scholarly journals Fundamental models in nonlinear acoustics part I. Analytical comparison

2018 ◽  
Vol 28 (12) ◽  
pp. 2403-2455 ◽  
Author(s):  
Barbara Kaltenbacher ◽  
Mechthild Thalhammer
Keyword(s):  
Thermal Conductivity ◽  
Initial Data ◽  
Wave Equations ◽  
Sound Propagation ◽  
Nonlinear Acoustics ◽  
Analytical Comparison ◽  
Classical Models ◽  
Nonlinear Damped Wave Equations ◽  
Theoretical Results ◽  
Consistent Initial Data

This work is concerned with the study of fundamental models from nonlinear acoustics. In Part I, a hierarchy of nonlinear damped wave equations arising in the description of sound propagation in thermoviscous fluids is deduced. In particular, a rigorous justification of two classical models, the Kuznetsov and Westervelt equations, retained as limiting systems for vanishing thermal conductivity and consistent initial data, is given. Numerical comparisons that confirm and complement the theoretical results are provided in Part II.

A MODEL FOR PREDICTING THE EFFECTIVE THERMAL CONDUCTIVITY OF NANOPARTICLE-FLUID SUSPENSIONS

2006 ◽  
Vol 05 (01) ◽  
pp. 23-33 ◽  
Author(s):  
S. M. S. MURSHED ◽  
K. C. LEONG ◽  
C. YANG
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Body Centered Cubic ◽  
Geometrical Structures ◽  
New Model ◽  
Water Based ◽  
Classical Models ◽  
Theoretical Results ◽  
Enhanced Thermal Conductivity ◽  
Good Agreement

The uniformity and homogeneously dispersed nanoparticles in base fluids contribute to enhanced thermal conductivity of the mixture. By considering the uniformity and geometrical structures (e.g., body-centered cubic) of homogeneously dispersed nanoparticles in base fluids, a model for determining the effective thermal conductivity (ETC) of such nanoparticle-fluid suspensions, commonly known as nanofluids is proposed in this study. The theoretical results of the effective thermal conductivities of TiO 2/Deionized (DI) water and Al 2 O 3/DI water-based nanofluids are presented, and they are found to be in good agreement with our experimental results and also with those reported in the literature. The new model presented in this study shows a better prediction of the effective thermal conductivity of nanofluids compared to other classical models attributed to Maxwell, Hamilton–Crosser, and Bruggeman.

Remarks on nonlinear elastic waves with null conditions

2020 ◽  
Vol 26 ◽  
pp. 121
Author(s):  
Dongbing Zha ◽  
Weimin Peng
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Elastic Waves ◽  
Wave Equations ◽  
Alternative Proof ◽  
Classical Solutions ◽  
Small Initial Data ◽  
Hyperelastic Materials ◽  
Variational Structure ◽  
Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

scholarly journals POLYHOMOGENEOUS SOLUTIONS OF NONLINEAR WAVE EQUATIONS WITHOUT CORNER CONDITIONS

2006 ◽  
Vol 03 (01) ◽  
pp. 81-141 ◽  
Author(s):  
PIOTR T. CHRUŚCIEL ◽  
SZYMON ŁȨSKI
Keyword(s):  
Initial Data ◽  
Wave Equations ◽  
Space Time ◽  
Einstein Equations ◽  
Nonlinear Wave Equations ◽  
Linear Wave ◽  
Cauchy Problems ◽  
Time Dimension ◽  
Wave Maps ◽  
Corner Conditions

The study of Einstein equations leads naturally to Cauchy problems with initial data on hypersurfaces which closely resemble hyperboloids in Minkowski space-time, and with initial data with polyhomogeneous asymptotics, that is, with asymptotic expansions in terms of powers of ln r and inverse powers of r. Such expansions also arise in the conformal method for analysing wave equations in odd space-time dimension. In recent work it has been shown that for non-linear wave equations, or for wave maps, polyhomogeneous initial data lead to solutions which are also polyhomogeneous provided that an infinite hierarchy of corner conditions holds. In this paper we show that the result is true regardless of corner conditions.

Anomalous Heat Conduction, Diffusion and Heat Rectification in Nanoscale Structures

2009 ◽  
Author(s):  
Gang Zhang ◽  
Nuo Yang ◽  
Gang Wu ◽  
Baowen Li
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Heat Transport ◽  
Nano Materials ◽  
Fourier Law ◽  
Nanoscale Structures ◽  
Recent Developments ◽  
Theoretical Results ◽  
Good Agreement ◽  
Anomalous Heat

In this paper, we report the recent developments in the study of heat transport in nano materials. First of all, we show that phonon transports in nanotube super-diffusively which leads to a length dependence thermal conductivity, thus breaks down the Fourier law. Then we discuss how the introduction of isotope doping can reduce the thermal conductivity efficiently. The theoretical results are in good agreement with experimental ones. Finally, we will demonstrate that nanoscale structures are promising candidates for heat rectification.

Summarizing Datacubes

2011 ◽  
pp. 19-39 ◽  
Author(s):  
Rosine Cicchetti ◽  
Lotfi Lakhal ◽  
Sébastien Nedjar ◽  
Noël Novelli ◽  
Alain Casali
Keyword(s):  
Initial Data ◽  
Research Work ◽  
Data Cube ◽  
Storage Space ◽  
Analytical Evaluation ◽  
Aggregated Data ◽  
Analytical Comparison ◽  
Data Cubes ◽  
Reduction Methods ◽  
Quotient Cube

Datacubes are especially useful for answering efficiently queries on data warehouses. Nevertheless the amount of generated aggregated data is huge with respect to the initial data which is itself very large. Recent research work has addressed the issue of summarizing Datacubes in order to reduce their size. In this chapter, we present three different approaches. They propose structures which make it possible to reduce the size of the data cube representation. The two former, the closed cube and the quotient cube, are said semantic and discard the redundancies captured within data cubes. The size of the underlying representations is especially reduced but the counterpart is an additional response time when answering the OLAP queries. The latter approach is rather syntactic since it enforces an optimization at the logical level. It is called Partition Cube and based on the concept of partition. We also give an algorithm to compute it. We propose a Relational Partition Cube, a novel R-Olap cubing solution for managing Partition Cubes using the relational technology. An analytical evaluation shows that the storage space of Partition Cubes is smaller than Datacubes. In order to confirm analytical comparison, experiments are performed in order to compare our approach with Datacubes and with two of the best reduction methods, the Quotient Cube and the Closed Cube.

Global well-posedness and self-similarity for semilinear wave equations in a time-weighted framework of Besov type

2020 ◽  
Vol 17 (01) ◽  
pp. 123-139
Author(s):  
Lucas C. F. Ferreira ◽  
Jhean E. Pérez-López
Keyword(s):  
Wave Equation ◽  
Initial Data ◽  
Besov Spaces ◽  
Wave Equations ◽  
Well Posedness ◽  
Self Similarity ◽  
Semilinear Wave Equations ◽  
Semilinear Wave Equation

We show global-in-time well-posedness and self-similarity for the semilinear wave equation with nonlinearity [Formula: see text] in a time-weighted framework based on the larger family of homogeneous Besov spaces [Formula: see text] for [Formula: see text]. As a consequence, in some cases of the power [Formula: see text], we cover a initial-data class larger than in some previous results. Our approach relies on dispersive-type estimates and a suitable [Formula: see text]-product estimate in Besov spaces.

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