We present a geometrically exact equilibrium theory for elastic structures that have in common that they are effectively described by a 1D elastic theory (i.e., an ODE). Apart from the elastic rod this includes higher-dimensional structures such as thin sheets, strips and braids that deform subject to kinematic constraints that can be eliminated...
Creator:
van der Heijden, Gert (Imperial College London)
Created:
2019-06-17
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Many nonlinear systems of partial differential equations have a striking phenomenon of spontaneous formation of singularities in a finite time (blow up). Blow up is often accompanied by a dramatic contraction of the spatial extent of solution, which is called by collapse. A collapse in a nonlinear Schrodinger equation (NLSE) describes the self-f...
Creator:
Lushnikov, Pavel M (University of New Mexico)
Created:
2016-11-04
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Consider electrostatic plasmas described by 1D Vlasov-Poisson with a fixed ion background. In 1946, Landau discovered the linear decay of electric field near a stable homogeneous state. The nonlinear Landau damping was recently proved for analytic perturbations by Villani and Mouhot, but for general perturbations the problem is still largely ope...
Creator:
Lin, Zhiwu (Georgia Institute of Technology)
Created:
2011-06-30
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Weakly conducting dielectric solid particles and liquid droplets in strong electric fields are known to undergo symmetry-breaking bifurcations leading to steady electrorotation. This so-called Quincke effect, which results from the antiparallel electrostatic dipole induced by the applied field inside the particles, is well described by the class...
Creator:
Saintillan, David (University of California, San Diego)
Created:
2018-03-12
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Functions whose values are unbounded linear operators describe a large number of processes in optics. The applications include photonic crystals with material properties of Drude-Lorentz type and computations of scattering resonances.In this talk we present new enclosures of the numerical range of an operator functions T. Contrary to the numeric...
Creator:
Engström, Christian (University of Umeà¥)
Created:
2016-12-14
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The nonlinear and stochastic dynamics of oscillating microcantilevers in the Atomic Force Microscope (AFM) are closely linked to the microscope's stability, resolution, minimum force detection, and the ability to generate material contrast. The bifurcations, stability, higher harmonics, and chaotic dynamics mechanisms are now well understood for...
Creator:
Raman, Arvind (Purdue University)
Created:
2016-04-15
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We develop an algorithmic theory of nonlinear optimization over setsof integer points presented by inequalities or by oracles. Using acombination of geometric and algebraic methods, involving zonotopes,Graver bases, multivariate polynomials and Frobenius numbers, we providepolynomial-time algorithms for broad classes of nonlinear combinatorialop...
Creator:
Onn, Shmuel (Technion-Israel Institute of Technology)
Created:
2008-11-20
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
This talk is concerned with optimizing nonlinear functions over the lattice points in a polyhedral set. We present three families of polynomial time algorithms for special cases of the general problem. Each such algorithm makes use of combinatorial, geometric or algebraic properties of the underlying problem. The first problem deals with optimiz...
Creator:
Weismantel, Robert (Otto-von-Guericke-Universität Magdeburg)
Created:
2008-11-20
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Electrical impedance tomography (EIT) is an imaging technique for the reconstruction of objects embedded in a given conductive background medium . Applications range over a broad spectrum such as non-destructive material testing, geophysics landslide identification or tumor detection inmedical imaging.In such situations, linearization technique...
Creator:
Constantinescu, Andrei (École Polytechnique)
Created:
2015-05-13
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
*also affiliated with Kavli Institute for Theoretical Physics, University of California, Santa BarbaraGraphene provides an ideal system to test the statistical mechanics of thermally fluctuating elastic membranes. Its high Young's modulus means that thermal fluctuations are already important at nanometer length scales, dramatically modifying the...
Creator:
Bowick, Mark (Syracuse University)
Created:
2017-05-17
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
This talk is about a class of particle systems in which energyexchange among particles is mediated by 'the environment',symbolized by a lattice of rotating disks in mechanical modelsand 'energy tanks' in stochastic versions of these models.A number of years ago, J-P Eckmann and I studied models ofthis type. Taking for granted mathematical issues...
Creator:
Young, Lai-Sang (New York University)
Created:
2014-10-31
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We consider a class of nonconvex quadratic optimization problems having one or two quadratic constraints (1QCQP or 2QCQP). The motivation of this work comes primarily from binary classification in machine learning, but the problems themselves are important; some types of 1QCQP and 2QCQP are well-studied as the trust-region subproblem (TRS) and C...
Creator:
Takeda, Akiko (University of Tokyo)
Created:
2015-02-26
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Given a finite group G, let C(G) be the set of all cosets of all proper subgroups of G, ordered by inclusion. In joint work with Russ Woodroofe, we show that the order complex of C(G) is not acyclic in characteristic two, and therefore not contractible. This answers a question of K. S. Brown. Our proof uses P. A. Smith Theory and the Classificat...
Creator:
Shareshian, John (Washington University)
Created:
2014-11-10
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In economic theory one typically discounts future benefits at aconstant rate. An example of this is the celebrated model of endogeneousgrowth, originating with Ramsey (1928), which leads to the so-called goldenrule in macroeconomics. There are now excellent reasons (intergenerationalequity, for instance) to use non-constant discount rates. There...
Creator:
Ekeland, Ivar (University of British Columbia)
Created:
2010-06-10
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Global attractors and their deconstructions provide us with a versatile tool for studying the long-time behavior of solutions to reaction-diffusion equations. The majority of global attractor theory assumes that the equation in question is dissipative, but recent work has shown that similar results can be obtained for non-dissipative reaction-di...
Creator:
Ben-Gal, Nitsan (University of Minnesota, Twin Cities)
Created:
2014-03-11
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.