Unification modulo a partial theory of exponentiation

Modular exponentiation is a common mathematical operation in modern cryptography. This, along with modular multiplication at the base and exponent levels (to different moduli) plays an important role in a large number of key agreement protocols. In our earlier work, we gave many decidability as well as undecidability results for multiple equational theories, involving various properties of modular exponentiation. Here, we consider a partial subtheory focussing only on exponentiation and multiplication operators. Two main results are proved. The first result is positive, namely, that the unification problem for the above theory (in which no additional property is assumed of the multiplication operators) is decidable. The second result is negative: if we assume that the two multiplication operators belong to two different abelian groups, then the unification problem becomes undecidable.Comment: In Proceedings UNIF 2010, arXiv:1012.455

Rheological model for short duration response of semi-solid metals

A thorough understanding of the rheological behavior of the semi-solid metal (SSM) alloys is of utmost importance for modeling and simulation of rheocasting and thixoforming processes. Since the duration of these processes is very short-fraction of a second-the primary focus should be on fast transient flows. We present here a relatively simple engineering model for unsteady state shear stress of semi-solid metal suspensions. The time dependent character of thixotropic semi-solids is introduced through scaling by a structural parameter, which represents the degree of connectivity or aggregation of particles in the fluid. The kinetic equation for change in structural parameter as a function of time incorporates both breakage and agglomeration of suspended entities. The proposed model simulates the fast transient, tracks the evolution or healing of structure with holding time in absence of applied shear, and computes the steady state structure for a given shearing rate after long shearing time. Moreover, it explicitly incorporates the shear yield stress as well as is in agreement with important rheological characteristics of semi-solid materials, namely, shear thickening behavior under isostructural conditions and power law relationship between steady state viscosity and shear rate. The model is validated with published data for short time measurements of Sn-15%Pb thixotropic systems with near step change in shear rate and steady state shear viscosity. It could have practical utility in simulation of flow of semi-solid materials in different die cavities

A combined experimental and computational fluid dynamics analysis of the dynamics of drop formation

This article presents a complementary experimental and computational investigation of the effect of viscosity and flowrate on the dynamics of drop formation in the dripping mode. In contrast to previous studies, numerical simulations are performed with two popular commercial computational fluid dynamics (CFD) packages, CFX and FLOW-3D, both of which employ the volume of fluid (VOF) method. Comparison with previously published experimental and computational data and new experimental results reported here highlight the capabilities and limitations of the aforementioned packages

Balling and granulation kinetics revisited

Balling of finely comminuted solids by random coalescence and granulation of iron ore fines and other minerals by autolayering are two major size enlargement processes. The existing kinetic model for random coalescence does not take into account the strong dependence of coordination number on the size distribution of agglomerating entities. We present a coordination number based coalescence model, which mimics the underlying physical process more realistically. Simulations show that in spite of highly diverse model structures, random and coordination coalescence models give remarkably similar results. Only static models of autolayering are available presently. These map the input size distribution of feed solids into steady state or terminal size distribution of granules, with little or no information on the path traversed by the process. We propose a continuous-time dynamic model of autolayering within the population balance framework. The model, which is based on the proportionate growth postulate of autolayering, agrees reasonably well with experimental data

A population balance model for flocculation of colloidal suspensions by polymer bridging

A detailed population balance model for flocculation of colloidal suspensions by polymer bridging under quiescent flow conditions is presented. The collision efficiency factor is estimated as a function of interaction forces between polymer coated particles. The total interaction energy is computed as a sum of van der Waals attraction, electrical double layer repulsion and bridging attraction or steric repulsion due to adsorbed polymer. The scaling theory is used to compute the forces due to adsorbed polymer and the van der Waals attraction is modified to account for presence of polymer layer around a particle. The irregular structure of flocs is taken into account by incorporating the mass fractal dimension of flocs. When tested with experimental floc size distribution data published in the literature, the model predicts the experimental behavior adequately. This is the first attempt towards incorporating theories of polymer-induced surface forces into a flocculation model, and as such the model presented here is more general than those proposed previously

Computer aided Design and Optimization of Mineral Processing Plants by a State of the Art Simulator

Tata Research Development and Design Centre (TRDDC) has developed a state of the art mineral processing simulator called SimL8. It performs modelling, simulation and optimisation functions and provides viable strategies for enhancement of the performance of mineral processing plants. A number of case studies on plant diagnostics, grinding,classification, flotation and pressure filtration are taken up to demonstrate the utility of modelling and simulation on SimL8 platform

Three Cuts for Accelerated Interval Propagation

This paper addresses the problem of nonlinear multivariate root finding. In an earlier paper we described a system called Newton which finds roots of systems of nonlinear equations using refinements of interval methods. The refinements are inspired by AI constraint propagation techniques. Newton is competative with continuation methods on most benchmarks and can handle a variety of cases that are infeasible for continuation methods. This paper presents three "cuts" which we believe capture the essential theoretical ideas behind the success of Newton. This paper describes the cuts in a concise and abstract manner which, we believe, makes the theoretical content of our work more apparent. Any implementation will need to adopt some heuristic control mechanism. Heuristic control of the cuts is only briefly discussed here

Imipramine blue sensitively and selectively targets FLT3-ITD positive acute myeloid leukemia cells.

Aberrant cytokine signaling initiated from mutant receptor tyrosine kinases (RTKs) provides critical growth and survival signals in high risk acute myeloid leukemia (AML). Inhibitors to FLT3 have already been tested in clinical trials, however, drug resistance limits clinical efficacy. Mutant receptor tyrosine kinases are mislocalized in the endoplasmic reticulum (ER) of AML and play an important role in the non-canonical activation of signal transducer and activator of transcription 5 (STAT5). Here, we have tested a potent new drug called imipramine blue (IB), which is a chimeric molecule with a dual mechanism of action. At 200-300 nM concentrations, IB is a potent inhibitor of STAT5 through liberation of endogenous phosphatase activity following NADPH oxidase (NOX) inhibition. However, at 75-150 nM concentrations, IB was highly effective at killing mutant FLT3-driven AML cells through a similar mechanism as thapsigargin (TG), involving increased cytosolic calcium. IB also potently inhibited survival of primary human FLT3/ITD+ AML cells compared to FLT3/ITDneg cells and spared normal umbilical cord blood cells. Therefore, IB functions through a mechanism involving vulnerability to dysregulated calcium metabolism and the combination of fusing a lipophilic amine to a NOX inhibiting dye shows promise for further pre-clinical development for targeting high risk AML