results lacking detail, consideration of linkage disequilibrium, mechanisms of action/functional SNPs, details of dietary intake, and sample reporting. Because of this, knowledge translation professionals may be unable or challenged in their attempt to use the findings from such research to inform clinical practice in nutritional genomics and personalized nutrition. The present article provides an overview of the issues at hand. It further pre­sents a checklist as well as table and figure templates for researchers to use when reporting the results of original research in nutritional genomics to inform knowledge translation.

<i>icepack</i>: a new glacier flow modeling package in Python, version 1.0

We introduce a new software package called icepack for modeling the flow of glaciers and ice sheets. Icepack is built on the finite element modeling library Firedrake, which uses the domain-specific language UFL for describing weak forms of partial differential equations. The diagnostic models in icepack are formulated through action principles that are specified in UFL. The components of each action functional can be substituted for different forms of the user’s choosing, which makes it easy to experiment with the model physics. The action functional itself can be used to define a solver convergence criterion that is independent of the mesh and requires little tuning on the part of the user. Icepack includes the 2D shallow ice and shallow stream models. We have also defined a 3D hybrid model based on spectral semi-discretization of the Blatter-Pattyn equations. Finally, icepack includes a Gauss-Newton solver for inverse problems that runs substantially faster than the BFGS method often used in the glaciological literature. The overall design philosophy of icepack is to be as usable as possible for a wide a swath of the glaciological community, including both experts and novices in computational science.

Оn momentum flow density of the gravitational field

Momentum is considered on the basis of the approach widely used in the calculus of variations and in the optimal control theory, where variation of a cost functional is investigated. In physical theory, it is the action functional. Action variation under Lie dragging can be expressed as a surface integral of some differential form. The momentum density flow is defined using this form. In this work, the momentum balance equation is obtained. This equation shows that the momentum field transforms into a momentum of a mass. Examples showing the momentum flow structure for a mass distribution representing a uniform thin layer are provided.

Variational principle for electromagnetic hydrodynamics of plasma

Within the framework of the Lagrangian approach, a mathematically correct procedure is given for obtaining the necessary conditions of locextr from the variational principle for a number of continuous media that fill a certain geometric region at each moment of time and does not leave it over time. The proposed method is based on the geometric properties of the set of diffeomorphisms of the indicated domain, which is the configuration space of a continuous medium, and on a certain embedding theorem. The efficiency of the method is demonstrated by examples of obtaining the necessary locextr conditions from variational principles for ideal gas dynamics and classical MHD plasma. The central result of the work is the construction of the variational principle, in particular, the Lagrangian and the action functional for the theory of electromagnetic hydrodynamics of plasma.