Percolation, sliding, localization and relaxation in topologically closed circuits

Considering a "random walk in a random environment" in a topologically closed circuit, we explore the implications of the percolation and sliding transitions for its relaxation modes. A complementary question regarding the "delocalization" of eigenstates of non-hermitian Hamiltonians has been addressed by Hatano, Nelson, and followers. But we show that for a conservative stochastic process the implied spectral properties are dramatically different. In particular we determine the threshold for under-damped relaxation, and observe "complexity saturation" as the bias is increased.Comment: 11 pages, 6 figures, 1 table, upgraded versio

The relaxation rate of a stochastic spreading process in a closed ring

The relaxation process of a diffusive ring becomes under-damped if the bias (so called affinity) exceeds a critical threshold value, aka delocalization transition. This is related to the spectral properties of the pertinent stochastic kernel. We find the dependence of the relaxation rate on the affinity and on the length of the ring. Additionally we study the implications of introducing a weak-link into the circuit, and illuminate some subtleties that arise while taking the continuum limit of the discrete model.Comment: 10 pages, 6 figure, improved versio

Non-equilibrium steady state of sparse systems

A resistor-network picture of transitions is appropriate for the study of energy absorption by weakly chaotic or weakly interacting driven systems. Such "sparse" systems reach a novel non-equilibrium steady state (NESS) once coupled to a bath. In the stochastic case there is an analogy to the physics of percolating glassy systems, and an extension of the fluctuation-dissipation phenomenology is proposed. In the mesoscopic case the quantum NESS might differ enormously from the stochastic NESS, with saturation temperature determined by the sparsity. A toy model where the sparsity of the system is modeled using a log-normal random ensemble is analyzed.Comment: 6 pages, 6 figures, EPL accepted versio

Missing salts on early Mars

Our understanding of the role of water on Mars has been profoundly influenced over the past several years by the detection of widespread aqueous alteration minerals. Clay minerals are found throughout ancient Noachian terrains and sulfate salts are abundant in younger Hesperian terrains, but these phases are rarely found together in the early Martian rock record. Full alteration assemblages are generally not recognized at local scales, hindering our ability to close mass balance in the ancient crust. Here we demonstrate the dissolution of basalt and subsequent formation of smectite results in an excess of cations that should reside with anions such as OH^−, Cl^−, SO^(2-)_3 SO^(2-)_4, SO^(2-)_4, or CO^(2-)_3 in a significant reservoir of complementary salts. Such salts are largely absent from Noachian terrains, yet the composition and/or fate of these ‘missing salts’ is critical to understanding the oxidation state and primary atmospheric volatile involved in crustal weathering on early Mars

The Sedimentary Cycle on Early Mars

Two decades of intensive research have demonstrated that early Mars (2 Gyr) had an active sedimentary cycle, including well-preserved stratigraphic records, understandable within a source-to-sink framework with remarkable fidelity. This early cycle exhibits first-order similarities to (e.g., facies relationships, groundwater diagenesis, recycling) and first-order differences from (e.g., greater aeolian versus subaqueous processes, basaltic versus granitic provenance, absence of plate tectonics) Earth's record. Mars’ sedimentary record preserves evidence for progressive desiccation and oxidation of the surface over time, but simple models for the nature and evolution of paleoenvironments (e.g., acid Mars, early warm and wet versus late cold and dry) have given way to the view that, similar to Earth, different climate regimes on Mars coexisted on regional scales and evolved on variable timescales, and redox chemistry played a pivotal role. A major accomplishment of Mars exploration has been to demonstrate that surface and subsurface sedimentary environments were both habitable and capable of preserving any biological record

Virtual Northern Analysis of the Human Genome

We applied the Virtual Northern technique to human brain mRNA to systematically measure human mRNA transcript lengths on a genome-wide scale. We used separation by gel electrophoresis followed by hybridization to cDNA microarrays to measure 8,774 mRNA transcript lengths representing at least 6,238 genes at high (>90%) confidence. By comparing these transcript lengths to the Refseq and H-Invitational full-length cDNA databases, we found that nearly half of our measurements appeared to represent novel transcript variants. Comparison of length measurements determined by hybridization to different cDNAs derived from the same gene identified clones that potentially correspond to alternative transcript variants. We observed a close linear relationship between ORF and mRNA lengths in human mRNAs, identical in form to the relationship we had previously identified in yeast. Some functional classes of protein are encoded by mRNAs whose untranslated regions (UTRs) tend to be longer or shorter than average; these functional classes were similar in both human and yeast. Human transcript diversity is extensive and largely unannotated. Our length dataset can be used as a new criterion for judging the completeness of cDNAs and annotating mRNA sequences. Similar relationships between the lengths of the UTRs in human and yeast mRNAs and the functions of the proteins they encode suggest that UTR sequences serve an important regulatory role among eukaryotes

Silica coatings on young Hawaiian basalts: Constraints on formation mechanism from silicon isotopes

Young basalts from Kilauea, on the big island of Hawai’i, frequently feature visually striking, white, orange and blue coatings, consisting of a 10-50 μm layer of amorphous silica, capped, in some cases, by a ~1 μm layer of Fe-Ti oxide [1]. The coatings provide an opportunity to study the early onset of acid-sulfate weathering, a process common to many volcanic environments. Silicon isotopes fractionate with the precipitation of clays and opaline silica, and have been demonstrated to be an indicator of weathering intensity [2,3]. Here we report in situ measurements of δ^(30)_Si of the silica coatings and their implications for coating formation