FHI-aims (Fritz Haber Institute Ab-initio Molecular Simulations) is a computational software package designed for performing quantum mechanical calculations of molecular and solid-state systems. It is particularly focused on simulations using density functional theory (DFT), a widely used computational method in chemistry and materials science for studying the electronic structure of atoms, molecules, and condensed matter systems.

Featherstone's algorithm is a mathematical method used for the efficient computation of forward dynamics in robotic systems. It is particularly well-known in the field of robotics for its application in modeling the motion of rigid body systems, such as robots and mechanical structures. The algorithm is notable for its ability to compute the dynamics of multi-body systems using a recursive approach, which significantly reduces computational complexity compared to traditional methods.

Field-theoretic simulation (FTS) is a computational technique used to study complex systems described by field theories, often in the context of statistical mechanics and quantum field theory. FTS integrates concepts from statistical field theory with numerical simulations, enabling researchers to analyze systems that exhibit emergent behavior across different scales.

The Fermi-Pasta-Ulam-Tsingou (FPUT) problem is a significant concept in the fields of statistical mechanics and nonlinear dynamics. It originates from a famous computational experiment conducted in 1955 by physicists Enrico Fermi, John Pasta, Stanislaw Ulam, and Mary Tsingou. The experiment aimed to explore the behavior of a system of oscillators, specifically focusing on a one-dimensional chain of particles connected by nonlinear springs.

Multiscale modeling is an approach used in various scientific and engineering disciplines to study complex systems that exhibit behavior across different scales, such as spatial scales (ranging from atomic to macroscopic) or temporal scales (ranging from picoseconds to years). The objective of multiscale modeling is to effectively link and integrate information and phenomena occurring at these different scales to provide a more comprehensive understanding of the system.

P3M typically stands for "Project, Program, and Portfolio Management." It encompasses the processes and practices used to manage projects, programs, and portfolios effectively within organizations. Here’s a brief overview of each component: 1. **Project Management (PM)**: The discipline of planning, organizing, and managing resources to achieve specific goals and objectives within a defined timeline. Projects have a clear beginning and end and often focus on delivering a specific product, service, or outcome.

Chaos theory is a branch of mathematics and science that deals with complex systems that are highly sensitive to initial conditions, a phenomenon often referred to as the "butterfly effect." It explores how small changes in initial conditions can lead to vastly different outcomes, making long-term prediction difficult or impossible in certain systems.

The auxiliary particle filter (APF) is an advanced version of the traditional particle filter, which is used for nonlinear and non-Gaussian state estimation problems, often in the context of dynamic systems. The particle filter represents the posterior distribution of a system's state using a set of weighted samples (particles). It is particularly useful in situations where the state transition and/or observation models are complex and cannot be easily linearized. **Key Characteristics of the Auxiliary Particle Filter:** 1.

The T-matrix method, or T-matrix approach, is a mathematical technique used to analyze scattering phenomena, particularly in the field of wave scattering and electromagnetism. It is particularly effective for solving problems involving the scattering of waves by arbitrary shapes, including particles or bodies of different geometries. ### Key Concepts: 1. **T-matrix Definition**: The T-matrix (or transition matrix) relates incoming and outgoing wave fields.

Time-dependent density functional theory (TDDFT) is a quantum mechanical theory used to investigate the time evolution of electronic systems. It extends the framework of density functional theory (DFT), which is primarily used for static properties of many-body quantum systems, to systems that are subject to time-dependent external perturbations, such as electric fields or laser pulses. In TDDFT, the central quantity is the electron density, which is a function of both position and time.

The variational method is a computational technique used in quantum mechanics to approximate the ground state energy and wave function of a quantum system. It is particularly useful for systems where exact solutions of the Schrödinger equation are not possible, such as many-body systems or complex potentials. The variational principle forms the foundation of this method.

Stan is a probabilistic programming language used for statistical modeling and data analysis. It is particularly well-suited for fitting complex statistical models using Bayesian inference. Stan provides a flexible platform for users to build models that can include a variety of distributions, hierarchical structures, and other statistical components.

The Vienna Ab initio Simulation Package (VASP) is a software tool for simulating the electronic structure of materials. It's widely used in the field of computational materials science and condensed matter physics. VASP is particularly known for its capabilities in performing density functional theory (DFT) calculations, which allow researchers to study the electronic properties of solids, surfaces, and nanostructures at an atomic level.

Non-uniform random numbers are random numbers that do not have a uniform distribution over a specified range. In a uniform distribution, every number within the defined interval has an equal probability of being selected. In contrast, non-uniform random numbers are generated according to a specific probability distribution, which means some values have a higher likelihood of being chosen than others.

Science software stubs refer to minimal implementations or placeholders for scientific software components that allow developers and researchers to build, test, and integrate larger systems before the complete functionality is developed. Stubs are often used in the context of software development, especially in scientific computing, where complex simulations or calculations can be broken down into smaller, modular parts.

Mikhail Kovalchuk is a name that may refer to various individuals, but the most prominent association is with a Russian scientist known for his work in the field of physics, particularly in relation to nuclear physics and the development of nuclear technologies.

Participatory budgeting (PB) is a democratic process through which community members deliberatively decide how to allocate parts of a public budget. The main goal is to give citizens a direct say in the budgeting process, fostering transparency, accountability, and civic engagement. The basic rules and steps often involved in participatory budgeting include: 1. **Citizen Engagement**: Residents are invited to participate, ensuring a broad representation of community members. This often involves meetings, workshops, or online platforms.

Michael Wolf is a statistician known for his contributions to various areas of statistical theory and applications. He has researched topics such as statistical modeling, multivariate analysis, and the study of statistical properties in high-dimensional data. His work often involves the intersection of statistics with other disciplines, including economics and the social sciences. In addition to his research, he may also be involved in teaching and mentoring students in statistics and data science.

CAD (Computer-Aided Design) file formats are specialized file types used to create, modify, analyze, and optimize designs in various fields such as architecture, engineering, manufacturing, and construction. These file formats can contain 2D drawings, 3D models, and various other detailed specifications that support the design and manufacturing processes. Here are some common CAD file formats: ### Common CAD File Formats: 1. **DWG** (Drawing): - Proprietary format developed by Autodesk.

Bootstrapping populations refers to a statistical resampling method used to estimate the distribution of a statistic (like the mean, median, variance, etc.) from a sample of data. It allows researchers to make inferences about a population parameter without requiring strong assumptions about the underlying population distribution.