Related papers: String Diagrammatic Electrical Circuit Theory
String graphs, that is, intersection graphs of curves in the plane, have been studied since the 1960s. We provide an expository presentation of several results, including very recent ones: some string graphs require an exponential number of…
The bulk macroscopic response of a system of particles or inclusions with field-induced forces is studied. The susceptibilities and transport coefficients in such a system are expressed as averages of a multiple scattering expansion. A…
Following up on the recently published circuit theory for thermodynamic devices, we consider networks of Thermo-Electric Converters (TECs) in stationary non-equilibrium. Assuming constant thermoelectric properties, the integration over a…
We present a theoretical and a numerical formalism for analysis and design of spintronic integrated circuits (SPINICs). The formalism encompasses a generalized circuit theory for spintronic integrated circuits based on nanomagnetic dynamics…
Diagram chasing is a customary proof method used in category theory and homological algebra. It involves an element-theoretic approach to show that certain properties hold for a commutative diagram. When dealing with abelian categories for…
This thesis details a project to define a fully compositional theory of synchronous sequential circuits built from primitive components, motivated by applying techniques successfully used in programming languages to hardware. The first part…
In this paper, a phenomenological theory of saturated ferromagnetoelastic conductors is established using a multi-continuum model and the classical laws of mechanics, thermodynamics and electromagnetics. The theory is nonlinear and is valid…
This paper presents a general framework for linear circuit analysis based on elementary aspects of projective geometry. We use a flexible approach in which no a priori assignment of an electrical nature to the circuit branches is necessary.…
The original idea of proof nets can be formulated by means of interaction nets syntax. Additional machinery as switching, jumps and graph connectivity is needed in order to ensure correspondence between a proof structure and a correct proof…
It is known that electrical networks with resistors are related to the Laplace operator and random walk on weighted graphs. In this paper we consider more general electrical networks with coils, capacitors, and resistors. We give two…
String diagrams provide a convenient graphical framework which may be used for equational reasoning about morphisms of monoidal categories. However, unlike term rewriting, rewriting string diagrams results in shorter equational proofs,…
Linear complementarity problems provide a powerful framework to model nonsmooth phenomena in a variety of real-world applications. In dynamical control systems, they appear coupled to a linear input-output system in the form of linear…
After a brief review of the key theorems concerning recurrent sequences, we give an explicit computation of the inverse of the Vandermonde matrix. This will then be used to derive sub-exponential decay error terms in the ergodic theorem of…
In frameworks of the phenomenological approach we analyze of the phase diagram of mixed compounds. We obtain space groups of symmetry of the real structures as result of phase transition from close-packed degenerate structure. The theory of…
A string background, which is in some precise sense {\em universal} (i.e., incorporating all orders in the Feynman diagram expansion), is proposed to represent pure gauge theories. S-duality at the level of the string metric is considered…
String theory and supersymmetry are theoretical ideas that go beyond the standard model of particle physics and show promise for unifying all forces. After a brief introduction to supersymmetry, we discuss the prospects for its experimental…
We apply in this article (non rigorous) statistical mechanics methods to the problem of counting long circuits in graphs. The outcomes of this approach have two complementary flavours. On the algorithmic side, we propose an approximate…
This paper continues the application of circuit theory to experimental design started by the first two authors. The theory gives a very special and detailed representation of the kernel of the design model matrix. This representation turns…
Motivated by the precision results in the electroweak theory studies of two-loopFeynman diagrams are performed. Specifically this paper gives a contribution to the knowledge of massive two-loop self-energy diagrams in arbitrary and…
We develop a scheme to make exactly solvable gauge theories whose electric flux lines host (1+1)-dimensional topological phases. We use this exact `decorated-string-net' framework to construct several classes of interesting models. In…