In the theory of automatic control, an urgent problem is development design methods bynonaffine control systems. such systems, affects input plant nonlinearly, so itaffects state variables non-additively. The purpose this article to develop a method thatensures stability zero equilibrium position closed system in certain area.The object described by nonlinear differential equations with one con...

Critical properties of frictionless spherical particles below jamming are studied using extensive numerical simulations, paying particular attention to the non-affine part displacements during athermal quasi-static compression. It is shown that squared norm displacement exhibits a power-law divergence toward transition point. A possible connection between this critical exponent and shear viscos...

While actin bundles are used by living cells for structural fortification, the microscopic origin of the elasticity of bundled networks is not understood. Here, we show that above a critical concentration of the actin binding protein fascin, a solution of actin filaments organizes into a pure network of bundles. While the elasticity of weakly cross-linked networks is dominated by the affine def...

We develop an effective medium approach to the mechanics of disordered, semiflexible polymer networks and study the response of such networks to uniform and nonuniform strain. We identify distinct elastic regimes in which the contributions of either filament bending or stretching to the macroscopic modulus vanish. We also show that our effective medium theory predicts a crossover between affine...

We show that, in the athermal quasistatic deformation of amorphous materials, the onset of failure is accompanied by universal scalings associated with a divergence of elastic constants. A normal mode analysis of the nonaffine elastic displacement field allows us to clarify its relation to the zero-frequency mode at the onset of failure and to the cracklike pattern which results from the subseq...

This paper contains a complete description of minimal non-gatherable triangle triples in the lambda-sequences for the classical root systems, F4 and E6. Such sequences are associated with reduced decompositions (words) in affine and non-affine Weyl groups. The existence of the non-gatherable triples is a combinatorial obstacle for using the technique of intertwiners for an explicit description ...