Related papers: Fractal solutions of reactor models
We study the kinetics of nonlinear irreversible fragmentation. Here fragmentation is induced by interactions/collisions between pairs of particles, and modelled by general classes of interaction kernels, and for several types of breakage…
We survey methods and results of fractional differential equations in which an unknown function is under the operation of integration and/or differentiation of fractional order. As an illustrative example, we review results on fractional…
We consider two types of the time-dependent Ginzburg-Landau equation in 2D bounded domains: the heat-flow equation and the Schroedinger equation. The system of ordinary differential equations is obtained that describes the evolution of the…
We summarize and to discuss briefly the geometrical practice of modeling attitudes so far popular in treating reaction kinetics of solid-state processes. The model equations existing in the literature have been explored to describe the…
The radiative properties of most structures are intimately connected to the way in which their constituents are ordered on the nano-scale. We have proposed a new representation for radiative heat transfer formalism in many-body systems. In…
We consider the following five-dimensional heat equation with critical boundary condition \begin{equation*} \partial_t u=\Delta u \mbox{ \ in \ } \mathbb{R}_+^5\times (0,T) , \quad -\partial_{x_5}u =|u|^\frac{2}{3}u \mbox{ \ on \ } \pp…
Scattering of neutron collision inside a reactor depends upon geometry of the reactor, diffusion coefficient and absorption coefficient etc. In general these parameters are not crisp and hence we may get uncertain neutron diffusion…
We analyze a reaction-diffusion system on $\mathbb{R}^{N}$ which models the dispersal of individuals between two exchanging environments for its diffusive component and incorporates a Fujita-type growth for its reactive component. The…
A detailed description and validation of a recently developed integration scheme is here reported for one- and two-dimensional reaction-diffusion models. As paradigmatic examples of this class of partial differential equations the complex…
We develop here a simple yet versatile model for nuclear fragmentation in heavy ion collisions. The model allows us to calculate thermodynamic properties such as phase transitions as well as the distribution of fragments at disassembly. In…
In the case of Xe+Sn at 32 MeV/nucleon multifragmentation reaction break-up fragments are built-up from the experimentally detected ones using evaluations of light particle evaporation multiplicities which thus settle fragment internal…
The emergence of periodic oscillations is observed in various complex systems in nature and engineering. Thermoacoustic oscillations in systems comprising turbulent reactive flow exemplify such complexity in the engineering context, where…
We present in detail a theoretical model for fragmentation reactions of three--body halo nuclei. The different reaction mechanisms corresponding to the different processes are described and discussed. Coulomb and nuclear interactions are…
In this Letter, we show numerically that the rectifying effect of heat flux in a one-dimensional two-segment Frenkel-Kontorova chain demonstrated in recent literature is merely available under the limit of the weak coupling between the two…
Faddeev-Yakubovski equations in configuration space are used to solve four nucleon problem for bound and scattering states. Different realistic interaction models are tested, elucidating open problems in nuclear interaction description. On…
A protocell model consisting of mutually catalyzing molecules is studied in order to investigate how chemical compositions are transferred recursively through cell divisions under replication errors. Depending on the path rate, the numbers…
Similarities between models of fragmenting nuclei and disordered systems in condensed matter suggest corresponding methods. Several theoretical models of fragmentation investigated in this fashion show marked differences, indicating…
A combination of reaction-diffusion models with moving-boundary problems yields a system in which the diffusion (spreading and penetration) and reaction (transformation) evolve the system's state and geometry over time. These systems can be…
Complex fission phenomena are studied in a unified way. Very general reflection asymmetrical equilibrium (saddle point) nuclear shapes are obtained by solving an integro-differential equation without being necessary to specify a certain…
We present a novel, generalised formulation to treat coupled structural integrity problems by combining phase field and multi-physics modelling. The approach exploits the versatility of the heat transfer equation and is therefore well…