Related papers: Symbolic-Numeric Integration of the Dynamical Coss…
A general formulation was developed to represent material models for applications in dynamic loading. Numerical methods were devised to calculate response to shock and ramp compression, and ramp decompression, generalizing previous…
We develop a new algebraic setting for treating piecewise functions and distributions together with suitable differential and Rota-Baxter structures. Our treatment aims to provide the algebraic underpinning for symbolic computation systems…
Nonlinear dynamics is a pervasive phenomenon observed in scientific and engineering disciplines. However, the task of deriving analytical expressions to describe nonlinear dynamics from limited data remains challenging. In this paper, we…
This paper deals with the numerical integration of Hamiltonian systems in which a stiff anharmonic potential causes highly oscillatory solution behavior with solution-dependent frequencies. The impulse method, which uses micro- and…
The paper presents a constraint-based collision model for Cosserat rods, able to handle dynamic or static contact between a large number of highly flexible structures. The model provides the required collision impulses prior to updating the…
A new algorithm for numerical integration of the rigid-body equations of motion is proposed. The algorithm uses the leapfrog scheme and the quantities involved are angular velocities and orientational variables which can be expressed in…
Nonlinear thermoelastic systems play a crucial role in understanding thermal conductivity, stresses, elasticity, and temperature interactions. This research focuses on finding solutions to these systems in their fractional forms, which is a…
We propose neural-symbolic integration for abstract concept explanation and interactive learning. Neural-symbolic integration and explanation allow users and domain-experts to learn about the data-driven decision making process of large…
In this work, we develop novel structure-preserving numerical schemes for a class of nonlinear Fokker--Planck equations with nonlocal interactions. Such equations can cover many cases of importance, such as porous medium equations with…
We propose a first example of a simple classical field theory with nonholonomic constraints. Our model is a straightforward modification of a Cosserat rod. Based on a mechanical analogy, we argue that the constraint forces should be modeled…
A new approach is developed to integrate numerically the equations of motion for systems of interacting rigid polyatomic molecules. With the aid of a leapfrog framework, we directly involve principal angular velocities into the integration,…
Two effective methods for writing the dynamical equations for non-holonomic systems are illustrated. They are based on the two types of representation of the constraints: by parametric equations or by implicit equations. They can be applied…
Integral asymptotics play an important role in the analysis of differential equations and in a variety of other settings. In this work, we apply an integral asymptotics approach to study spatially localized solutions of a heterogeneous…
This paper aims to initialize a dynamical aspect of symbolic integration by studying stability problems in differential fields. We present some basic properties of stable elementary functions and D-finite power series that enable us to…
We present a new geometrically nonlinear Cosserat shell model incorporating effects up to order $O(h^5)$ in the shell thickness $h$. The method that we follow is an educated 8-parameter ansatz for the three-dimensional elastic shell…
Collision detection plays a key role in the simulation of interacting rigid bodies. However, owing to its computational complexity current methods typically prioritize either maximizing processing speed or fidelity to real-world behaviors.…
In this paper, we introduce an iterative numerical method to solve systems of nonlinear equations. The third-order convergence of this method is analyzed. Several examples are given to illustrate the efficiency of the proposed method.
The semiring of discrete dynamical systems is a simple algebraic model for modularity in deterministic systems. The objects of the semiring are finite transformations (viewed as directed graphs and regarded up to isomorphism), the sum of…
Nonlinear dynamics and pattern formation in the systems with quadratic nonlinearity is computed symbolically by specially developed MATHEMATICA package. A Web interface for the presented methods is developed, which turns the implementations…
The quest for analytical solutions to differential equations has traditionally been constrained by the need for extensive mathematical expertise. Machine learning methods like genetic algorithms have shown promise in this domain, but are…