The aims of the present study are to predict and improve inclusion
separation capacity of a six strand tundish by employing flow
modifiers (dams and weirs) and to assess the influence of inclusion properties
(diameter and density) together with velocity of liquid steel at the
inlet gate on the inclusion removal efficiency of a six-strand tundish. Computational
solutions of the Reynolds-Averaged Navier-Strokes (RANS) equations together
with the energy equation are performed to obtain the steady, three-dimensional
velocity and temperature fields using the standard k-ε model of turbulence. These flow fields are then used to
predict the inclusion sepapration by numerically solving the inclusion
transport equation. To account for the effects of turbulence on particle
paths a discrete random walk model is employed. It was observed that with the
employment of flow modifiers, the inclusion separation capacity of tundish
increases without any large variation in the outlet temperatures. It is shown that
inclusion properties and velocity are important parameters in
defining the operating conditions of a six-strand tundish.

Abstract:
The study attempts to find out the trends in dividend payment and determinants of dividend decision. Asample of 607 BSE-listed Indian companies has been considered for the period from 1993-94 to 2004-05.Study results show that number of non-payers and low-payers of dividend has increased. Again, averagedividend payments are on the rise continuously. It means that there is no room for moderate dividendpayment. Average dividend for the past three years is the most consistent and significant determinant ofdividend payment. Current profit, past profit and expected future profit have significant positive role to playin setting dividend rate. Again, cash position and cash flow has significant negative relationship with onlydividend rate. Interest expenses, capital expenditure, tax ratio and share price behaviour has almost no role toplay in the matter of dividend payment. That the stability of dividend is the primary concern for the managersat the time of taking dividend decision is upheld.

Abstract:
We investigate the break-up of Newtonian/viscoelastic droplets in a viscoelastic/Newtonian matrix under the hydrodynamic conditions of a confined shear flow. Our numerical approach is based on a combination of Lattice-Boltzmann models (LBM) and Finite Difference (FD) schemes. LBM are used to model two immiscible fluids with variable viscosity ratio (i.e. the ratio of the droplet to matrix viscosity); FD schemes are used to model viscoelasticity, and the kinetics of the polymers is introduced using constitutive equations for viscoelastic fluids with finitely extensible non-linear elastic dumbbells with Peterlin's closure (FENE-P). We study both strongly and weakly confined cases to highlight the role of matrix and droplet viscoelasticity in changing the droplet dynamics after the startup of a shear flow. Simulations provide easy access to quantities such as droplet deformation and orientation and will be used to quantitatively predict the critical Capillary number at which the droplet breaks, the latter being strongly correlated to the formation of multiple neckings at break-up. This study complements our previous investigation on the role of droplet viscoelasticity (A. Gupta \& M. Sbragaglia, {\it Phys. Rev. E} {\bf 90}, 023305 (2014)), and is here further extended to the case of matrix viscoelasticity.

Abstract:
Based on mesoscale lattice Boltzmann (LB) numerical simulations, we investigate the effects of viscoelasticity on the break-up of liquid threads in microfluidic cross-junctions, where droplets are formed by focusing a liquid thread of a dispersed (d) phase into another co-flowing continuous (c) immiscible phase. Working at small Capillary numbers, we investigate the effects of non-Newtonian phases in the transition from droplet formation at the cross-junction (DCJ) to droplet formation downstream of the cross-junction (DC) (Liu $\&$ Zhang, ${\it Phys. ~Fluids.}$ ${\bf 23}$, 082101 (2011)). We will analyze cases with ${\it Droplet ~Viscoelasticity}$ (DV), where viscoelastic properties are confined in the dispersed phase, as well as cases with ${\it Matrix ~Viscoelasticity}$ (MV), where viscoelastic properties are confined in the continuous phase. Moderate flow-rate ratios $Q \approx {\cal O}(1)$ of the two phases are considered in the present study. Overall, we find that the effects are more pronounced in the case with MV, where viscoelasticity is found to influence the break-up point of the threads, which moves closer to the cross-junction and stabilizes. This is attributed to an increase of the polymer feedback stress forming in the corner flows, where the side channels of the device meet the main channel. Quantitative predictions on the break-up point of the threads are provided as a function of the Deborah number, i.e. the dimensionless number measuring the importance of viscoelasticity with respect to Capillary forces.

Abstract:
The effects of elasticity on the break-up of liquid threads in microfluidic cross-junctions is investigated using numerical simulations based on the "lattice Boltzmann models" (LBM). Working at small Capillary numbers, we investigate the effects of non-Newtonian phases in the transition from droplet formation at the cross-junction (DCJ) and droplet formation downstream of the cross-junction (DC) (Liu & Zhang, ${\it Phys. Fluids.}$ ${\bf 23}$, 082101 (2011)). Viscoelasticity is found to influence the break-up point of the threads, which moves closer to the cross-junction and stabilizes. This is attributed to an increase of the polymer feedback stress forming in the corner flows, where the side channels of the device meet the main channel.

