ترغب بنشر مسار تعليمي؟ اضغط هنا

Two solvable systems of coagulation equations with limited aggregations

255   0   0.0 ( 0 )
 نشر من قبل Jean Bertoin
 تاريخ النشر 2008
  مجال البحث فيزياء
والبحث باللغة English
 تأليف Jean Bertoin




اسأل ChatGPT حول البحث

We consider two simple models for the formation of polymers where at the initial time, each monomer has a certain number of potential links (called arms in the text) that are consumed when aggregations occur. Loosely speaking, this imposes restrictions on the number of aggregations. The dynamics of concentrations are governed by modifications of Smoluchowskis coagulation equations. Applying classical techniques based on generating functions, resolution of quasi-linear PDEs, and Lagrange inversion formula, we obtain explicit solutions to these non-linear systems of ODEs. We also discuss the asymptotic behavior of the solutions and point at some connexions with certain known solutions to Smoluchowskis coagulation equations with additive or multiplicative kernels.



قيم البحث

اقرأ أيضاً

A novel family of exactly solvable quantum systems on curved space is presented. The family is the quantum version of the classical Perlick family, which comprises all maximally superintegrable 3-dimensional Hamiltonian systems with spherical symmetr y. The high number of symmetries (both geometrical and dynamical) exhibited by the classical systems has a counterpart in the accidental degeneracy in the spectrum of the quantum systems. This family of quantum problem is completely solved with the techniques of the SUSYQM (supersymmetric quantum mechanics). We also analyze in detail the ordering problem arising in the quantization of the kinetic term of the classical Hamiltonian, stressing the link existing between two physically meaningful quantizations: the geometrical quantization and the position dependent mass quantization.
Within the framework of quantum mechanics working with one-dimensional, manifestly non-Hermitian Hamiltonians $H=T+V$ the traditional class of the exactly solvable models with local point interactions $V=V(x)$ is generalized. The consequences of the use of the nonlocal point interactions such that $(V f)(x) = int K(x,s) f(s) ds$ are discussed using the suitably adapted formalism of boundary triplets.
The method, proposed in the given work, allows the application of well developed standard methods used in quantum mechanics for approximate solution of the systems of ordinary linear differential equations with periodical coefficients.
150 - Dimitry Leites 2019
1) The differential equation considered in terms of exterior differential forms, as E.Cartan did, singles out a differential ideal in the supercommutative superalgebra of differential forms, hence an affine supervariety. In view of this observation, it is evident that every differential equation has a supersymmetry (perhaps trivial). Superymmetries of which (systems of) classical differential equations are missed yet? 2) Why criteria of formal integrability of differential equations are never used in practice?
The invariants of solvable Lie algebras with nilradicals isomorphic to the algebra of strongly upper triangular matrices and diagonal nilindependent elements are studied exhaustively. Bases of the invariant sets of all such algebras are constructed b y an original purely algebraic algorithm based on Cartans method of moving frames.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا