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Here a real life optimal control problem under fuzzy time period using variational principle is formulated and Solved. The unit production cost is a function of production rate and also dependent on raw material cost, development cost due to durability and wear-tear cost. The holding cost is assumed to be non-linear, dependent on time. The profit function which consists of revenue, production cost and holding cost is formulated as a Fuzzy-Final Time and Fixed State System optimal control problem with fuzzy time period. Here production rate is unknown and considered as a control variable and stock level is taken as a state variable. It is formulated to optimize the production rate so that total profit is maximum. The non-linear optimization technique-Generalised Reduced Gradient Method (LINGO 11.0) is used. The optimum results are illustrated both numerically and graphically., Comment: arXiv admin note: substantial text overlap with arXiv:2006.01740

Breakability rate of fragile item depends on the accumulated stress of heaped stock level. So breakablility rate can be considered as dependent parameter of stock variable. The unit production cost is a function of production rate and also dependent on raw material cost, development cost and wear-tear cost. The holding cost is assumed to be non-linear, dependent on time. Here optimal control problem for a fragile item under finite time horizon is considered. The profit function which consists of revenue, production and holding costs is formulated as a Fixed-Final Time and Fixed State System(cf. Naidu (2000)) optimal control problem with finite time horizon. Here production rate is unknown and considered as a control variable and stock level is taken as a state variable. It is formulated to optimize the production rate so that total profit is maximum. As particular cases, models are evaluated with and without breakability. The models are solved by using conventional Variational Principle along with the non-linear optimization technique-Generalised Reduced Gradient Method (LINGO 12.0). The optimum results are illustrated both numerically and graphically. Some sensitivity analysis on breakability coefficient are presented., Comment: 14 pages 5 figures

We study the transport properties of junctions of normal and superconducting Weyl semi-metal with tilted dispersion, in the presence of magnetization induced by magnetic strips. The sub gap tunnelling conductance shows robust signatures in the presence of different orientation and strength of magnetization of the magnetic strips. We obtain the analytical results for the normal-magnetic-superconducting junction in the thin barrier limit and demonstrate that these results have no analogues to their conventional counterparts and junctions with Dirac electrons in two-dimensions. We discuss possible experimental setups to test our theoretical predictions., Comment: To be published in Journal of Physics: Condensed Matter

We study the Loschmidt echo for quenches in open one-dimensional lattice models with symmetry protected topological phases. For quenches where dynamical quantum phase transitions do occur we find that cusps in the bulk return rate at critical times tc are associated with sudden changes in the boundary contribution. For our main example, the Su-Schrieffer-Heeger model, we show that these sudden changes are related to the periodical appearance of two eigenvalues close to zero in the dynamical Loschmidt matrix. We demonstrate, furthermore, that the structure of the Loschmidt spectrum is linked to the periodic creation of long-range entanglement between the edges of the system.

We demonstrate that the current-voltage (I-V) characteristics of resistively and capacitively shunted Josephson junctions (RCSJs) hosting localized subgap Majorana states provides a phase sensitive method for their detection. The I-V characteristics of such RCSJs, in contrast to their resistively shunted counterparts, exhibit subharmonic odd Shapiro steps; such steps occur even in the absence of any $2\pi$ periodic terms in the current-phase relation of these junctions. These steps, owing to their subharmonic nature, exhibit qualitatively different properties compared to harmonic odd steps of conventional junctions. In addition, the RCSJs hosting Majorana bound states also display an additional sequence of steps in the devil staircase structure seen in their I-V characteristics; such sequence of steps make their I-V characteristics qualitatively distinct from that of their conventional counterparts. A similar study for RCSJs with graphene superconducting junctions hosting Dirac-like quasiparticles reveals that the Shapiro step width in their I-V curves bears a signature of the transmission resonance phenomenon of their underlying Dirac quasiparticles; consequently, these step widths exhibit a $\pi$ periodic oscillatory behavior with variation of the junction barrier potential. We discuss experiments which can test our theory., Comment: v3: 8 pages 5 figs; more comments and numerical estimates; final version accepted fpr publication in PRB

We present a detailed study of the fidelity, the entanglement entropy, and the entanglement spectrum, for a dimerized chain of spinless fermions---a simplified Su-Schrieffer-Heeger (SSH) model---with open boundary conditions which is a well-known example for a model supporting a symmetry protected topological (SPT) phase. In the non-interacting case the Hamiltonian matrix is tridiagonal and the eigenvalues and -vectors can be given explicitly as a function of a single parameter which is known analytically for odd chain lengths and can be determined numerically in the even length case. From a scaling analysis of these data for essentially semi-infinite chains we obtain the fidelity susceptibility and show that it contains a boundary contribution which is different in the topologically ordered than in the topologically trivial phase. For the entanglement spectrum and entropy we confirm predictions from massive field theory for a block in the middle of an infinite chain but also consider blocks containing the edge of the chain. For the latter case we show that in the SPT phase additional entanglement---as compared to the trivial phase---is present which is localized at the boundary. Finally, we extend our study to the dimerized chain with a nearest-neighbour interaction using exact diagonalization, Arnoldi, and density-matrix renormalization group methods and show that a phase transition into a topologically trivial charge-density wave phase occurs., Comment: References added

