165 research outputs found
On computational irreducibility and the predictability of complex physical systems
Using elementary cellular automata (CA) as an example, we show how to
coarse-grain CA in all classes of Wolfram's classification. We find that
computationally irreducible (CIR) physical processes can be predictable and
even computationally reducible at a coarse-grained level of description. The
resulting coarse-grained CA which we construct emulate the large-scale behavior
of the original systems without accounting for small-scale details. At least
one of the CA that can be coarse-grained is irreducible and known to be a
universal Turing machine.Comment: 4 pages, 2 figures, to be published in PR
Novel continuum modeling of crystal surface evolution
We propose a novel approach to continuum modeling of the dynamics of crystal
surfaces. Our model follows the evolution of an ensemble of step
configurations, which are consistent with the macroscopic surface profile.
Contrary to the usual approach where the continuum limit is achieved when
typical surface features consist of many steps, our continuum limit is
approached when the number of step configurations of the ensemble is very
large. The model can handle singular surface structures such as corners and
facets. It has a clear computational advantage over discrete models.Comment: 4 pages, 3 postscript figure
Coarse-graining of cellular automata, emergence, and the predictability of complex systems
We study the predictability of emergent phenomena in complex systems. Using
nearest neighbor, one-dimensional Cellular Automata (CA) as an example, we show
how to construct local coarse-grained descriptions of CA in all classes of
Wolfram's classification. The resulting coarse-grained CA that we construct are
capable of emulating the large-scale behavior of the original systems without
accounting for small-scale details. Several CA that can be coarse-grained by
this construction are known to be universal Turing machines; they can emulate
any CA or other computing devices and are therefore undecidable. We thus show
that because in practice one only seeks coarse-grained information, complex
physical systems can be predictable and even decidable at some level of
description. The renormalization group flows that we construct induce a
hierarchy of CA rules. This hierarchy agrees well with apparent rule complexity
and is therefore a good candidate for a complexity measure and a classification
method. Finally we argue that the large scale dynamics of CA can be very
simple, at least when measured by the Kolmogorov complexity of the large scale
update rule, and moreover exhibits a novel scaling law. We show that because of
this large-scale simplicity, the probability of finding a coarse-grained
description of CA approaches unity as one goes to increasingly coarser scales.
We interpret this large scale simplicity as a pattern formation mechanism in
which large scale patterns are forced upon the system by the simplicity of the
rules that govern the large scale dynamics.Comment: 18 pages, 9 figure
Decay of one dimensional surface modulations
The relaxation process of one dimensional surface modulations is re-examined.
Surface evolution is described in terms of a standard step flow model.
Numerical evidence that the surface slope, D(x,t), obeys the scaling ansatz
D(x,t)=alpha(t)F(x) is provided. We use the scaling ansatz to transform the
discrete step model into a continuum model for surface dynamics. The model
consists of differential equations for the functions alpha(t) and F(x). The
solutions of these equations agree with simulation results of the discrete step
model. We identify two types of possible scaling solutions. Solutions of the
first type have facets at the extremum points, while in solutions of the second
type the facets are replaced by cusps. Interactions between steps of opposite
signs determine whether a system is of the first or second type. Finally, we
relate our model to an actual experiment and find good agreement between a
measured AFM snapshot and a solution of our continuum model.Comment: 18 pages, 6 figures in 9 eps file
The profile of a decaying crystalline cone
The decay of a crystalline cone below the roughening transition is studied.
We consider local mass transport through surface diffusion, focusing on the two
cases of diffusion limited and attachment-detachment limited step kinetics. In
both cases, we describe the decay kinetics in terms of step flow models.
