A note on Newton’s problem of minimal resistance for convex bodies

Alexander Plakhov

doi:10.1007/s00526-020-01833-2

The minimal resistance problem in a class of non convex bodies

ESAIM Control Optimisation and Calculus of Variations ◽

10.1051/cocv/2018016 ◽

2019 ◽

Vol 25 ◽

pp. 27 ◽

Cited By ~ 1

Author(s):

Edoardo Mainini ◽

Manuel Monteverde ◽

Edouard Oudet ◽

Danilo Percivale

Keyword(s):

Optimization Algorithm ◽

Numerical Optimization ◽

Convex Bodies ◽

One Dimensional ◽

Minimal Resistance

We characterize the solution to the Newton minimal resistance problem in a class of radial q-concave profiles. We also give the corresponding result for one-dimensional profiles. Moreover, we provide a numerical optimization algorithm for the general nonradial case.

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Non-optimality of conical parts for Newton’s problem of minimal resistance in the class of convex bodies and the limiting case of infinite height

Calculus of Variations and Partial Differential Equations ◽

10.1007/s00526-021-02118-y ◽

2022 ◽

Vol 61 (1) ◽

Author(s):

Lev Lokutsievskiy ◽

Gerd Wachsmuth ◽

Mikhail Zelikin

Keyword(s):

Convex Body ◽

Existence Of Solutions ◽

Convex Bodies ◽

Radial Symmetry ◽

Finite Height ◽

Infinite Height ◽

Limiting Case ◽

Minimal Resistance

AbstractWe consider Newton’s problem of minimal resistance, in particular we address the problem arising in the limit if the height goes to infinity. We establish existence of solutions and lack radial symmetry of solutions. Moreover, we show that certain conical parts contained in the boundary of a convex body inhibit the optimality in the classical Newton’s problem with finite height. This result is applied to certain bodies considered in the literature, which are conjectured to be optimal for the classical Newton’s problem, and we show that they are not.

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Optimal Roughening of Convex Bodies

Canadian Journal of Mathematics ◽

10.4153/cjm-2011-070-9 ◽

2012 ◽

Vol 64 (5) ◽

pp. 1058-1074 ◽

Cited By ~ 11

Author(s):

Alexander Plakhov

Keyword(s):

Body Surface ◽

Convex Bodies ◽

The Body ◽

Point Particles ◽

Minimal Resistance ◽

Bounded Convex

AbstractA body moves in a rare fied medium composed of point particles at rest. The particles make elastic reflections when colliding with the body surface and do not interact with each other. We consider a generalization of Newton’s minimal resistance problem: given two bounded convex bodiesC1andC2ℝ3such that C1⊂ c2⊂ and, minimize the resistance in the class of connected bodiesBsuch thatC1⊂ B ⊂C1. We prove that the infimum of resistance is zero; that is, there exist ”almost perfectly streamlined” bodies.

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Convex Bodies: The Brunn–Minkowski Theory

10.1017/cbo9780511526282 ◽

1993 ◽

Cited By ~ 891

Author(s):

Rolf Schneider

Keyword(s):

Convex Bodies

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In silico ADME, Bioactivity and Toxicity Parameters Calculation of Some Selected Anti-Tubercular Drugs

International Journal of Pharmaceutical and Phytopharmacological Research ◽

10.24896/eijppr.2016661 ◽

2016 ◽

Vol 6 (6) ◽

pp. 77 ◽

Cited By ~ 1

Author(s):

Shashank Shekhar Mishra ◽

Chandra Shekhar Sharma ◽

Hemendra Pratap Singh ◽

Harshda Pandiya ◽

Neeraj Kumar

Keyword(s):

Antibiotic Resistance ◽

In Silico ◽

Bacillus Calmette Guerin ◽

Computational Investigation ◽

Pharmacological Profile ◽

In Silico Toxicity ◽

Is Development ◽

Potent Drug ◽

Minimal Resistance ◽

Parameters Calculation

Tuberculosis, one of the most frequent infectious diseases, is caused by a mycobacterium tuberculosis bacteria and it infects several hundred million people each year, results in several million deaths annually. Because there is development of antibiotic resistance, the disease becomes incurable. So, in the absence of effective and potent drug with minimal resistance problems, the mortality rate increases annually. In this computational investigation, we performed In-silico ADME, bioactivity and toxicity parameters calculation of some selected anti-tuberculosis agents. To design a new molecule having good pharmacological profile, this study will provide the lead information.Key Words: Tuberculosis (TB), Bacillus Calmette-Guerin vaccine, TPSA, In Silico toxicity

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Excess entropy of the systems of molecules differing in size and shape

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19830192 ◽

1983 ◽

Vol 48 (1) ◽

pp. 192-198 ◽

Cited By ~ 5

Author(s):

Tomáš Boublík

Keyword(s):

Equation Of State ◽

Hard Spheres ◽

Excess Entropy ◽

Convex Bodies ◽

Pure Substance ◽

Liquid Equilibrium ◽

Simple Rules ◽

Different Shapes ◽

The Mean

The excess entropy of mixing of mixtures of hard spheres and spherocylinders is determined from an equation of state of hard convex bodies. The obtained dependence of excess entropy on composition was used to find the accuracy of determining ΔSE from relations employed for the correlation and prediction of vapour-liquid equilibrium. Simple rules were proposed for establishing the mean parameter of nonsphericity for mixtures of hard bodies of different shapes allowing to describe the P-V-T behaviour of solutions in terms of the equation of state fo pure substance. The determination of ΔSE by means of these rules is discussed.

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Some Hermite–Hadamard type integral inequalities for convex functions defined on convex bodies in ℝn\mathbb{R}^{n}

Journal of Applied Analysis ◽

10.1515/jaa-2020-2005 ◽

2020 ◽

Vol 26 (1) ◽

pp. 67-77 ◽

Cited By ~ 1

Author(s):

Silvestru Sever Dragomir

Keyword(s):

Euclidean Space ◽

Convex Functions ◽

Convex Bodies ◽

Integral Inequalities ◽

Divergence Theorem ◽

Several Variables ◽

Type Integral ◽

Bounded Convex

AbstractIn this paper, by the use of the divergence theorem, we establish some integral inequalities of Hermite–Hadamard type for convex functions of several variables defined on closed and bounded convex bodies in the Euclidean space {\mathbb{R}^{n}} for any {n\geq 2}.

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