Embedding the Pentagon

The Pentagon Model is an explicit supersymmetric extension of the Standard Model, which involves a new strongly-interacting SU(5) gauge theory at TeV-scale energies. We show that the Pentagon can be embedded into an SU(5) x SU(5) x SU(5) gauge group at the GUT scale. The doublet-triplet splitting problem, and proton decay compatible with experimental bounds, can be successfully addressed in this context. The simplest approach fails to provide masses for the lighter two generations of quarks and leptons; however, this problem can be solved by the addition of a pair of antisymmetric tensor fields and an axion.Comment: 39 page

Ion beam sputter etching

An ion beam etching process which forms extremely high aspect ratio surface microstructures using thin sputter masks is utilized in the fabrication of integrated circuits. A carbon rich sputter mask together with unmasked portions of a substrate is bombarded with inert gas ions while simultaneous carbon deposition occurs. The arrival of the carbon deposit is adjusted to enable the sputter mask to have a near zero or even slightly positive increase in thickness with time while the unmasked portions have a high net sputter etch rate

The linear regulator problem for parabolic systems

An approximation framework is presented for computation (in finite imensional spaces) of Riccati operators that can be guaranteed to converge to the Riccati operator in feedback controls for abstract evolution systems in a Hilbert space. It is shown how these results may be used in the linear optimal regulator problem for a large class of parabolic systems

A numerical algorithm for optimal feedback gains in high dimensional LQR problems

A hybrid method for computing the feedback gains in linear quadratic regulator problems is proposed. The method, which combines the use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated so as to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantage of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed and numerical evidence of the efficacy of our ideas presented

A unified framework for approximation in inverse problems for distributed parameter systems

A theoretical framework is presented that can be used to treat approximation techniques for very general classes of parameter estimation problems involving distributed systems that are either first or second order in time. Using the approach developed, one can obtain both convergence and stability (continuous dependence of parameter estimates with respect to the observations) under very weak regularity and compactness assumptions on the set of admissible parameters. This unified theory can be used for many problems found in the recent literature and in many cases offers significant improvements to existing results

Open String on Symmetric Product

We develop some basic properties of the open string on the symmetric product which is supposed to describe the open string field theory in discrete lightcone quantization (DLCQ). After preparing the consistency conditions of the twisted boundary conditions for Annulus/M\"obius/Klein Bottle amplitudes in generic non-abelian orbifold, we classify the most general solutions of the constraints when the discrete group is $S_N$. We calculate the corresponding orbifold amplitudes from two viewpoints -- from the boundary state formalism and from the trace over the open string Hilbert space. It is shown that the topology of the world sheet for the short string and that of the long string in general do not coincide. For example the annulus sector for the short string contains all the sectors (torus, annulus, Klein bottle, M\"obius strip) of the long strings. The boundary/cross-cap states of the short strings are classified into three categories in terms of the long string, the ordinary boundary and the cross-cap states, and the ``joint'' state which describes the connection of two short strings. We show that the sum of the all possible boundary conditions is equal to the exponential of the sum of the irreducible amplitude -- one body amplitude of long open (closed) strings. This is typical structure of DLCQ partition function. We examined that the tadpole cancellation condition in our language and derived the well-known gauge group $SO(2^{13})$.Comment: 56 pages, 11 figures, Late

Computational methods for estimation of parameters in hyperbolic systems

Approximation techniques for estimating spatially varying coefficients and unknown boundary parameters in second order hyperbolic systems are discussed. Methods for state approximation (cubic splines, tau-Legendre) and approximation of function space parameters (interpolatory splines) are outlined and numerical findings for use of the resulting schemes in model "one dimensional seismic inversion' problems are summarized

Ammonia removal in anaerobic digestion by biogas stripping: an evaluation of process alternatives using a first order rate model based on experimental findings

The feasibility of biogas stripping to remove ammonia in the anaerobic digestion of source segregated food waste was investigated. It was found in batch experiments that ammonia could be removed from digestate and that the removal followed 1st order kinetics with respect to total ammonia nitrogen concentration. Increasing temperature, biogas flow rate and initial pH all increased removal rates. Using kinetic data gathered in these experiments allowed the integration of ammonia stripping with an anaerobic digestion plant to be modelled for different configurations. Four scenarios were identified: post digestion, in situ, side-stream and pre-digestion ammonia removal relating to where in the process the ammonia stripping was performed. The modelling showed that in situ ammonia removal may be best able to reduce in-digester ammonia concentrations over a wide range of organic loading rates whereas pre-digestion showed most promise in terms of application due to the flexibility to control each part of the process separately. Further experimental work is required into these scenarios to confirm their viability

Estimation of coefficients and boundary parameters in hyperbolic systems

Semi-discrete Galerkin approximation schemes are considered in connection with inverse problems for the estimation of spatially varying coefficients and boundary condition parameters in second order hyperbolic systems typical of those arising in 1-D surface seismic problems. Spline based algorithms are proposed for which theoretical convergence results along with a representative sample of numerical findings are given

New developments in the representation of Saharan dust sources in the aerosol–climate model ECHAM6-HAM2

In the aerosol–climate model ECHAM6-HAM2, dust source activation (DSA) observations from Meteosat Second Generation (MSG) satellite are proposed to replace the original source area parameterization over the Sahara Desert. The new setup is tested in nudged simulations for the period 2007 to 2008. The evaluation is based on comparisons to dust emission events inferred from MSG dust index imagery, Aerosol Robotic Network (AERONET) sun photometer observations, and satellite retrievals of aerosol optical thickness (AOT).<br><br>The model results agree well with AERONET measurements especially in terms of seasonal variability, and a good spatial correlation was found between model results and MSG-SEVIRI (Spinning-Enhanced Visible and InfraRed Imager) dust AOT as well as Multi-angle Imaging SpectroRadiometer (MISR) AOT. ECHAM6-HAM2 computes a more realistic geographical distribution and up to 20 % higher annual Saharan dust emissions, using the MSG-based source map. The representation of dust AOT is partly improved in the southern Sahara and Sahel. In addition, the spatial variability is increased towards a better agreement with observations depending on the season. Thus, using the MSG DSA map can help to circumvent the issue of uncertain soil input parameters.<br><br>An important issue remains the need to improve the model representation of moist convection and stable nighttime conditions. Compared to sub-daily DSA information from MSG-SEVIRI and results from a regional model, ECHAM6-HAM2 notably underestimates the important fraction of morning dust events by the breakdown of the nocturnal low-level jet, while a major contribution is from afternoon-to-evening emissions