Matrix String Description of Cosmic Singularities in a Class of Time-dependent Solutions

A large class of time-dependent solutions with 1/2 supersymmetry were found previously. These solutions involve cosmic singularities at early time. In this paper, we study if matrix string description of the singularities in these solutions with backgrounds is possible and present several examples where the solutions can be described well in the perturbative picture.Comment: 12 pages, v2: typos corrected, a ref. adde

Holography and Cosmological Singularities

Certain null singularities in ten dimensional supergravity have natural holographic duals in terms of Matrix Theory and generalizations of the AdS/CFT correspondence. In many situations the holographic duals appear to be well defined in regions where the supergravity develops singularities. We describe some recent progress in this area.Comment: Anomaly equation corrected. References adde

Solid--on--Solid Model for Adsorption on Self--Affine Substrate: A Transfer Matrix Approach

We study a $d=2$ discrete solid--on--solid model of complete wetting of a rough substrate with random self--affine boundary, having roughness exponent $\zeta_s$. A suitable transfer matrix approach allows to discuss adsorption isotherms, as well as geometrical and thermal fluctuations of the interface. For $\zeta_s\leq 1/2$ the same wetting exponent $\psi=1/3$ as for flat substrate is obtained for the dependence of the coverage, $\theta$, on the chemical potential, $h$ ($\theta\sim h^{-\psi}$ for $h\to 0$). The expected existence of a zero temperature fixed point, leading to $\psi=\zeta_s /(2-\zeta_s)$ for $\zeta_s>1/2$, is verified numerically in spite of an unexpected, very slow convergence to asymptotics.Comment: Standard TeX, 13 pages. 5 PostScript figures available on request. Preprint UDPHIR 94/04/G

Analysis of Antarctic Ice-Sheet Mass Balance from ICESat Measurements

If protoplanets formed from 10 to 20 kilometer diameter planetesimals in a runaway accretion process prior to their oligarchic growth into the terrestrial planets, it is only logical to ask where these planetesimals may have formed in order to assess the initial composition of the Earth. We have used Weidenschilling's model for the formation of comets (1997) to calculate an efficiency factor for the formation of planetesimals from the solar nebula, then used this factor to calculate the feeding zones that contribute to material contained within 10, 15 and 20 kilometer diameter planetesimals at 1 A.V. as a function of nebular mass. We find that for all reasonable nebular masses, these planetesimals contain a minimum of 3% water as ice by mass. The fraction of ice increases as the planetesimals increase in size and as the nebular mass decreases, since both factors increase the feeding zones from which solids in the final planetesimals are drawn. Is there really a problem with the current accretion scenario that makes the Earth too dry, or is it possible that the nascent Earth lost significant quantities of water in the final stages of accretion

Toward the End of Time

The null-brane space-time provides a simple model of a big crunch/big bang singularity. A non-perturbative definition of M-theory on this space-time was recently provided using matrix theory. We derive the fermion couplings for this matrix model and study the leading quantum effects. These effects include particle production and a time-dependent potential. Our results suggest that as the null-brane develops a big crunch singularity, the usual notion of space-time is replaced by an interacting gluon phase. This gluon phase appears to constitute the end of our conventional picture of space and time.Comment: 31 pages, reference adde

Exact scaling in the expansion-modification system

This work is devoted to the study of the scaling, and the consequent power-law behavior, of the correlation function in a mutation-replication model known as the expansion-modification system. The latter is a biology inspired random substitution model for the genome evolution, which is defined on a binary alphabet and depends on a parameter interpreted as a \emph{mutation probability}. We prove that the time-evolution of this system is such that any initial measure converges towards a unique stationary one exhibiting decay of correlations not slower than a power-law. We then prove, for a significant range of mutation probabilities, that the decay of correlations indeed follows a power-law with scaling exponent smoothly depending on the mutation probability. Finally we put forward an argument which allows us to give a closed expression for the corresponding scaling exponent for all the values of the mutation probability. Such a scaling exponent turns out to be a piecewise smooth function of the parameter.Comment: 22 pages, 2 figure

A Matrix Model for the Null-Brane

The null-brane background is a simple smooth 1/2 BPS solution of string theory. By tuning a parameter, this background develops a big crunch/big bang type singularity. We construct the DLCQ description of this space-time in terms of a Yang-Mills theory on a time-dependent space-time. Our dual Matrix description provides a non-perturbative framework in which the fate of both (null) time, and the string S-matrix can be studied.Comment: 26 pages, LaTeX; references adde

Time-Dependent Supersymmetric Solutions in M-Theory and the Compactification-Decompactification Transition

We show that the diagonal light-like solution with 16 supersymmetries in eleven-dimensional supergravity derived in our previous paper (hep-th/0509173) can be generalised to non-diagonal solutions preserving the same number of supersymmetries. This class of solutions contains a subclass equivalent to the class of solutions found by Bin Chen that are dependent on the spatial-coordinates. Utilising these solutions, we construct toroidally compactified solutions that smoothly connect a static compactified region with a dynamically decompactifying region along a null hypersurface.Comment: 28 pages, 3 figures; the published versio

From MinX to MinC: Semantics-Driven Decompilation of Recursive Datatypes

Reconstructing the meaning of a program from its binary executable is known as reverse engineering; it has a wide range of applications in software security, exposing piracy, legacy systems, etc. Since reversing is ultimately a search for meaning, there is much interest in inferring a type (a meaning) for the elements of a binary in a consistent way. Unfortunately existing approaches do not guarantee any semantic relevance for their reconstructed types. This paper presents a new and semantically-founded approach that provides strong guarantees for the reconstructed types. Key to our approach is the derivation of a witness program in a high-level language alongside the reconstructed types. This witness has the same semantics as the binary, is type correct by construction, and it induces a (justifiable) type assignment on the binary. Moreover, the approach effectively yields a type-directed decompiler. We formalise and implement the approach for reversing Minx, an abstraction of x86, to MinC, a type-safe dialect of C with recursive datatypes. Our evaluation compiles a range of textbook C algorithms to MinX and then recovers the original structures

Optimal Energy Dissipation in Sliding Friction Simulations

Non-equilibrium molecular dynamics simulations, of crucial importance in sliding friction, are hampered by arbitrariness and uncertainties in the removal of the frictionally generated Joule heat. Building upon general pre-existing formulation, we implement a fully microscopic dissipation approach which, based on a parameter-free, non-Markovian, stochastic dynamics, absorbs Joule heat equivalently to a semi-infinite solid and harmonic substrate. As a test case, we investigate the stick-slip friction of a slider over a two-dimensional Lennard-Jones solid, comparing our virtually exact frictional results with approximate ones from commonly adopted dissipation schemes. Remarkably, the exact results can be closely reproduced by a standard Langevin dissipation scheme, once its parameters are determined according to a general and self-standing variational procedure