# On the existence of optimal shapes in architecture

@article{Hinz2020OnTE, title={On the existence of optimal shapes in architecture}, author={Michael Hinz and Fr{\'e}d{\'e}ric Magoul{\`e}s and Anna Rozanova-Pierrat and Marina I. Rynkovskaya and Alexander Teplyaev}, journal={Applied Mathematical Modelling}, year={2020} }

## 9 Citations

### Boundary value problems on non-Lipschitz uniform domains: stability, compactness and the existence of optimal shapes

- MathematicsAsymptotic Analysis
- 2023

We study boundary value problems for bounded uniform domains in R n , n ⩾ 2, with non-Lipschitz, and possibly fractal, boundaries. We prove Poincaré inequalities with uniform constants and trace…

### Shape optimization for the heat propagation and other engineering problems

- Mathematics
- 2021

The mathematical theory of shape optimization is a developing area of applied mathematics. Its progress allows to solve or give some ideas on how to solve different problems of a real engineer…

### Mixed boundary valued problems for linear and nonlinear wave equations in domains with fractal boundaries

- MathematicsCalculus of Variations and Partial Differential Equations
- 2022

The weak well-posedness, with the mixed boundary conditions, of the strongly damped linear wave equation and of the non linear Westervelt equation is proved in a large natural class of Sobolev…

### FORMATION OF COMPUTATIONAL SCHEMES OF ADDITIONAL TARGETED CONSTRAINTS THAT REGULATE THE FREQUENCY SPECTRUM OF NATURAL OSCILLATIONS OF ELASTIC SYSTEMS WITH A FINITE NUMBER OF DEGREES OF MASS FREEDOM, THE DIRECTIONS OF MOVEMENT OF WHICH ARE PARALLEL, BUT D

- Computer ScienceInternational Journal for Computational Civil and Structural Engineering
- 2022

The distinctive paper proposes an approach that allows researcher to create computational schemes for additional targeted constraints for elastic systems with a finite number of degrees of freedom of masses, when, during its formation, rods appear that “pass” through the original system.

### Shape Optimization of a Shell in Comsol Multiphysics

- PhysicsComput.
- 2022

Optimization calculations are currently an actual and in-demand direction of computer-aided design. It allows not only the identification of the future characteristics of an object, but also the…

### Spectral theory applications in the localization phenomena, scattering, and inverse problems for the wave absorption by rough boundaries

- Mathematics
- 2022

It is well-known that rough (fractal) boundaries have improved noise absorption properties, and it is conjectured that such boundaries may even be optimal absorbers for certain problems. The main…

### Mixed boundary valued problems for linear and nonlinear wave equations in domains with fractal boundaries

- Materials ScienceCalculus of Variations and Partial Differential Equations
- 2022

The weak well-posedness, with the mixed boundary conditions, of the strongly damped linear wave equation and of the non linear Westervelt equation is proved in a large natural class of Sobolev…

### Topic 9

- 2020

he present study was conducted to investigate the impact of adding different levels of dried Pomegranate by-products (DPB):10g/head /day (R2), 20g/head /day (R3), 30g/head /day (R4),versus an…

### Special aspects of calculation of infiltration in residential and public buildings

- EngineeringE3S Web of Conferences
- 2023

In the current paper, the methods of calculating infiltration for different ways of the ventilation system operation have been reviewed. The calculation of infiltration losses of buildings in cases…

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A by-product of this proof is the result that the class of bounded (e, ∞)-domains with fixed e is stable under Hausdorff convergence, which is the Mosco convergence of Robin-type energy functionals on converging domains.

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In this paper we study a transmission problem with a fractal interface K, where a second order transmission condition is imposed. We consider the case in which the interface K is the Koch curve and…

### CONSIDERATIONS ON MIXED INITIAL-BOUNDARY VALUE PROBLEMS FOR MICOPOLAR POROUS BODIES

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This paper is dedicated to some results in the thermodynamic theory of porous elastic bodies. Unlike other studies, here is included the voidage time derivative among the independent constitutive…

### Magnetostatic Problems in Fractal Domains

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We consider a magnetostatic problem in a 3D "cylindrical" domain of Koch type. We prove existence and uniqueness results for both the fractal and pre-fractal problems and we investigate the…

### Mixed boundary valued problems for linear and nonlinear wave equations in domains with fractal boundaries

- MathematicsCalculus of Variations and Partial Differential Equations
- 2022

The weak well-posedness, with the mixed boundary conditions, of the strongly damped linear wave equation and of the non linear Westervelt equation is proved in a large natural class of Sobolev…

### Optimal absorption of acoustical waves by a boundary

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In the aim to find the simplest and most efficient shape of a noise absorbing wall to dissipate the energy of a sound wave, we consider a frequency model (the Helmholtz equation) with a damping on…

### Generalization of Rellich-Kondrachov theorem and trace compacteness in the framework of irregular and fractal boundaries

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We present a survey of recent results of the functional analysis allowing to solve PDEs in a large class of domains with irregular boundaries. We extend the previously introduced concept of…

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This work proposes a shape and topology optimization framework oriented towards conceptual architectural design. A particular emphasis is put on the possibility for the user to interfere on the…

### Optimal and efficient shapes in acoustic boundary absorption

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In the aim to find the simplest and most efficient shape of a noise absorbing wall to dissipate the acoustical energy of a sound wave, we consider a frequency model described by the Helmholtz…

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We discuss the spectral properties of the Laplacian for domains Ω with fractal boundaries. The main goal of the article is to find the second term of spectral asymptotics of the counting functionN(λ)…