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The following outline is provided as an overview of and topical guide to chemistry:
Biophysics is an interdisciplinary science that applies approaches and methods traditionally used in physics to study biological phenomena. Biophysics covers all scales of biological organization, from molecular to organismic and populations. Biophysical research shares significant overlap with biochemistry, molecular biology, physical chemistry, physiology, nanotechnology, bioengineering, computational biology, biomechanics, developmental biology and systems biology.
Computational physics is the study and implementation of numerical analysis to solve problems in physics. Historically, computational physics was the first application of modern computers in science, and is now a subset of computational science. It is sometimes regarded as a subdiscipline of theoretical physics, but others consider it an intermediate branch between theoretical and experimental physics — an area of study which supplements both theory and experiment.
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists since most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems.
Computational biology refers to the use of data analysis, mathematical modeling and computational simulations to understand biological systems and relationships. An intersection of computer science, biology, and big data, the field also has foundations in applied mathematics, chemistry, and genetics. It differs from biological computing, a subfield of computer science and engineering which uses bioengineering to build computers.
Systems biology is the computational and mathematical analysis and modeling of complex biological systems. It is a biology-based interdisciplinary field of study that focuses on complex interactions within biological systems, using a holistic approach to biological research.
Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of experiments to prove and validate the scientific theories. The field is sometimes called mathematical biology or biomathematics to stress the mathematical side, or theoretical biology to stress the biological side. Theoretical biology focuses more on the development of theoretical principles for biology while mathematical biology focuses on the use of mathematical tools to study biological systems, even though the two terms are sometimes interchanged.
Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle. When difference equations are employed, the theory is called discrete dynamical systems. When the time variable runs over a set that is discrete over some intervals and continuous over other intervals or is any arbitrary time-set such as a Cantor set, one gets dynamic equations on time scales. Some situations may also be modeled by mixed operators, such as differential-difference equations.
Walter Maurice Elsasser was a German-born American physicist, a developer of the presently accepted dynamo theory as an explanation of the Earth's magnetism. He proposed that this magnetic field resulted from electric currents induced in the fluid outer core of the Earth. He revealed the history of the Earth's magnetic field by the study of the magnetic orientation of minerals in rocks. He was also the first to suggest that the wave-like nature of matter might be investigated by electron scattering experiments using crystalline solids.
A biologist is a scientist who conducts research in biology. Biologists are interested in studying life on Earth, whether it is an individual cell, a multicellular organism, or a community of interacting populations. They usually specialize in a particular branch of biology and have a specific research focus.
In mathematics, a heteroclinic network is an invariant set in the phase space of a dynamical system. It can be thought of loosely as the union of more than one heteroclinic cycle. Heteroclinic networks arise naturally in a number of different types of applications, including fluid dynamics and populations dynamics.
The Max Planck Institute for Dynamics and Self-Organization in Göttingen, Germany, is a research institute for investigations of complex non-equilibrium systems, particularly in physics and biology.
Molecular biophysics is a rapidly evolving interdisciplinary area of research that combines concepts in physics, chemistry, engineering, mathematics and biology. It seeks to understand biomolecular systems and explain biological function in terms of molecular structure, structural organization, and dynamic behaviour at various levels of complexity. This discipline covers topics such as the measurement of molecular forces, molecular associations, allosteric interactions, Brownian motion, and cable theory. Additional areas of study can be found on Outline of Biophysics. The discipline has required development of specialized equipment and procedures capable of imaging and manipulating minute living structures, as well as novel experimental approaches.
In mathematics, the concept of graph dynamical systems can be used to capture a wide range of processes taking place on graphs or networks. A major theme in the mathematical and computational analysis of GDSs is to relate their structural properties and the global dynamics that result.
A coupled map lattice (CML) is a dynamical system that models the behavior of nonlinear systems. They are predominantly used to qualitatively study the chaotic dynamics of spatially extended systems. This includes the dynamics of spatiotemporal chaos where the number of effective degrees of freedom diverges as the size of the system increases.
Valentin Afraimovich was a Soviet, Russian and Mexican mathematician. He made contributions to dynamical systems theory, qualitative theory of ordinary differential equations, bifurcation theory, concept of attractor, strange attractors, space-time chaos, mathematical models of non-equilibrium media and biological systems, travelling waves in lattices, complexity of orbits and dimension-like characteristics in dynamical systems.
The following outline is provided as an overview of and topical guide to biophysics:
From a biological standpoint, the goal-directed molecular motions inside living cells are carried out by biopolymers acting like molecular machines. These molecular machines are driven by conformons, that is sequence-specific mechanical strains generated by free energy released in chemical reactions or stress induced destabilisations in supercoiled biopolymer chains. Therefore, conformons can be defined as packets of conformational energy generated from substrate binding or chemical reactions and confined within biopolymers.
DmitriiValerevich Treschev is a Russian mathematician and mathematical physicist, specializing in dynamical systems of classical mechanics.
Alan Garfinkel is Professor at the University of California, Los Angeles in the departments of Medicine (Cardiology) and Integrative Biology and Physiology. His research work applies nonlinear dynamics to cardiac arrhythmias and to the creation of biological patterns in space and time. As a teacher, he created a new course to teach dynamics and modeling to biology students, with no “calculus” prerequisite.
References
- ↑ Craig, Nancy (2014). Molecular Biology, Principles of Genome Function. OUP Oxford. ISBN 9780199658572.
- ↑ Mosconi, Francesco; Julou, Thomas; Desprat, Nicolas; Sinha, Deepak Kumar; Allemand, Jean-François; Vincent Croquette; Bensimon, David (2008). "Some nonlinear challenges in biology". Nonlinearity. 21 (8): T131. Bibcode:2008Nonli..21..131M. doi:10.1088/0951-7715/21/8/T03. ISSN 0951-7715. S2CID 119808230.
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