scholarly journals Optimal boarding policies for thin passengers

2007 ◽  
Vol 39 (4) ◽  
pp. 1098-1114 ◽  
Author(s):  
Eitan Bachmat ◽  
Daniel Berend ◽  
Luba Sapir ◽  
Steven Skiena
Keyword(s):  
Calculus Of Variations ◽  
Optimal Policy ◽  
Constant Time ◽  
Optimal Solutions ◽  
Discrete Structure ◽  
All Solutions ◽  
Elementary Methods ◽  
Simplifying Assumptions ◽  
Asymptotic Problem

We deal with the problem of seating an airplane's passengers optimally, namely in the fastest way. Under several simplifying assumptions, whereby the passengers are infinitely thin and react within a constant time to boarding announcements, we are able to rewrite the asymptotic problem as a calculus of variations problem with constraints. This problem is solved in turn using elementary methods. While the optimal policy is not unique, we identify a rigid discrete structure which is common to all solutions. We also compare the (nontrivial) optimal solutions we find with some simple boarding policies, one of which is shown to be near-optimal.

scholarly journals Optimal boarding policies for thin passengers

2007 ◽  
Vol 39 (04) ◽  
pp. 1098-1114
Author(s):  
Eitan Bachmat ◽  
Daniel Berend ◽  
Luba Sapir ◽  
Steven Skiena
Keyword(s):  
Calculus Of Variations ◽  
Optimal Policy ◽  
Constant Time ◽  
Optimal Solutions ◽  
Discrete Structure ◽  
All Solutions ◽  
Elementary Methods ◽  
Simplifying Assumptions ◽  
Asymptotic Problem

We deal with the problem of seating an airplane's passengers optimally, namely in the fastest way. Under several simplifying assumptions, whereby the passengers are infinitely thin and react within a constant time to boarding announcements, we are able to rewrite the asymptotic problem as a calculus of variations problem with constraints. This problem is solved in turn using elementary methods. While the optimal policy is not unique, we identify a rigid discrete structure which is common to all solutions. We also compare the (nontrivial) optimal solutions we find with some simple boarding policies, one of which is shown to be near-optimal.

scholarly journals A mathematical model of rat ascending Henle limb. I. Cotransporter function

2010 ◽  
Vol 298 (3) ◽  
pp. F512-F524 ◽  
Author(s):  
Alan M. Weinstein
Keyword(s):  
Binding Sites ◽  
Ion Flux ◽  
Model Parameters ◽  
Ion Binding ◽  
Optimal Solutions ◽  
Coupled Transport ◽  
Model Calculations ◽  
Intermediate Variable ◽  
In Series ◽  
Simplifying Assumptions

Kinetic models of Na+-K+-2Cl− costransporter (NKCC2) and K+-Cl− cotransporter (KCC4), two of the key cotransporters of the Henle limb, are fashioned with inclusion of terms representing binding and transport of NH4+. The models are simplified using assumptions of equilibrium ion binding, binding symmetry, and identity of Cl− binding sites. Model parameters are selected to be consistent with flux data from expression of these transporters in oocytes, specifically inwardly directed coupled transport of rubidium. In the analysis of these models, it is found that despite the simplifying assumptions to reduce the number of model parameters, neither model is uniquely determined by the data. For NKCC or KCC there are two- or three-parameter families of “optimal” solutions. As a consequence, one may specify several carrier translocation rates and/or ion affinities before fitting the remaining coefficients to the data, with no loss of fidelity in simulating the experiments. Model calculations suggest that with respect to NKCC2 near its operating point, the curve of ion flux as a function of cell Cl− is steep, and with respect to KCC4, its curve of ion flux as a function of peritubular K+ is also steep. The implication is that the kinetics are suitable for these two transporters in series to act as a sensor for peritubular K+, to modulate AHL Na+ reabsorption, with cytosolic Cl− as the intermediate variable. The models also reveal the potential for luminal NH4+ to be a potent catalyst for NKCC2 Na+ reabsorption, provided suitable exit mechanisms for NH4+ (from cell-to-lumen) are operative. It is found that KCC4 is likely to augment the secretory NH4+ flux, with peritubular NH4+ uptake driven by the cell-to-blood K+ gradient.

scholarly journals Multi-Objective Optimization of Spatially Truss Structures Based on Node Movement

2020 ◽  
Vol 10 (6) ◽  
pp. 1964
Author(s):  
Bo Nan ◽  
Yikui Bai ◽  
Yue Wu
Keyword(s):  
Optimization Problems ◽  
Front Surface ◽  
Truss Structures ◽  
Optimal Solutions ◽  
Discrete Structure ◽  
Maximum Displacement ◽  
C Language ◽  
Multi Objective ◽  
Finite Element Software ◽  
Discrete Structures