The determination of the absolute scale of the neutrino masses is one of the most challenging present questions in particle physics. The most stringent limit, $m(\bar{\nu}_{\mathrm{e}})<2$eV, was achieved for the electron anti-neutrino mass \cite{numass}. Different approaches are followed to achieve a sensitivity on neutrino masses in the sub-eV range. Among them, experiments exploring the beta decay or electron capture of suitable nuclides can provide information on the electron neutrino mass value. We present the Electron Capture $^{163}$Ho experiment ECHo, which aims to investigate the electron neutrino mass in the sub-eV range by means of the analysis of the calorimetrically measured energy spectrum following electron capture of $^{163}$Ho. A high precision and high statistics spectrum will be measured with arrays of metallic magnetic calorimeters. We discuss some of the essential aspects of ECHo to reach the proposed sensitivity: detector optimization and performance, multiplexed readout, $^{163}$Ho source production and purification, as well as a precise theoretical and experimental parameterization of the calorimetric EC spectrum including in particular the value of $Q_{\mathrm{EC}}$. We present preliminary results obtained with a first prototype of single channel detectors as well as a first 64-pixel chip with integrated micro-wave SQUID multiplexer, which will already allow to investigate $m(\nu_{\mathrm{e}})$ in the eV range., Comment: Contribution to the LTD15 Conference Proceedings

The determination of the absolute scale of the neutrino masses is one of the most challenging questions in particle physics. Different approaches are followed to achieve a sensitivity on neutrino masses in the sub-eV range. Among them, experiments exploring the beta decay and electron capture processes of suitable nuclides can provide necessary information on the electron neutrino mass value. In this talk we present the Electron Capture 163-Ho experiment ECHo, which aims to investigate the electron neutrino mass in the sub-eV range by means of the analysis of the calorimetrically measured energy spectrum following the electron capture process of 163-Ho. A high precision and high statistics spectrum will be measured by means of low temperature magnetic calorimeter arrays. We present preliminary results obtained with a first prototype of single channel detectors as well as the participating groups and their on-going developments., Comment: Part of the white paper for the NuMass 2013 Workshop (Milano, Italy 4-7 February 2013)

In this review we focus on the effect of the Dirac nature of graphene quasiparticles on two separate aspects. The first of these involves transport across superconducting graphene junctions with barriers of thickness $d_0$ and arbitrary gate voltages $V_0$ applied across the barrier region. The second aspect involves study of the presence of localized magnetic impurities in graphene and we show that Kondo effect in graphene is unconventional and can be tuned by gate voltage. We also discuss scanning tunneling conductance spectra phenomenon for both doped and undoped graphene. We show that the position of the impurity on or in graphene plays a subtle role and affects the underlying physics of STM spectra in doped graphene., Comment: Invited review article for WSPC's Annual Review on Graphene

An accurate knowledge of the neutron capture cross sections of 62,63Ni is crucial since both isotopes take key positions which affect the whole reaction flow in the weak s process up to A=90. No experimental value for the 63Ni(n,gamma) cross section exists so far, and until recently the experimental values for 62Ni(n,gamma) at stellar temperatures (kT=30 keV) ranged between 12 and 37 mb. This latter discrepancy could now be solved by two activations with following AMS using the GAMS setup at the Munich tandem accelerator which are also in perfect agreement with a recent time-of-flight measurement. The resulting (preliminary) Maxwellian cross section at kT=30 keV was determined to be 30keV = 23.4 +/- 4.6 mb. Additionally, we have measured the 64Ni(gamma,n)63Ni cross section close to threshold. Photoactivations at 13.5 MeV, 11.4 MeV and 10.3 MeV were carried out with the ELBE accelerator at Forschungszentrum Dresden-Rossendorf. A first AMS measurement of the sample activated at 13.5 MeV revealed a cross section smaller by more than a factor of 2 compared to NON-SMOKER predictions., Comment: Proceedings of the 11th International Conference on Accelerator Mass Spectrometry in Rome, Sept. 14-19, 2008; to be published in Nucl. Instr. Meth. A

We report, for the first time, photometric variability of L dwarfs in $R$ band. Out of three L1 dwarfs (2MASS 1300+19, 2MASS 1439+19, and 2MASS 1658+70) observed, we have detected R band variability in 2MASS 1300+19 and 2MASS 1439+19. The objects exhibit variability of amplitude ranging from 0.01 mag to 0.02 mag. Object 2MASS 1658+70, turns out to be non-variable in both $R$ and $I$ band. However, more observations are needed to infer its variability. No periodic behaviour in the variability is found from the two L1 dwarfs that are variable. All the three L1 dwarfs have either negligible or no $H_{\alpha}$ activity. In the absence of any direct evidence for the presence of sufficiently strong magnetic field, the detection of polarization at the optical favors the presence of dust in the atmosphere of L dwarfs. We suggest that the observed $R$ band photometric variability is most likely due to atmospheric dust activity., Comment: 13 pages (latex, aastex style) including 3 eps figures. Accepted for publication in The Astrophysical Journal Letters