scholarly journals A strict inequality for the minimization of the Willmore functional under isoperimetric constraint

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Andrea Mondino ◽  
Christian Scharrer
Keyword(s):  
Lipid Bilayer ◽  
Minimization Problem ◽  
Strict Inequality ◽  
Simplified Model ◽  
Minimal Energy ◽  
Willmore Functional ◽  
Connected Sum ◽  
Existence Of Minimizers ◽  
Isoperimetric Constraint ◽  
Isoperimetric Constraints

Abstract Inspired by previous work of Kusner and Bauer–Kuwert, we prove a strict inequality between the Willmore energies of two surfaces and their connected sum in the context of isoperimetric constraints. Building on previous work by Keller, Mondino and Rivière, our strict inequality leads to existence of minimizers for the isoperimetric constrained Willmore problem in every genus, provided the minimal energy lies strictly below 8 ⁢ π {8\pi} . Besides the geometric interest, such a minimization problem has been studied in the literature as a simplified model in the theory of lipid bilayer cell membranes.

Shape Optimization With Isoperimetric Constraints for Isothermal Pipes Embedded in an Insulated Slab

2014 ◽  
Vol 136 (9) ◽  
Author(s):  
Theodoros Leontiou ◽  
Marios M. Fyrillas
Keyword(s):  
Heat Transfer ◽  
Heat Conduction Problem ◽  
Classical Problem ◽  
Lower Surface ◽  
Optimum Shape ◽  
Practical Applications ◽  
Wide Range ◽  
Geometrical Constraints ◽  
Isoperimetric Constraint ◽  
Isoperimetric Constraints

In this paper, we consider the heat transfer from a periodic array of isothermal pipes embedded in a rectangular slab. The upper surface of the slab is sustained at a constant temperature while the lower surface is insulated. The particular configuration is a classical heat conduction problem with a wide range of practical applications. We consider both the classical problem, i.e., estimating the shape factor of a given configuration, and the inverse problem, i.e., calculating the optimum shape that maximizes the heat transfer rate associated with a set of geometrical constraints. The way the present formulation differs from previous formulations is that: (i) the array of pipes does not have to be placed at the midsection of the slab and (ii) we have included an isoperimetric constraint (not changing in perimeter) through which we can control the deviation of the optimum shape from that of a circle. This is very important considering that most of the applications deal with buried pipes and a realistic shape is a practical necessity. The isoperimetric constraint is included through the isoperimetric quotient (IQ), which is the ratio between the area and the perimeter of a closed curve.

scholarly journals The existence of minimizers for an isoperimetric problem with Wasserstein penalty term in unbounded domains

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Qinglan Xia ◽  
Bohan Zhou
Keyword(s):  
Unbounded Domain ◽  
Minimization Problem ◽  
Open Problem ◽  
Isoperimetric Problem ◽  
Unbounded Domains ◽  
Wasserstein Distance ◽  
Penalty Term ◽  
Singular Measures ◽  
Existence Of Minimizers

Abstract In this article, we consider the (double) minimization problem min ⁡ { P ⁢ ( E ; Ω ) + λ ⁢ W p ⁢ ( E , F ) : E ⊆ Ω , F ⊆ R d , | E ∩ F | = 0 , | E | = | F | = 1 } , \min\{P(E;\Omega)+\lambda W_{p}(E,F):E\subseteq\Omega,\,F\subseteq\mathbb{R}^{d},\,\lvert E\cap F\rvert=0,\,\lvert E\rvert=\lvert F\rvert=1\}, where λ ⩾ 0 \lambda\geqslant 0 , p ⩾ 1 p\geqslant 1 , Ω is a (possibly unbounded) domain in R d \mathbb{R}^{d} , P ⁢ ( E ; Ω ) P(E;\Omega) denotes the relative perimeter of 𝐸 in Ω and W p W_{p} denotes the 𝑝-Wasserstein distance. When Ω is unbounded and d ⩾ 3 d\geqslant 3 , it is an open problem proposed by Buttazzo, Carlier and Laborde in the paper On the Wasserstein distance between mutually singular measures. We prove the existence of minimizers to this problem when the dimension d ⩾ 1 d\geqslant 1 , 1 p + 2 d > 1 \frac{1}{p}+\frac{2}{d}>1 , Ω = R d \Omega=\mathbb{R}^{d} and 𝜆 is sufficiently small.

