107,327 research outputs found
Separating club-guessing principles in the presence of fat forcing axioms
We separate various weak forms of Club Guessing at in the presence of large, Martin's Axiom, and related forcing axioms. We also answer a question of Abraham and Cummings concerning the consistency of the failure of a certain polychromatic Ramsey statement together with the continuum large. All these models are generic extensions via finite support iterations with symmetric systems of structures as side conditions, possibly enhanced with -sequences of predicates, and in which the iterands are taken from a relatively small class of forcing notions. We also prove that the natural forcing for adding a large symmetric system of structures (the first member in all our iterations) adds -many reals but preserves CH
A Partial Order Where All Monotone Maps Are Definable
It is consistent that there is a partial order (P,<) of size aleph_1 such
that every monotone (unary) function from P to P is first order definable in
(P,<).
The partial order is constructed in an extension obtained by finite support
iteration of Cohen forcing.
The main points is that (1) all monotone functions from P to P will
(essentially) have countable range (this uses a Delta-system argument) and (2)
that all countable subsets of P will be first order definable, so we have to
code these countable sets into the partial order. Amalgamation of finite
structures plays an essential role.Comment: This is paper number GoSh:554 in Shelah's list. The paper is to
appear in Fundamenta Mathematicae
Cohen-like first order structures
We study forcing notions similar to the Cohen forcing, whichadd some
struc-tures in given first-order language. These structures can beseen as
versions of uncountable Fra\"iss\'e limits with finite conditions. Among them,
we are primarily interested in linear orders.Comment: version with Theorem 5 adde
Finite size corrections to scaling in high Reynolds number turbulence
We study analytically and numerically the corrections to scaling in
turbulence which arise due to the finite ratio of the outer scale of
turbulence to the viscous scale , i.e., they are due to finite size
effects as anisotropic forcing or boundary conditions at large scales. We find
that the deviations \dzm from the classical Kolmogorov scaling of the velocity moments \langle |\u(\k)|^m\rangle \propto k^{-\zeta_m}
decrease like . Our numerics employ a
reduced wave vector set approximation for which the small scale structures are
not fully resolved. Within this approximation we do not find independent
anomalous scaling within the inertial subrange. If anomalous scaling in the
inertial subrange can be verified in the large limit, this supports the
suggestion that small scale structures should be responsible, originating from
viscosity either in the bulk (vortex tubes or sheets) or from the boundary
layers (plumes or swirls)
Statistical Theory for the Kardar-Parisi-Zhang Equation in 1+1 Dimension
The Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimension dynamically develops
sharply connected valley structures within which the height derivative {\it is
not} continuous. There are two different regimes before and after creation of
the sharp valleys. We develop a statistical theory for the KPZ equation in 1+1
dimension driven with a random forcing which is white in time and Gaussian
correlated in space. A master equation is derived for the joint probability
density function of height difference and height gradient when the forcing correlation length is much smaller than
the system size and much bigger than the typical sharp valley width. In the
time scales before the creation of the sharp valleys we find the exact
generating function of and . Then we express the time
scale when the sharp valleys develop, in terms of the forcing characteristics.
In the stationary state, when the sharp valleys are fully developed, finite
size corrections to the scaling laws of the structure functions are also obtained.Comment: 50 Pages, 5 figure
Homogeneous and Isotropic Turbulence: a short survey on recent developments
We present a detailed review of some of the most recent developments on
Eulerian and Lagrangian turbulence in homogeneous and isotropic statistics. In
particular, we review phenomenological and numerical results concerning the
issue of universality with respect to the large scale forcing and the viscous
dissipative physics. We discuss the state-of-the-art of numerical versus
experimental comparisons and we discuss the dicotomy between phenomenology
based on coherent structures or on statistical approaches. A detailed
discussion of finite Reynolds effects is also presented.Comment: based on the talk presented by R. Benzi at DSFD 2-14. postprint
version, published online on 6 July 2015 J. Stat. Phy
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