Message in the Sky

We argue that the cosmic microwave background (CMB) provides a stupendous opportunity for the Creator of universe our (assuming one exists) to have sent a message to its occupants, using known physics. Our work does not support the Intelligent Design movement in any way whatsoever, but asks, and attempts to answer, the entirely scientific question of what the medium and message might be IF there was actually a message. The medium for the message is unique. We elaborate on this observation, noting that it requires only careful adjustment of the fundamental Lagrangian, but no direct intervention in the subsequent evolution of the universe.Comment: 3 pages, revtex; to appear in Mod.Phys.Lett.

A speculative relation between the cosmological constant and the Planck mass

We propose the relation $M_\Lambda \sim (M_{Pl} M_U)^{1/2}$ where $M_\Lambda$, $M_{Pl},$ and $M_U$ denote the mass scale associated with the cosmological constant, the gravitational interaction, and the size of the universe respectively.Comment: 3 page

PDF turbulence modeling and DNS

The problem of time discontinuity (or jump condition) in the coalescence/dispersion (C/D) mixing model is addressed in probability density function (pdf). A C/D mixing model continuous in time is introduced. With the continuous mixing model, the process of chemical reaction can be fully coupled with mixing. In the case of homogeneous turbulence decay, the new model predicts a pdf very close to a Gaussian distribution, with finite higher moments also close to that of a Gaussian distribution. Results from the continuous mixing model are compared with both experimental data and numerical results from conventional C/D models. The effect of Coriolis forces on compressible homogeneous turbulence is studied using direct numerical simulation (DNS). The numerical method used in this study is an eight order compact difference scheme. Contrary to the conclusions reached by previous DNS studies on incompressible isotropic turbulence, the present results show that the Coriolis force increases the dissipation rate of turbulent kinetic energy, and that anisotropy develops as the Coriolis force increases. The Taylor-Proudman theory does apply since the derivatives in the direction of the rotation axis vanishes rapidly. A closer analysis reveals that the dissipation rate of the incompressible component of the turbulent kinetic energy indeed decreases with a higher rotation rate, consistent with incompressible flow simulations (Bardina), while the dissipation rate of the compressible part increases; the net gain is positive. Inertial waves are observed in the simulation results

Calculating and understanding the value of any type of match evidence when there are potential testing errors

It is well known that Bayes’ theorem (with likelihood ratios) can be used to calculate the impact of evidence, such as a ‘match’ of some feature of a person. Typically the feature of interest is the DNA profile, but the method applies in principle to any feature of a person or object, including not just DNA, fingerprints, or footprints, but also more basic features such as skin colour, height, hair colour or even name. Notwithstanding concerns about the extensiveness of databases of such features, a serious challenge to the use of Bayes in such legal contexts is that its standard formulaic representations are not readily understandable to non-statisticians. Attempts to get round this problem usually involve representations based around some variation of an event tree. While this approach works well in explaining the most trivial instance of Bayes’ theorem (involving a single hypothesis and a single piece of evidence) it does not scale up to realistic situations. In particular, even with a single piece of match evidence, if we wish to incorporate the possibility that there are potential errors (both false positives and false negatives) introduced at any stage in the investigative process, matters become very complex. As a result we have observed expert witnesses (in different areas of speciality) routinely ignore the possibility of errors when presenting their evidence. To counter this, we produce what we believe is the first full probabilistic solution of the simple case of generic match evidence incorporating both classes of testing errors. Unfortunately, the resultant event tree solution is too complex for intuitive comprehension. And, crucially, the event tree also fails to represent the causal information that underpins the argument. In contrast, we also present a simple-to-construct graphical Bayesian Network (BN) solution that automatically performs the calculations and may also be intuitively simpler to understand. Although there have been multiple previous applications of BNs for analysing forensic evidence—including very detailed models for the DNA matching problem, these models have not widely penetrated the expert witness community. Nor have they addressed the basic generic match problem incorporating the two types of testing error. Hence we believe our basic BN solution provides an important mechanism for convincing experts—and eventually the legal community—that it is possible to rigorously analyse and communicate the full impact of match evidence on a case, in the presence of possible error

Summertime evaluation of REFAME over the Unites States for near real-time high resolution precipitation estimation

Precipitation is the key input for hydrometeorological modeling and applications. In many regions of the world, including populated areas, ground-based measurement of precipitation (whether from radar or rain gauge) is either sparse in time and space or nonexistent. Therefore, high-resolution satellite-based precipitation products are recognized as critical data sources, especially for rapidly-evolving hydrometeorological events such as flash floods which primarily occur during summer/warm seasons. As " proof of concept" , a recently proposed algorithm called Rain Estimation using Forward Adjusted-advection of Microwave Estimates (REFAME) and its variation REFAMEgeo are evaluated over the contiguous United States during summers of 2009 and 2011. Both methods are originally designed for near real-time high resolution precipitation estimation from remotely sensed data. High-resolution Q2 (ground radar) precipitation data, in conjunction with two operational near real-time satellite-based precipitation products (PERSIANN, PERSIANN-CCS) are used as evaluation reference and for comparison. The study is performed at half-hour temporal resolution and at a range of spatial resolutions (0.08-, 0.25-, 0.5-, and 1-degree latitude/longitude). The statistical analyses suggest that REFAMEgeo performs favorably among the studied products in terms of capturing both spatial coverage and intensity of precipitation at near real-time with the temporal resolution offered by geostationary satellites. With respect to volume precipitation, REFAMEgeo together with REFAME demonstrates slight overestimation of intense precipitation and underestimation of light precipitation events. Compared to REFAME, It is observed that REFAMEgeo maintains stable performance, even when the amount of accessible microwave (MW) overpasses is limited. Based on the encouraging outcome of this study which was intended as " proof of concept" , further testing for other seasons and data-rich regions is the next logical step. Upon confirmation of the relative reliability of the algorithm, it is reasonable to recommend the use of its precipitation estimates for data-sparse regions of the world. © 2012 Elsevier B.V

A sequential formula for electronic coupling in long range bridge-assisted electron transfer: Formulation of theory and application to alkanethiol monolayers

A recursion relation is formulated for the Green's function for calculating the effective electron coupling in bridge-assisted electronic transfer systems, within the framework of the tight-binding Hamiltonian. The recursion expression relates the Green's function of a chain bridge to that of the bridge that is one unit less. It is applicable regardless of the number of orbitals per unit. This method is applied to the system of a ferrocenylcarboxy-terminated alkanethiol on the Au(111) surface. At larger numbers of bridge units, the effective coupling strength shows an exponential decay as the number of methylene(–CH2–) units increases. This sequential formalism shows numerical stability even for a very long chain bridge and, since it uses only small matrices, requires much less computer time for the calculation. Identical bridge units are not a requirement, and so the method can be applied to more complicated systems