PhD Thesis

Hydrodynamics of Crystals

My doctoral research bridges two seemingly distinct fields: hydrodynamics (the study of fluid dynamics) and crystallography (the study of solids). By applying hydrodynamic principles to crystal systems, this work provides a unified framework for understanding how defects and thermal effects propagate through crystalline materials without requiring a perfect lattice as a theoretical foundation.

The research develops both phenomenological and microscopic approaches to describe the behavior of crystals, incorporating strain fields, temperature coupling, and entropy production in a consistent theoretical framework.

Author Florian Miserez
Degree Doctor of Natural Sciences (Dr. rer. nat.)
Institution University of Konstanz
Year 2023

Key Research Areas

Generalized Hydrodynamics

Extending classical hydrodynamic theory to solids, incorporating broken symmetry variables that naturally describe crystal lattice defects and their dynamics.

Microscopic Derivation

Using the Zwanzig–Mori formalism to derive macroscopic equations of motion from microscopic particle dynamics, connecting transport coefficients to fundamental molecular interactions.

Thermodynamic Framework

Developing a comprehensive free energy expansion that consistently describes elastic, thermal, and dissipative properties of crystalline systems at finite temperatures.

Key Equations

Continuity Equation

$$\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{v}) = 0$$

Conservation of mass in fluid dynamics

Strain Tensor

$$u_{\alpha\beta} = \frac{1}{2}\left(\frac{\partial u_\alpha}{\partial x_\beta} + \frac{\partial u_\beta}{\partial x_\alpha}\right)$$

Symmetric deformation in solids

Free Energy Density

$$f = f_0 + \frac{\partial f}{\partial n}\bigg|_u \Delta n + \frac{1}{2}C_{\alpha\beta}u_{\alpha\beta}u_{\alpha\beta}$$

Expanded around equilibrium

Green-Kubo Relations

$$\eta = \frac{V}{k_B T}\int_0^\infty \langle P_{xy}(t)P_{xy}(0)\rangle dt$$

Microscopic to macroscopic transport

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