This paper discusses the solutions for topology optimization of spatially discrete structures. The optimization objects are the structural weight and the maximum displacement. The optimization variables include structural node coordinates, and the improved MOEA (Multi-objective Evolutionary Algorithm) method is used to optimize the structure. The innovation of this study is that it breaks through the shortage of constant node position in the optimization thought of traditionally discrete structure in the “Ground Structure Approach” and uses the coordinate of the node as the optimization variable for the optimization calculation. The result is not a single one but a set of optimal solutions through the evolution (i.e., Pareto optimal solutions); on this basis, the most suitable solution can be found according to the boundary conditions or other related requirements. Using the C# language to compile the calculation program, ANSYS finite element software is used to analyze the structure, and the Pareto front surface was automatically drawn to determine the optimal layout form of the discrete structure. The analysis results show that the improved MOEA method can provide an effective method to solve such optimization problems.

COMPOSITION FUNCTIONALS IN CALCULUS OF VARIATIONS: APPLICATION TO PRODUCTS AND QUOTIENTS

2008 ◽  
Vol 18 (01) ◽  
pp. 47-75 ◽  
Author(s):  
ENRIQUE CASTILLO ◽  
ALBERTO LUCEÑO ◽  
PABLO PEDREGAL
Keyword(s):  
Slope Stability ◽  
Calculus Of Variations ◽  
Stability Problem ◽  
Sufficient Conditions ◽  
Scalar Function ◽  
Junction Conditions ◽  
Optimal Solutions ◽  
Existence Of Optimal Solutions ◽  
Valued Field ◽  
Vector Valued

This paper deals with the problem of the Calculus of Variations for a functional which is the composition of a certain scalar function H with the integral of a vector valued field f, i.e. of the form [Formula: see text] where H : ℝn → ℝ and f : ℝ3 → ℝn. The integral of f is calculated here componentwise. We examine sufficient conditions for the existence of optimal solutions, and provide rules to obtain the necessary Euler–Lagrange, natural, transversality, Weierstrass–Erdmann and junction conditions for such a functional. Particular attention is paid to the cases of the product and the quotient as we take these as model situations. Finally, the theory is illustrated with a slope stability problem, and an example coming from Economics.

Exogeneous factors are not necessary in attachment, spreading and polarization of hela cells

1978 ◽  
Vol 36 (2) ◽  
pp. 310-311
Author(s):  
W. Liebrich
Keyword(s):  
Hela Cells ◽  
Calf Serum ◽  
Glass Tube ◽  
Serum Free Medium ◽  
Nacl Solution ◽  
Free Medium ◽  
Minimum Essential Medium ◽  
Serum Free ◽  
All Solutions ◽  
Glass Support

HeLa cells were grown for 2-3 days in EAGLE'S minimum essential medium with 10% calf serum (S-MEM; Seromed, München) and then incubated for 24 hours in serum free medium (MEM). After detaching the cells with a solution of 0. 14 % EDTA and 0. 07 % trypsin (Difco, 1 : 250) they were suspended in various solutions (S-MEM = control, MEM, buffered salt solutions with or without Me++ions, 0. 9 % NaCl solution) and allowed to settle on glass tube slips (Leighton-tubes). After 5, 10, 15, 20, 25, 30, 1 45, 60 minutes 2, 3, 4, 5 hours cells were prepared for scanning electron microscopy as described by Paweletz and Schroeter. The preparations were examined in a Jeol SEM (JSM-U3) at 25 KV without tilting.The suspended spherical HeLa cells are able to adhere to the glass support in all solutions. The rate of attachment, however, is faster in solutions without serum than in the control. The latter is in agreement with the findings of other authors.

On Asymmetric Distances

2013 ◽  
Vol 1 ◽  
pp. 200-231 ◽  
Author(s):  
Andrea C.G. Mennucci
Keyword(s):  
Total Variation ◽  
Calculus Of Variations ◽  
Distance Function ◽  
Metric Space ◽  
Metric Spaces ◽  
Geodesic Segment ◽  
Intrinsic Metric ◽  
Typical Application ◽  
Variation Formula

Abstract In this paper we discuss asymmetric length structures and asymmetric metric spaces. A length structure induces a (semi)distance function; by using the total variation formula, a (semi)distance function induces a length. In the first part we identify a topology in the set of paths that best describes when the above operations are idempotent. As a typical application, we consider the length of paths defined by a Finslerian functional in Calculus of Variations. In the second part we generalize the setting of General metric spaces of Busemann, and discuss the newly found aspects of the theory: we identify three interesting classes of paths, and compare them; we note that a geodesic segment (as defined by Busemann) is not necessarily continuous in our setting; hence we present three different notions of intrinsic metric space.

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