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Sphere packings are essential to the development of physical models for powders, composite materials, and the atomic structure of the liquid state. There is a strong scientific need to be able to assess the fit of packing models to data,…

This paper is concerned with determining the shortest path for a pursuer aiming to intercept a moving target travelling at a constant speed. To address this challenge, we introduce an efficient mathematical model outlined as an optimal…

Problem definition: Data-driven models in machine learning have enabled efficient management of production systems. However, a majority of machine learning models are devoted to modeling the mean response or average pattern, which is…

Lobe dynamics and escape from a potential well are general frameworks introduced to study phase space transport in chaotic dynamical systems. While the former approach studies how regions of phase space are transported by reducing the flow…

We present a mathematical model to predict pedestrian motion over a finite horizon, intended for use in collision avoidance algorithms for autonomous driving. The model is based on a road map structure, and assumes a rational pedestrian…

In this review, we present some advanced algorithms and programs used in our scientific school with short description of types of astrophysical systems, which we study. However, we discuss mainly mathematical methods, which may be applied…

With advancements in technology, commercial aircraft formation flying is becoming increasingly feasible as an efficient and environmentally friendly flight method. However, gaps remain in practical implementation, particularly in collision…

In trajectory planning and control design for unmanned air vehicles, highly simplified models are typically used to represent the vehicle dynamics and the operating environment. The goal of this work is to perform real-time, but realistic…

Computational modeling of aerodynamics is a key problem in aerospace engineering, often involving flows interacting with solid objects such as airfoils. Deep surrogate models have emerged as purely data-driven approaches that learn direct…

Designing robust machine learning systems remains an open problem, and there is a need for benchmark problems that cover both environmental changes and evaluation on a downstream task. In this work, we introduce AVOIDDS, a realistic object…

Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to…

This brief review focuses on methods and applications of modeling exoplanetary atmospheres. We discuss various kinds of state of the art self-consistent and retrieval models in 1D and multi-D with a focus on open questions and short- and…

Autonomous unpowered flight is a challenge for control and guidance systems: all the energy the aircraft might use during flight has to be harvested directly from the atmosphere. We investigate the design of an algorithm that optimizes the…

In this paper we investigate mixing and transport in correspondence of a meandering jet. The large-scale flow field is a kinematically assigned streamfunction. Two basic mixing mechanisms are considered, first separately and then combined…

A most important aspect in the field of traffic modeling is the simulation of bottleneck situations. For their realistic description a macroscopic multi-lane model for uni-directional freeways including acceleration, deceleration, velocity…

In recent years modelling crowd and evacuation dynamics has become very important, with increasing huge numbers of people gathering around the world for many reasons and events. The fact that our global population grows dramatically every…

Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…

Machine learning (ML) has been increasingly used to aid aerodynamic shape optimization (ASO), thanks to the availability of aerodynamic data and continued developments in deep learning. We review the applications of ML in ASO to date and…

This work aims to describe a mathematical model and a numerical method to simulate a thin anisotropic composite membrane moving and deforming in 3D space under a dynamic load of an arbitrary time and space profile. The model and the method…

Over-the-air computation (AirComp) leveraging the superposition property of wireless multiple-access channel (MAC), is a promising technique for effective data collection and computation of large-scale wireless sensor measurements in…