Nano-pore Lipid Bilayer Formed by Self-spreading Method

2019 ◽  
Vol 139 (10) ◽  
pp. 1146-1152
Author(s):  
Zugui Peng ◽  
Kenta Shimba ◽  
Yoshitaka Miyamoto ◽  
Tohru Yagi
Keyword(s):  
Lipid Bilayer

Eco-Friendly Synthesis of Pyrazoline Derivatives

2017 ◽  
Vol 9 (04) ◽  
Author(s):  
Mahesh G. Kharatmol ◽  
Deepali Jagdale
Keyword(s):  
Ionic Liquids ◽  
Microwave Irradiation ◽  
Organic Synthesis ◽  
Ultrasonic Irradiation ◽  
Minimal Energy ◽  
Anticancer Activities ◽  
Conventional Methods

Pyrazoline class of compounds serve as better moieties for an array of treatments, they have antibacterial, antifungal, antiinflammatory, antipyretic, diuretic, cardiovascular activities. Apart from these they also have anticancer activities. So, pertaining to its importance, many attempts are made to synthesize pyrazolines. Since conventional methods of organic synthesis are energy and time consuming. There are elaborate pathways for green and eco-friendly synthesis of pyrazoline derivatives including microwave irradiation, ultrasonic irradiation, grinding and use of ionic liquids which assures the synthesis of the same within much lesser time and by use of minimal energy

Spotting Differences in Molecular Dynamic Simulations of Influenza A M2 Protein-Ligand Complexes by Varying M2 construct, Lipid Bilayer and Force Field

2019 ◽  
Author(s):  
Dimitrios Kolokouris ◽  
Iris Kalenderoglou ◽  
Panagiotis Lagarias ◽  
Antonios Kolocouris
Keyword(s):  
Molecular Dynamic ◽  
Lipid Bilayer ◽  
Influenza A ◽  
Md Simulations ◽  
Membrane Curvature ◽  
Buffer Size ◽  
M2 Protein ◽  
Dynamic Simulations ◽  
Amphipathic Helices ◽  
Drug Protein Binding

<p>We studied by molecular dynamic (MD) simulations systems including the inward<sub>closed</sub> state of influenza A M2 protein in complex with aminoadamantane drugs in membrane bilayers. We varied the M2 construct and performed MD simulations in M2TM or M2TM with amphipathic helices (M2AH). We also varied the lipid bilayer by changing either the lipid, DMPC or POPC, POPE or POPC/cholesterol (chol), or the lipids buffer size, 10x10 Å<sup>2 </sup>or 20x20 Å<sup>2</sup>. We aimed to suggest optimal system conditions for the computational description of this ion channel and related systems. Measures performed include quantities that are available experimentally and include: (a) the position of ligand, waters and chlorine anion inside the M2 pore, (b) the passage of waters from the outward Val27 gate of M2 S31N in complex with an aminoadamantane-aryl head blocker, (c) M2 orientation, (d) the AHs conformation and structure which is affected from interactions with lipids and chol and is important for membrane curvature and virus budding. In several cases we tested OPLS2005, which is routinely applied to describe drug-protein binding, and CHARMM36 which describes reliably protein conformation. We found that for the description of the ligands position inside the M2 pore, a 10x10 Å<sup>2</sup> lipids buffer in DMPC is needed when M2TM is used but 20x20 Å<sup>2</sup> lipids buffer of the softer POPC; when M2AH is used all 10x10 Å<sup>2</sup> lipid buffers with any of the tested lipids can be used. For the passage of waters at least M2AH with a 10x10 Å<sup>2</sup> lipid buffer is needed. The folding conformation of AHs which is defined from hydrogen bonding interactions with the bilayer and the complex with chol is described well with a 10x10 Å<sup>2</sup> lipids buffer and CHARMM36. </p>

An Augmented Iteratively Re-weighted and Refined Least Squares Method for lp Minimization Problem in Inverse Modeling of Potential Field Magnetic Data

2020 ◽  
Vol 1 (3) ◽  
Author(s):  
Maysam Abedi
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
Least Squares ◽  
Minimization Problem ◽  
Potential Field ◽  
Field Data ◽  
Least Squares Method ◽  
Porphyry Copper ◽  
Magnetic Data ◽  
Magnetic Field Data

The presented work examines application of an Augmented Iteratively Re-weighted and Refined Least Squares method (AIRRLS) to construct a 3D magnetic susceptibility property from potential field magnetic anomalies. This algorithm replaces an lp minimization problem by a sequence of weighted linear systems in which the retrieved magnetic susceptibility model is successively converged to an optimum solution, while the regularization parameter is the stopping iteration numbers. To avoid the natural tendency of causative magnetic sources to concentrate at shallow depth, a prior depth weighting function is incorporated in the original formulation of the objective function. The speed of lp minimization problem is increased by inserting a pre-conditioner conjugate gradient method (PCCG) to solve the central system of equation in cases of large scale magnetic field data. It is assumed that there is no remanent magnetization since this study focuses on inversion of a geological structure with low magnetic susceptibility property. The method is applied on a multi-source noise-corrupted synthetic magnetic field data to demonstrate its suitability for 3D inversion, and then is applied to a real data pertaining to a geologically plausible porphyry copper unit.  The real case study located in  Semnan province of  Iran  consists  of  an arc-shaped  porphyry  andesite  covered  by  sedimentary  units  which  may  have  potential  of  mineral  occurrences, especially  porphyry copper. It is demonstrated that such structure extends down at depth, and consequently exploratory drilling is highly recommended for acquiring more pieces of information about its potential for ore-bearing mineralization.

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