1,266 research outputs found
Balance laws with integrable unbounded sources
We consider the Cauchy problem for a strictly hyperbolic system
of balance laws each characteristic field being genuinely nonlinear or linearly
degenerate. Assuming that the norm of
and \|u_o\|_{BV(\reali)} are small enough, we
prove the existence and uniqueness of global entropy solutions of bounded total
variation extending the result in [1] to unbounded (in ) sources.
Furthermore, we apply this result to the fluid flow in a pipe with
discontinuous cross sectional area, showing existence and uniqueness of the
underlying semigroup.Comment: 26 pages, 4 figure
Kinetic layers and coupling conditions for macroscopic equations on networks I: the wave equation
We consider kinetic and associated macroscopic equations on networks. The
general approach will be explained in this paper for a linear kinetic BGK model
and the corresponding limit for small Knudsen number, which is the wave
equation. Coupling conditions for the macroscopic equations are derived from
the kinetic conditions via an asymptotic analysis near the nodes of the
network. This analysis leads to the consideration of a fixpoint problem
involving the coupled solutions of kinetic half-space problems. A new
approximate method for the solution of kinetic half-space problems is derived
and used for the determination of the coupling conditions. Numerical
comparisons between the solutions of the macroscopic equation with different
coupling conditions and the kinetic solution are presented for the case of
tripod and more complicated networks
The Futility of Utility: how market dynamics marginalize Adam Smith
Econometrics is based on the nonempiric notion of utility. Prices, dynamics,
and market equilibria are supposed to be derived from utility. Utility is
usually treated by economists as a price potential, other times utility rates
are treated as Lagrangians. Assumptions of integrability of Lagrangians and
dynamics are implicitly and uncritically made. In particular, economists assume
that price is the gradient of utility in equilibrium, but I show that price as
the gradient of utility is an integrability condition for the Hamiltonian
dynamics of an optimization problem in econometric control theory. One
consequence is that, in a nonintegrable dynamical system, price cannot be
expressed as a function of demand or supply variables. Another consequence is
that utility maximization does not describe equiulibrium. I point out that the
maximization of Gibbs entropy would describe equilibrium, if equilibrium could
be achieved, but equilibrium does not describe real markets. To emphasize the
inconsistency of the economists' notion of 'equilibrium', I discuss both
deterministic and stochastic dynamics of excess demand and observe that Adam
Smith's stabilizing hand is not to be found either in deterministic or
stochastic dynamical models of markets, nor in the observed motions of asset
prices. Evidence for stability of prices of assets in free markets simply has
not been found.Comment: 46 pages. accepte
The Futility of Utility: how market dynamics marginalize Adam Smith
General Equilibrium Theory in econometrics is based on the vague notion of utility. Prices, dynamics, and market equilibria are supposed to be derived from utility. Utility is sometimes treated like a potential, other times like a Lagrangian. Illegal assumptions of integrability of actions and dynamics are usually made. Economists usually assume that price is the gradient of utility in equilibrium, but I observe instead that price as the gradient of utility is an integrability condition for the Hamiltonian dynamics of an optimization problem. I discuss both deterministic and statistical descriptions of the dynamics of excess demand and observe that Adam Smith's stabilizing hand is not to be found either in deterministic or stochastic dynamical models of markets nor in the observed motions of asset prices. Evidence for stability of prices of assets in free markets has not been found.Utility; general equilibrium; nonintegrability; control dynamics; conservation laws; chaos; instability; supply-demand curves; nonequilibrium dynamics
Thermal behavior induced by vacuum polarization on causal horizons in comparison with the standard heat bath formalism
Modular theory of operator algebras and the associated KMS property are used
to obtain a unified description for the thermal aspects of the standard heat
bath situation and those caused by quantum vacuum fluctuations from
localization. An algebraic variant of lightfront holography reveals that the
vacuum polarization on wedge horizons is compressed into the lightray
direction. Their absence in the transverse direction is the prerequisite to an
area (generalized Bekenstein-) behavior of entropy-like measures which reveal
the loss of purity of the vacuum due to restrictions to wedges and their
horizons. Besides the well-known fact that localization-induced (generalized
Hawking-) temperature is fixed by the geometric aspects, this area behavior
(versus the standard volume dependence) constitutes the main difference between
localization-caused and standard thermal behavior.Comment: 15 page Latex, dedicated to A. A. Belavin on the occasion of his 60th
birthda
- …