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Dynamical screening in correlated electron systems  from lattice models to realistic materials 
Posted on 20160325
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Recent progress in treating the dynamically screened nature of the Coulomb interaction in strongly correlated lattice models and materials is reviewed with a focus on computational schemes based on the dynamical mean field approximation. We discuss approximate and exact methods for the solution of impurity models with retarded interactions, and explain how these models appear as auxiliary problems in various extensions of the dynamical mean field formalism. The current state of the field is illustrated with results from recent applications of t . . . . 






Introduction to the Modeling and Analysis of Complex Systems 
Posted on 20160316
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Introduction to the Modeling and Analysis of Complex Systems
introduces students to
mathematical/computational modeling and analysis developed in the emerging interdis
ciplinary field of
Complex Systems Science
. Complex systems are systems made of a
large number of microscopic components interacting with each other in nontrivial ways.
Many realworld systems can be understood as complex systems, where critically impor
tant information resides in the relationships between the parts and not necessarily within
the parts themselves.
T . . . . 






Copyright Oxford University Press 2006 v1. 0 Statistical Mechanics Entropy, Order Parameters, and Complexity 
Posted on 20160316
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This text is careful to address the interests and background not only
of physicists, but of sophisticated students and researchers in mathe
matics, biology, engineering, comput
er science, and the social sciences.
It therefore does not presume an extensive background in physics, and
(except for Chapter
7
) explicitly does not assume that the reader knows
or cares about quantum mechanics. T
he text treats the intersection of
the interests of all of these groups
, while the exercises encompass the
union of interests. Statistical me . . . . 






Stochastic dynamics and relaxation in molecular systems 
Posted on 20160117
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Contents: Langevin’s approach to Brownian dynamics; Diffusion processes and the FokkerPlanck equation; Diffusive motions in simple liquids; Protein dynamics; Elements of probability theory; Autoregressive model; Bibliography. . . . . 






Stochastic Differential Equations: Models and Numerics 
Posted on 20160117
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The goal of this course is to give useful understanding for solving problems formulated by
stochastic differential equations models in science, engineering and mathematical finance.
Typically, these problems require numerical methods to obtain a solution and therefore
the course focuses on basic understanding of stochastic and partial differential equations
to construct reliable and efficient computational methods.
Stochastic and deterministic differential equations are fundamental for the modeling
in Science and Engineering. . . . . 






Control Principles of Complex Networks 
Posted on 20160102
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A reflection of our ultimate understanding of a complex system is our ability to control its behavior. Typically, control has multiple prerequisites: It requires an accurate map of the network that governs the interactions between the system's components, a quantitative description of the dynamical laws that govern the temporal behavior of each component, and an ability to influence the state and temporal behavior of a selected subset of the components. With deep roots in nonlinear dynamics and control theory, notions of control and controllabi . . . . 






