Pavel Grinfeld
Encyclopedia
Pavel Grinfeld is an applied mathematician
. He is a member of the Mathematics
department at Drexel University
. He studies problems with moving surfaces in applied mathematics
(particularly Calculus of Variations
), geometry
, physics
, and engineering
.
Grinfeld received his PhD
in Applied Mathematics from the MIT in 2003. He spent two years as a postdoctoral fellow at the MIT Department of Earth, Atmosphere and Planetary Sciences, conducting research in geodynamics
.
Grinfeld is the author of the dynamic fluid film equations
.
Grinfeld is a co-author (with Haruo Kojima of Rutgers University
) of the instability of the 2S electron bubbles
.
Grinfeld currently teaches Linear Algebra, Differential Equations, and Tensor Calculus Analysis.
, thermodynamics
and phase transformations
, minimal surfaces and calculus of variations
.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. He is a member of the Mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
department at Drexel University
Drexel University
Drexel University is a private research university with the main campus located in Philadelphia, Pennsylvania, USA. It was founded in 1891 by Anthony J. Drexel, a noted financier and philanthropist. Drexel offers 70 full-time undergraduate programs and accelerated degrees...
. He studies problems with moving surfaces in applied mathematics
Applied mathematics
Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge...
(particularly Calculus of Variations
Calculus of variations
Calculus of variations is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite integrals involving unknown...
), geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, and engineering
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...
.
Grinfeld received his PhD
PHD
PHD may refer to:*Ph.D., a doctorate of philosophy*Ph.D. , a 1980s British group*PHD finger, a protein sequence*PHD Mountain Software, an outdoor clothing and equipment company*PhD Docbook renderer, an XML renderer...
in Applied Mathematics from the MIT in 2003. He spent two years as a postdoctoral fellow at the MIT Department of Earth, Atmosphere and Planetary Sciences, conducting research in geodynamics
Geodynamics
Geodynamics is a subfield of geophysics dealing with dynamics of the Earth. It applies physics, chemistry and mathematics to the understanding of how mantle convection leads to plate tectonics and geologic phenomena such as seafloor spreading, mountain building, volcanoes, earthquakes, faulting and...
.
Grinfeld is the author of the dynamic fluid film equations
Dynamic fluid film equations
Fluid films, such as soap films, are commonly encountered in everyday experience. A soap film can be formed by dipping a closed contour wire into a soapy solution as in the figure on the right...
.
Grinfeld is a co-author (with Haruo Kojima of Rutgers University
Rutgers University
Rutgers, The State University of New Jersey , is the largest institution for higher education in New Jersey, United States. It was originally chartered as Queen's College in 1766. It is the eighth-oldest college in the United States and one of the nine Colonial colleges founded before the American...
) of the instability of the 2S electron bubbles
Electron bubble
An electron bubble is the empty space created around a free electron in a cryogenic gas or liquid, such as neon or helium. They are typically very small, about 2 nm in diameter at atmospheric pressure.-Electron bubbles in helium:...
.
Grinfeld currently teaches Linear Algebra, Differential Equations, and Tensor Calculus Analysis.
Research interests
Hydrodynamics and fluid films dynamicsDynamics
Dynamics may refer to:-Physics and engineering:* Dynamics , the time evolution of physical processes** Aerodynamics, the study of gases in motion...
, thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
and phase transformations
Phase transition
A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....
, minimal surfaces and calculus of variations
Calculus of variations
Calculus of variations is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite integrals involving unknown...
.