4,230 research outputs found
Wellposedness of the discontinuous ODE associated with two-phase flows
We consider the initial value problem \dot x (t) = v(t,x(t)) \;\mbox{ for
} t\in (a,b), \;\; x(t_0)=x_0 which determines the pathlines of a two-phase
flow, i.e.\ is a given velocity field of the type with denoting the bulk phases
of the two-phase fluid system under consideration. The bulk phases are
separated by a moving and deforming interface . Since we allow for
flows with phase change, these pathlines are allowed to cross or touch the
interface. Imposing a kind of transversality condition at , which
is intimately related to the mass balance in such systems, we show existence
and uniqueness of absolutely continuous solutions of the above ODE in case the
one-sided velocity fields are continuous in and locally Lipschitz continuous in
. Note that this is a necessary prerequisite for the existence of
well-defined co-moving control volumes for two-phase flows, a basic concept for
mathematical modeling of two-phase continua
The determinants of public sector size: Theoretical approaches and empirical estimates for local government in the Federal Republic of Germany
The growth of government has become a global phenomenon which, over the years, has attracted a great deal of attention and continues to do so. This growth has not been uniform, neither in time nor in space, and it was the factors underlying these differences interest has focused on. No comprehensive theory, however, has yet emerged from the prolific and varied literature. Instead, a number of approaches was developed, each of them an incomplete explanation of a complex phenomenon. A problem common to all of them when it comes to testing hypotheses empirically, is the measurement of total public sector economic activity. For lack of data, it is usually approximated by public expenditures. Most probably, this understates the role of government in economic life, since many of its activities, while unrecorded in the budget, redirect resources just as taxation and public spending do. Typical examples are consumer and worker safety regulation, public utility price and output regulation in certain industries, and tax expenditures.
Thermodynamically consistent modeling for dissolution/growth of bubbles in an incompressible solvent
We derive mathematical models of the elementary process of dissolution/growth
of bubbles in a liquid under pressure control. The modeling starts with a fully
compressible version, both for the liquid and the gas phase so that the entropy
principle can be easily evaluated. This yields a full PDE system for a
compressible two-phase fluid with mass transfer of the gaseous species. Then
the passage to an incompressible solvent in the liquid phase is discussed,
where a carefully chosen equation of state for the liquid mixture pressure
allows for a limit in which the solvent density is constant. We finally provide
a simplification of the PDE system in case of a dilute solution
Global Strong Solutions for a Class of Heterogeneous Catalysis Models
We consider a mathematical model for heterogeneous catalysis in a finite
three-dimensional pore of cylinder-like geometry, with the lateral walls acting
as a catalytic surface. The system under consideration consists of a
diffusion-advection system inside the bulk phase and a
reaction-diffusion-sorption system modeling the processes on the catalytic wall
and the exchange between bulk and surface. We assume Fickian diffusion with
constant coefficients, sorption kinetics with linear growth bound and a network
of chemical reactions which possesses a certain triangular structure. Our main
result gives sufficient conditions for the existence of a unique global strong
-solution to this model, thereby extending by now classical results on
reaction-diffusion systems to the more complicated case of heterogeneous
catalysis.Comment: 30 page
Continuum thermodynamics of chemically reacting fluid mixtures
We consider viscous, heat conducting mixtures of molecularly miscible
chemical species forming a fluid in which the constituents can undergo chemical
reactions. Assuming a common temperature for all components, we derive a closed
system of partial mass and partial momentum balances plus a mixture balance of
internal energy. This is achieved by careful exploitation of the entropy
principle and requires appropriate definitions of absolute temperature and
chemical potentials, based on an adequate definition of thermal energy
excluding diffusive contributions. The resulting interaction forces split into
a thermo-mechanical and a chemical part, where the former turns out to be
symmetric in case of binary interactions. For chemically reacting systems and
as a new result, the chemical interaction force is a contribution being
non-symmetric outside of chemical equilibrium. The theory also provides a
rigorous derivation of the so-called generalized thermodynamic driving forces,
avoiding the use of approximate solutions to the Boltzmann equations. Moreover,
using an appropriately extended version of the entropy principle and
introducing cross-effects already before closure as entropy invariant couplings
between principal dissipative mechanisms, the Onsager symmetry relations become
a strict consequence. With a classification of the factors in the binary
products of the entropy production according to their parity--instead of the
classical partition into so-called fluxes and driving forces--the apparent
anti-symmetry of certain couplings is thereby also revealed. If the diffusion
velocities are small compared to the speed of sound, the Maxwell-Stefan
equations follow in the case without chemistry, thereby neglecting wave
phenomena in the diffusive motion. This results in a reduced model with only
mass being balanced individually. In the reactive case ..
Global existence for a class of reaction-diffusion systems with mass action kinetics and concentration-dependent diffusivities
In this work we study the existence of classical solutions for a class of
reaction-diffusion systems with quadratic growth naturally arising in mass
action chemistry when studying networks of reactions of the type with Fickian diffusion, where the diffusion
coefficients might depend on time, space and on all the concentrations of
the chemical species. In the case of one single reaction, we prove global
existence for space dimensions . In the more restrictive case of
diffusion coefficients of the type , we use an -approach to
prove global existence for . In the general case of networks of such
reactions we extend the previous method to get global solutions for general
diffusivities if and for diffusion of type if .
In the latter quasi-linear case of and for space dimensions
and , global existence holds for more than quadratic reactions. We can
actually allow for more general rate functions including fractional power
terms, important in applications. We obtain global existence under appropriate
growth restrictions with an explicit dependence on the space dimension
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