Quest for consistent modelling of statistical decay of the compound nucleus

A statistical model description of heavy ion induced fusion-fission reactions is presented where shell effects, collective enhancement of level density, tilting away effect of compound nuclear spin and dissipation are included. It is shown that the inclusion of all these effects provides a consistent picture of fission where fission hindrance is required to explain the experimental values of both pre-scission neutron multiplicities and evaporation residue cross-sections in contrast to some of the earlier works where a fission hindrance is required for pre-scission neutrons but a fission enhancement for evaporation residue cross-sections.Comment: 14 pages, 2 figure

Alleviating the inconsistencies in modelling decay of fissile compound nuclei

This work attempts to overcome the existing inconsistencies in modelling decay of fissile nucleus by inclusion of important physical effects in the model and through a systematic analysis of a large set of data over a wide range of CN mass (ACN). The model includes shell effect in the level density (LD) parameter, shell correction in the fission barrier, effect of the orientation degree of freedom of the CN spin (Kor), collective enhancement of level density (CELD) and dissipation in fission. Input parameters are not tuned to reproduce observables from specific reaction(s) and the reduced dissipation coefficient is treated as the only adjustable parameter. Calculated evaporation residue (ER) cross sections, fission cross sections and particle, i.e. neutron, proton and alpha-particle, multiplicities are compared with data covering ACN = 156-248. The model produces reasonable fits to ER and fission excitation functions for all the reactions considered in this work. Pre-scission neutron multiplicities are underestimated by the calculation beyond ACN~200. An increasingly higher value of pre-saddle dissipation strength is required to reproduce the data with increasing ACN. Proton and alpha-particle multiplicities, measured in coincidence with both ERs and fission fragments, are in qualitative agreement with model predictions. The present work mitigates the existing inconsistencies in modelling statistical decay of the fissile CN to a large extent.Comment: 15 pages, 9 figure

Split rank of triangle and quadrilateral inequalities

A simple relaxation of two rows of a simplex tableau is a mixed integer set consisting of two equations with two free integer variables and non-negative continuous variables. Recently Andersen et al. [2] and Cornu´ejols and Margot [13] showed that the facet-defining inequalities of this set are either split cuts or intersection cuts obtained from lattice-free triangles and quadrilaterals. Through a result by Cook et al. [12], it is known that one particular class of facet- defining triangle inequality does not have a finite split rank. In this paper, we show that all other facet-defining triangle and quadrilateral inequalities have finite split rank. The proof is constructive and given a facet-defining triangle or quadrilateral inequality we present an explicit sequence of split inequalities that can be used to generate it.mixed integer programs, split rank, group relaxations

Electron transport through a quantum interferometer with side-coupled quantum dots: Green's function approach

We study electron transport through a quantum interferometer with side-coupled quantum dots. The interferometer, threaded by a magnetic flux $\phi$, is attached symmetrically to two semi-infinite one-dimensional metallic electrodes. The calculations are based on the tight-binding model and the Green's function method, which numerically compute the conductance-energy and current-voltage characteristics. Our results predict that under certain conditions this particular geometry exhibits anti-resonant states. These states are specific to the interferometric nature of the scattering and do not occur in conventional one-dimensional scattering problems of potential barriers. Most importantly we show that, such a simple geometric model can also be used as a classical XOR gate, where the two gate voltages, viz, $V_a$ and $V_b$, are applied, respectively, in the two dots those are treated as the two inputs of the XOR gate. For $\phi=\phi_0/2$ ($\phi_0=ch/e$, the elementary flux-quantum), a high output current (1) (in the logical sense) appears if one, and only one, of the inputs to the gate is high (1), while if both inputs are low (0) or both are high (1), a low output current (0) appears. It clearly demonstrates the XOR gate behavior and this aspect may be utilized in designing the electronic logic gate.Comment: 8 pages, 5 figure

Some lower bounds on sparse outer approximations of polytopes

Motivated by the need to better understand the properties of sparse cutting-planes used in mixed integer programming solvers, the paper [2] studied the idealized problem of how well a polytope is approximated by the use of sparse valid inequalities. As an extension to this work, we study the following less idealized questions in this paper: (1) Are there integer programs, such that sparse inequalities do not approximate the integer hull well even when added to a linear programming relaxation? (2) Are there polytopes, where the quality of approximation by sparse inequalities cannot be significantly improved by adding a budgeted number of arbitrary (possibly dense) valid inequalities? (3) Are there polytopes that are difficult to approximate under every rotation? (4) Are there polytopes that are difficult to approximate in all directions using sparse inequalities? We answer each of the above questions in the positive