Equi-energy sampler with applications in statistical inference and statistical mechanics

We introduce a new sampling algorithm, the equi-energy sampler, for efficient statistical sampling and estimation. Complementary to the widely used temperature-domain methods, the equi-energy sampler, utilizing the temperature--energy duality, targets the energy directly. The focus on the energy function not only facilitates efficient sampling, but also provides a powerful means for statistical estimation, for example, the calculation of the density of states and microcanonical averages in statistical mechanics. The equi-energy sampler is applied to a variety of problems, including exponential regression in statistics, motif sampling in computational biology and protein folding in biophysics.Comment: This paper discussed in: [math.ST/0611217], [math.ST/0611219], [math.ST/0611221], [math.ST/0611222]. Rejoinder in [math.ST/0611224]. Published at http://dx.doi.org/10.1214/009053606000000515 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Numerical study of large-eddy breakup and its effect on the drag characteristics of boundary layers

The break-up of a field of eddies by a flat-plate obstacle embedded in a boundary layer is studied using numerical solutions to the two-dimensional Navier-Stokes equations. The flow is taken to be incompressible and unsteady. The flow field is initiated from rest. A train of eddies of predetermined size and strength are swept into the computational domain upstream of the plate. The undisturbed velocity profile is given by the Blasius solution. The disturbance vorticity generated at the plate and wall, plus that introduced with the eddies, mix with the background vorticity and is transported throughout the entire flow. All quantities are scaled by the plate length, the unidsturbed free-stream velocity, and the fluid kinematic viscosity. The Reynolds number is 1000, the Blasius boundary layer thickness is 2.0, and the plate is positioned a distance of 1.0 above the wall. The computational domain is four units high and sixteen units long

Stabilisation of peat with colloidal nanosilica

Colloidal nanosilica hydrosols are electrochemically stabilised polymerised amorphous silica in low viscosity suspensions. They have no known adverse impact on soil health and ecosystem service functions, thereby having a scope for use in groundworks as an alternative low-viscose stabilising material. Six grades of colloidal nanosilica are synthesised through an in-house procedure and introduced to a natural peat soil. The peak and residual compressive strength of compacted and modified soils are measured immediately after treatment and in four strain levels post treatment. Findings suggest that, despite the direct correlation between the nanosilica content and compressive strength, an increase in nanosilica content does not necessarily offer stability at larger strains. This is a major limitation. The particle-level kinematics in modified peat is discussed to gain a new insight into the role played by silica flocs on the build-up of macro-mechanical quantities such as peak and critical state strength. Overall, modification of peat with nanosilica leads to improvements in strength and formation of composites with generally more dilative behaviour. When used as a single stabiliser, a design 15 % to 20 % grade nanosilica solution yields a reasonably high strength although precautions against excessive straining of modified peat soils need to be taken in the first seven days post treatment. At this optimum grade, the loss of strength on further straining is capped to 9 % at plastic strains 1.5 times the peak strain

Exotic fermion multiplets as a solution to baryon asymmetry, dark matter and neutrino masses

We propose an extension to the standard model where three exotic fermion 5-plets and one scalar 6-plet are added to the particle content. By demanding that all interactions are renormalizable and standard model gauge invariant, we show that the lightest exotic particle in this model can be a dark matter candidate as long as the new 6-plet scalar does not develop a nonzero vacuum expectation value. Furthermore, light neutrino masses are generated radiatively at one-loop while the baryon asymmetry is produced by the CP-violating decays of the second lightest exotic particle. We have demonstrated using concrete examples that there is a parameter space where a consistent solution to the problems of baryon asymmetry, dark matter and neutrino masses can be obtained.Comment: 17 pages, 2 figures (REVTeX4.1), v2: some refs added, v3: typos corrected, Sec.VI.B, C modified, this version to appear in PR

Quantum many-body models with cold atoms coupled to photonic crystals

Using cold atoms to simulate strongly interacting quantum systems represents an exciting frontier of physics. However, as atoms are nominally neutral point particles, this limits the types of interactions that can be produced. We propose to use the powerful new platform of cold atoms trapped near nanophotonic systems to extend these limits, enabling a novel quantum material in which atomic spin degrees of freedom, motion, and photons strongly couple over long distances. In this system, an atom trapped near a photonic crystal seeds a localized, tunable cavity mode around the atomic position. We find that this effective cavity facilitates interactions with other atoms within the cavity length, in a way that can be made robust against realistic imperfections. Finally, we show that such phenomena should be accessible using one-dimensional photonic crystal waveguides in which coupling to atoms has already been experimentally demonstrated

Approximate gauge symmetry of composite vector bosons

It can be shown in a solvable field theory model that the couplings of the composite vector bosons made of a fermion pair approach the gauge couplings in the limit of strong binding. Although this phenomenon may appear accidental and special to the vector boson made of a fermion pair, we extend it to the case of bosons being constituents and find that the same phenomenon occurs in more an intriguing way. The functional formalism not only facilitates computation but also provides us with a better insight into the generating mechanism of approximate gauge symmetry, in particular, how the strong binding and global current conservation conspire to generate such an approximate symmetry. Remarks are made on its possible relevance or irrelevance to electroweak and higher symmetries.Comment: Correction of typos. The published versio

Numerical evidences of spin-1/2 chain approaching spin-1 chain

In this article, we study the one dimensional Heisenberg spin-1/2 alternating bond chain in which the nearest neighbor exchange couplings are ferromagnetic (FM) and antiferromagnetic (AF) alternatively. By using exact diagonalization and density matrix renormalization groups (DMRG) method, we discuss how the system approaches to the AF uniform spin-1 chain under certain condition. When the ratio of AF to FM coupling strength}$\alpha$ $(\alpha=J_{AF}/J_{F})$ \textit{is very small, the physical quantities of the alternating bond chain such as the spin-spin correlation, the string correlation function and the spin density coincide with that of the AF uniform spin-1 chain. The edge state problem is discussed in the present model with small}$\alpha$\textit{limit. In addition, the Haldane gap of the AF uniform spin-1 chain is 4-times of the gap of the system considered.Comment: 9pages,8page