Non-classical thermal transport and phase change at the nanoscale

Premi Extraordinari de Doctorat, promoció 2018-2019. Àmbit de CiènciesFor 200 years, Fourier’s law has been used to describe heat transfer with excellent results. However, as technology advances, more and more situations arise where heat conduction is not well described by the classical equations. Examples are applications with extremely short time scales such as ultra fast laser heating, or very small length scales such as the heat conduction through nanowires or nanostructures in general. In this thesis we investigate alternative models which aim to correctly describe the non-classical effects that appear in extreme situations and which Fourier’s law fails to describe. A popular approach is the Guyer-Krumhansl equation and the framework of phonon hydrodynamics. This formalism is particularly appealing from a mathematical point of view since it is analogous to the Navier-Stokes equations of fluid mechanics, and from a physical point of view, since it is able to describe the physics in a simple and elegant way. In the first part of the thesis we use phonon hydrodynamics to predict the size-dependent thermal conductivity observed experimentally in nanostructures such as nanowires or thin films. In particular, we show that the Guyer-Krumhansl equation is suitable to capture the dependence of the thermal conductivity on the size of the physical system under consider- ation. During the modelling process we use the analogy with fluids to incorporate a slip boundary condition with a slip coefficient that depends on the ratio of the phonon mean free path to the characteristic size of the system. With only one fitting parameter we are able to accurately reproduce experimental observations corresponding to nanowires and nanorods of different sizes. The second part of the thesis consists of studying the effect of the non-classical fea- tures on melting and solidification processes. We consider different extensions and in- corporate them into the mathematical description of a solidification process in a simple, one-dimensional geometry. In chapter 5 we employ an effective Fourier law which replaces the original thermal conductivity by a size-dependent expression that accounts for non-local effects. In chapter 6 we use the Maxwell-Cattaneo and the Guyer-Krumhansl equations to formulate the Maxwell-Cattaneo-Stefan and the Guyer-Krumhansl-Stefan problems respec- tively. After performing a detailed asymptotic analysis we are able to reduce both models to a system of two ordinary differential equations and obtain excellent agreement with the cor- responding numerical solutions. In situations near Fourier resonance, which is a particular case where non-classical effects in the Guyer-Krumhansl model cancel each other out, the solidification kinetics are very similar to those described by the classical model. However, in this case we see that non-classical effects are still observable in the evolution of the heat flux through the solid, which suggests that this is a quantity which is more convenient to determine the presence of these effects in phase change processes.La llei de Fourier ha estat una peça clau per a descriure la conducció de calor des de que fou proposada fa gairabé 200 anys. No obstant, a mesura que avança la tecnologia ens hi trobem més sovint amb situacions on les equacions clàssiques perden la seva validesa. En aquesta tesi investiguem alguns models alternatius que tenen com a objectiu descriure la conducció de calor en situacions on la llei de Fourier no és aplicable. Un model que s'ha aconseguit establir com un extensió vàlida de la llei de Fourier és l'equació de Guyer i Krumhansl i el marc de la hidrodinàmica de fonons derivat d'aquesta. Es tracta d'un model particularment interessant, ja que les equacions són anàlogues a les equacions per a fluids dins de la hidrodinàmica clàssica. A la primera part de la tesi considerem aquesta equació per a descriure la conducció de calor estàtica per nanofibres de seccions transversals circulars i rectangulars. En particular, calculem una conductivitat tèrmica efectiva i trobem que és possible reproduïr els resultats experimentals amb un sol paràmetre d'adjust. En el cas de nanofibres cilíndriques, no és necessari cap paràmetre d'adjust si es consideren unes certes condicions de vora per al flux. Una conseqüència d'haver de considerar extensions per a la llei de Fourier és que s'ha d'estudiar l'efecte que tenen aquests canvis en la descripció de processos de canvi de fase. En la segona part de la tesi investiguem els efectes que tenen diversos models sobre la solidificació d'un líquid unidimensional. Al capítol 5 estudiem el cas en el que considerem la conductivitat tèrmica com a una funció de la mida del sòlid i que incorpora característiques que són importants quan el tamany del sòlid és comparable a les longituds característiques dels fonons, mentres que al capítol 6 considerem l'equació de Guyer i Krumhansl dels capítols anteriors. En ambdós casos, un anàlisi asimptòtic ens permet reduïr la complexitat del problema i proposar models reduïts formats per un parell de'equacions diferencials ordinàries.Award-winningPostprint (published version

Exploring the Role of Molecular Dynamics Simulations in Most Recent Cancer Research: Insights into Treatment Strategies

Cancer is a complex disease that is characterized by uncontrolled growth and division of cells. It involves a complex interplay between genetic and environmental factors that lead to the initiation and progression of tumors. Recent advances in molecular dynamics simulations have revolutionized our understanding of the molecular mechanisms underlying cancer initiation and progression. Molecular dynamics simulations enable researchers to study the behavior of biomolecules at an atomic level, providing insights into the dynamics and interactions of proteins, nucleic acids, and other molecules involved in cancer development. In this review paper, we provide an overview of the latest advances in molecular dynamics simulations of cancer cells. We will discuss the principles of molecular dynamics simulations and their applications in cancer research. We also explore the role of molecular dynamics simulations in understanding the interactions between cancer cells and their microenvironment, including signaling pathways, proteinprotein interactions, and other molecular processes involved in tumor initiation and progression. In addition, we highlight the current challenges and opportunities in this field and discuss the potential for developing more accurate and personalized simulations. Overall, this review paper aims to provide a comprehensive overview of the current state of molecular dynamics simulations in cancer research, with a focus on the molecular mechanisms underlying cancer initiation and progression.Comment: 49 pages, 2 figure

Description of Courses, 1979-80

Official publication of Cornell University V.71 1979/8