arXiv subjects

Ryan H. Allaire

Publications and source records attributed to Ryan H. Allaire.

4 recordsLinked to original sources

arXiv2024

Using Thermal Crowding to Direct Pattern Formation on the Nanoscale

Metal films and other geometries of nanoscale thickness, when exposed to laser irradiation, melt and evolve as fluids as long as their temperature is sufficiently high. This evolution often leads to pattern formation, which may be influenced strongly by material parameters that are temperature dependent. In addition, the laser heat absorption itself depends on the time-dependent metal thickness. Self-consistent modeling of evolving metal films shows that, by controlling the amount and geometry of deposited metal, one could control the instability development. In particular, depositing additional metal leads to elevated temperatures through the `thermal crowding' effect, which strongly influences the metal film evolution. This influence may proceed via disjoint metal geometries, by heat diffusion through the underlying substrate. Fully self-consistent modeling focusing on the dominant effects, as well as accurate time-dependent simulations, allow us to describe the main features of thermal crowding and provide a route to control fluid instabilities and pattern formation on the nanoscale.

cond-mat.mtrl-sci↗

arXiv2024

Designing Problems for Improved Instruction and Learning -- Linear Algebra

One of the grand challenges of Mathematics instruction is to provide students with problems that are both accessible and have a reasonably elegant solution. Instructors commonly resort to resources like course textbooks, online-learning platforms, or other automated problem-generating software to select problems for exams and assignments. However, reliance on such tools may result in limited control over problem parameters, potentially yielding intricate solutions that impede students' understanding. This article centers on Linear Algebra, wherein we devise algorithms for reverse engineering matrices of integers with integer outcomes through operations such as the inverse, LU decomposition, and QR decomposition. The focus is on empowering instructors to manipulate matrix properties deliberately, ensuring the creation of problems that enrich instruction and foster student confidence. The intellectual endeavor of reverse engineering such problems, grounded in both theory and matrix properties, proves mutually beneficial for both students and instructors alike.

math.HO↗

arXiv2021

The influence of thermal effects on the breakup of thin films of nanometric thickness

We apply a previously developed asymptotic model (J. Fluid. Mech. 915, A133 (2021)) to study instabilities of free surface films of nanometric thickness on thermally conductive substrates in two and three spatial dimensions. While the specific focus is on metal films exposed to laser heating, the model itself applies to any setup involving films on the nanoscale whose material parameters are temperature-dependent. For the particular case of metal films heated from above, an important aspect is that the considered heating is volumetric, since the absorption length of the applied laser pulse is comparable to the film thickness. In such a setup, absorption of thermal energy and film evolution are closely correlated and must be considered self-consistently. The asymptotic model allows for a significant simplification, which is crucial from both modeling and computational points of view, since it allows for asymptotically correct averaging of the temperature over the film thickness. We find that the properties of the thermally conductive substrate -- in particular its thickness and rate of heat loss -- play a critical role in controlling the film temperature and dynamics. The film evolution is simulated using efficient GPU-based simulations which, when combined with the developed asymptotic model, allow for fully nonlinear time-dependent simulations in large three-dimensional computational domains. In addition to uncovering the role of the substrate and its properties in determining the film evolution, one important finding is that, at least for the considered range of material parameters, strong in-plane thermal diffusion in the film results in negligible spatial variations of temperature, and the film evolution is predominantly influenced by temporal variation of film viscosity and surface tension (dictated by average film temperature), as well as thermal conductivity of the substrate.

physics.flu-dyn↗

arXiv2021

On efficient asymptotic modelling of thin films on thermally conductive substrates

We consider a free surface thin film placed on a thermally conductive substrate and exposed to an external heat source in a setup where the heat absorption depends on the local film thickness. Our focus is on modeling film evolution while the film is molten. The evolution of the film modifies local heat flow, which in turn may influence the film surface evolution through thermal variation of the film's material properties. Thermal conductivity of the substrate plays an important role in determining the heat flow and the temperature field in the evolving film and in the substrate itself. In order to reach a tractable formulation, we use asymptotic analysis to develop a novel thermal model that is accurate, computationally efficient, and that accounts for the heat flow in both the in-plane and out-of plane directions. We apply this model to metal films of nanoscale thickness exposed to heating and melting by laser pulses, a setup commonly used for self and directed assembly of various metal geometries via dewetting while the films are in the liquid phase. We find that thermal effects play an important role, and in particular that the inclusion of temperature dependence in the metal viscosity modifies the time scale of the evolution significantly. On the other hand, in the considered setup the Marangoni (thermocapillary) effect turns out to be insignificant.

physics.flu-dyn↗