There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

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Convex Analysisの二,三の進展について

The spatiotemporal expression of genes in an organism is determined by regulatory systems that involve a large number of genes connected through a complex network of interactions. As an intuitive understanding of the behavior of these systems is hard to obtain, computer tools for the modeling and simulation of genetic regulatory networks will be indispensable. This report reviews formalisms that have been employed in mathematical biology and bioinformatics to describe genetic regulatory systems, in particular directed graphs, Bayesian networks, ordinary and partial differential equations, stochastic equations, Boolean networks and their generalizations, qualitative differential equations, and rule-based formalisms. In addition, the report discusses how these formalisms have been used in the modeling and simulation of regulatory systems.

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Modeling and simulation of genetic regulatory systems: a literature review.

A survey of models, analysis tools and compensation methods for the control of machines with friction

The aim of this paper is to understand the influence of clearances in the kinematic joints, dimensional and geometrical tolerances associated with the parts, on the performance of a circuit breaker mechanism in the trip operation. Operating mechanism and trip unit are the essential components of a miniature circuit breaker. The operating and trip mechanisms are made of ten parts with revolute and cylindrical joints with clearance, and five unilateral contacts with friction. This mechanism is based on quick-make and quick-break principle. The Moreau-Jean nonsmooth contact dynamics (NSCD) numerical method is used to perform the simulations. The numerical results are validated by careful comparisons with experimental data.

/pdf/influence-of-imperfect-joints-and-geometrical-tolerances-on-4yalx1cxm2.pdf

Influence of imperfect joints and geometrical tolerances on a circuit breaker dynamics

Interestingly enough, some controllers and stability results in Haddad and Lee (2020) can be shown to be equivalent to algorithms obtained from the implicit Euler discretization of a set-valued system, which is known to preserve many nice properties of the continuous-time dynamics after discretization, like the convergence towards the (discrete) sliding surface in a ﬁnite number of steps.

Comments on “Finite-time stability of discrete autonomous systems” [Automatica 122 (2020) 109282]

Lagrange dynamics of lumped-mass multibody models of overhead cranes in 2D operational space

Analysis of the implicit Euler time-discretization of a class of descriptor-variable linear cone complementarity systems

It has been seen in Chaps. 1, 2 and 3 that electrical circuits with nonsmooth multivalued electronic devices, can be recast under various mathematical formalisms (see Sect. 2.7 for a summary). For the sake of the numerical integration of those circuits, one needs a small set of general formulations which are suitable for a subsequent time-discretization. In other words, the simple examples that are analyzed in details in Chaps. 1 and 2 possess a too simple dynamics to be characteristic representatives of the general issue of nonsmooth circuits. Especially, the material of Chap. 3 teaches us that DAEs are ubiquitous in circuits (a well-known fact, indeed). It is therefore necessary to obtain mathematical formalisms that incorporate not only the nonsmooth and multivalued models of the electronic devices (ideal diodes, Zener diodes, etc.), but also the equations obtained from the MNA (see Sects. 3.5 and 3.6).

Bernard Brogliato

Papers

Influence of imperfect joints and geometrical tolerances on a circuit breaker dynamics

Comments on “Finite-time stability of discrete autonomous systems” [Automatica 122 (2020) 109282]

Lagrange dynamics of lumped-mass multibody models of overhead cranes in 2D operational space

Analysis of the implicit Euler time-discretization of a class of descriptor-variable linear cone complementarity systems

Time-Stepping Schemes and One Step Solvers