Abstract:
The effects of viscoelasticity on the dynamics and break-up of fluid threads in microfluidic T-junctions are investigated using numerical simulations of dilute polymer solutions at changing the Capillary number ($\mbox {Ca}$), i.e. at changing the balance between the viscous forces and the surface tension at the interface, up to $\mbox{Ca} \approx 3 \times 10^{-2}$. A Navier-Stokes (NS) description of the solvent based on the lattice Boltzmann models (LBM) is here coupled to constitutive equations for finite extensible non-linear elastic dumbbells with the closure proposed by Peterlin (FENE-P model). We present the results of three-dimensional simulations in a range of $\mbox{Ca}$ which is broad enough to characterize all the three characteristic mechanisms of breakup in the confined T-junction, i.e. ${\it squeezing}$, ${\it dripping}$ and ${\it jetting}$ regimes. The various model parameters of the FENE-P constitutive equations, including the polymer relaxation time $\tau_P$ and the finite extensibility parameter $L^2$, are changed to provide quantitative details on how the dynamics and break-up properties are affected by viscoelasticity. We will analyze cases with ${\it Droplet ~Viscoelasticity}$ (DV), where viscoelastic properties are confined in the dispersed (d) phase, as well as cases with ${\it Matrix ~Viscoelasticity}$ (MV), where viscoelastic properties are confined in the continuous (c) phase. Moderate flow-rate ratios $Q \approx {\cal O}(1)$ of the two phases are considered in the present study. Overall, we find that the effects are more pronounced in the case with MV, as the flow driving the break-up process upstream of the emerging thread can be sensibly perturbed by the polymer stresses.

Abstract:
We consider the problem of solving packing/covering LPs online, when the columns of the constraint matrix are presented in random order. This problem has received much attention and the main focus is to figure out how large the right-hand sides of the LPs have to be (compared to the entries on the left-hand side of the constraints) to allow $(1+\epsilon)$-approximations online. It is known that the right-hand sides have to be $\Omega(\epsilon^{-2} \log m)$ times the left-hand sides, where $m$ is the number of constraints. In this paper we give a primal-dual algorithm that achieve this bound for mixed packing/covering LPs. Our algorithms construct dual solutions using a regret-minimizing online learning algorithm in a black-box fashion, and use them to construct primal solutions. The adversarial guarantee that holds for the constructed duals helps us to take care of most of the correlations that arise in the algorithm; the remaining correlations are handled via martingale concentration and maximal inequalities. These ideas lead to conceptually simple and modular algorithms, which we hope will be useful in other contexts.

Abstract:
We study local search algorithms for metric instances of facility location problems: the uncapacitated facility location problem (UFL), as well as uncapacitated versions of the $k$-median, $k$-center and $k$-means problems. All these problems admit natural local search heuristics: for example, in the UFL problem the natural moves are to open a new facility, close an existing facility, and to swap a closed facility for an open one; in $k$-medians, we are allowed only swap moves. The local-search algorithm for $k$-median was analyzed by Arya et al. (SIAM J. Comput. 33(3):544-562, 2004), who used a clever ``coupling'' argument to show that local optima had cost at most constant times the global optimum. They also used this argument to show that the local search algorithm for UFL was 3-approximation; their techniques have since been applied to other facility location problems. In this paper, we give a proof of the $k$-median result which avoids this coupling argument. These arguments can be used in other settings where the Arya et al. arguments have been used. We also show that for the problem of opening $k$ facilities $F$ to minimize the objective function $\Phi_p(F) = \big(\sum_{j \in V} d(j, F)^p\big)^{1/p}$, the natural swap-based local-search algorithm is a $\Theta(p)$-approximation. This implies constant-factor approximations for $k$-medians (when $p=1$), and $k$-means (when $p = 2$), and an $O(\log n)$-approximation algorithm for the $k$-center problem (which is essentially $p = \log n$).

Abstract:
A covering integer program (CIP) is a mathematical program of the form: min {c^T x : Ax >= 1, 0 <= x <= u, x integer}, where A is an m x n matrix, and c and u are n-dimensional vectors, all having non-negative entries. In the online setting, the constraints (i.e., the rows of the constraint matrix A) arrive over time, and the algorithm can only increase the coordinates of vector x to maintain feasibility. As an intermediate step, we consider solving the covering linear program (CLP) online, where the integrality requirement on x is dropped. Our main results are (a) an O(log k)-competitive online algorithm for solving the CLP, and (b) an O(log k log L)-competitive randomized online algorithm for solving the CIP. Here k<=n and L<=m respectively denote the maximum number of non-zero entries in any row and column of the constraint matrix A. By a result of Feige and Korman, this is the best possible for polynomial-time online algorithms, even in the special case of set cover.

Abstract:
We study a general stochastic probing problem defined on a universe V, where each element e in V is "active" independently with probability p_e. Elements have weights {w_e} and the goal is to maximize the weight of a chosen subset S of active elements. However, we are given only the p_e values-- to determine whether or not an element e is active, our algorithm must probe e. If element e is probed and happens to be active, then e must irrevocably be added to the chosen set S; if e is not active then it is not included in S. Moreover, the following conditions must hold in every random instantiation: (1) the set Q of probed elements satisfy an "outer" packing constraint, and (2) the set S of chosen elements satisfy an "inner" packing constraint. The kinds of packing constraints we consider are intersections of matroids and knapsacks. Our results provide a simple and unified view of results in stochastic matching and Bayesian mechanism design, and can also handle more general constraints. As an application, we obtain the first polynomial-time $\Omega(1/k)$-approximate "Sequential Posted Price Mechanism" under k-matroid intersection feasibility constraints.