Numerical simulations of the models indicate that in the attachment-detachment
limited case the system undergoes a step bunching instability if the repulsive
interactions between steps are weak. Such an instability does not occur in the
diffusion limited case. In stable cases the height profile, h(r,t), is flat at
radii r<R(t)\sim t^{1/4}. Outside this flat region the height profile obeys the
scaling scenario \partial h/\partial r = {\cal F}(r t^{-1/4}). A scaling ansatz
for the time-dependent profile of the cone yields analytical values for the
scaling exponents and a differential equation for the scaling function. In the
long time limit this equation provides an exact description of the discrete
step dynamics. It admits a family of solutions and the mechanism responsible
for the selection of a unique scaling function is discussed in detail. Finally
we generalize the model and consider permeable steps by allowing direct adatom
hops between neighboring terraces. We argue that step permeability does not
change the scaling behavior of the system, and its only effect is a
renormalization of some of the parameters.Comment: 25 pages, 18 postscript figure
Multi-Particle Collision Dynamics -- a Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids
In this review, we describe and analyze a mesoscale simulation method for
fluid flow, which was introduced by Malevanets and Kapral in 1999, and is now
called multi-particle collision dynamics (MPC) or stochastic rotation dynamics
(SRD). The method consists of alternating streaming and collision steps in an
ensemble of point particles. The multi-particle collisions are performed by
grouping particles in collision cells, and mass, momentum, and energy are
locally conserved. This simulation technique captures both full hydrodynamic
interactions and thermal fluctuations. The first part of the review begins with
a description of several widely used MPC algorithms and then discusses
important features of the original SRD algorithm and frequently used
variations. Two complementary approaches for deriving the hydrodynamic
equations and evaluating the transport coefficients are reviewed. It is then
shown how MPC algorithms can be generalized to model non-ideal fluids, and
binary mixtures with a consolute point. The importance of angular-momentum
conservation for systems like phase-separated liquids with different
viscosities is discussed. The second part of the review describes a number of
recent applications of MPC algorithms to study colloid and polymer dynamics,
the behavior of vesicles and cells in hydrodynamic flows, and the dynamics of
viscoelastic fluids
Progesterone regulation of implantation-related genes: new insights into the role of oestrogen
Genomic profiling was performed on explants of late proliferative phase human endometrium after 24-h treatment with progesterone (P) or oestradiol and progesterone (17β-E2+P) and on explants of menstrual phase endometrium treated with 17β-E2+P. Gene expression was validated with real-time PCR in the samples used for the arrays, in endometrium collected from early and mid-secretory phase endometrium, and in additional experiments performed on new samples collected in the menstrual and late proliferative phase. The results show that late proliferative phase human endometrium is more responsive to progestins than menstrual phase endometrium, that the expression of several genes associated with embryo implantation (i.e. thrombomodulin, monoamine oxidase A, SPARC-like 1) can be induced by P in vitro, and that genes that are fully dependent on the continuous presence of 17β-E2 during P exposure can be distinguished from those that are P-dependent to a lesser extent. Therefore, 17β-E2 selectively primes implantation-related genes for the effects of P
A High Resolution Genetic Map Anchoring Scaffolds of the Sequenced Watermelon Genome
As part of our ongoing efforts to sequence and map the watermelon (Citrullus spp.) genome, we have constructed a high density genetic linkage map. The map positioned 234 watermelon genome sequence scaffolds (an average size of 1.41 Mb) that cover about 330 Mb and account for 93.5% of the 353 Mb of the assembled genomic sequences of the elite Chinese watermelon line 97103 (Citrullus lanatus var. lanatus). The genetic map was constructed using an F8 population of 103 recombinant inbred lines (RILs). The RILs are derived from a cross between the line 97103 and the United States Plant Introduction (PI) 296341-FR (C. lanatus var. citroides) that contains resistance to fusarium wilt (races 0, 1, and 2). The genetic map consists of eleven linkage groups that include 698 simple sequence repeat (SSR), 219 insertion-deletion (InDel) and 36 structure variation (SV) markers and spans ∼800 cM with a mean marker interval of 0.8 cM. Using fluorescent in situ hybridization (FISH) with 11 BACs that produced chromosome-specifc signals, we have depicted watermelon chromosomes that correspond to the eleven linkage groups constructed in this study. The high resolution genetic map developed here should be a useful platform for the assembly of the watermelon genome, for the development of sequence-based markers used in breeding programs, and for the identification of genes associated with important agricultural traits
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