NTMpy: An open source package for solving coupled parabolic differential equations in the framework of the three-temperature model

The NTMpy code package allows for simulating the one-dimensional thermal response of multilayer samples after optical excitation, as in a typical pump-probe experiment. Several Python routines are combined and optimized to solve coupled heat diffusion equations in one dimension, on arbitrary piecewise homogeneous material stacks, in the framework of the so-called three-temperature model. The energy source deposited in the material is modelled as a light pulse of arbitrary cross-section and temporal profile. A transfer matrix method enables the calculation of realistic light absorption in presence of scattering interfaces as in multilayer samples. The open source code is fully object-oriented to enable a user-friendly and intuitive interface for adjusting the physically relevant input parameters. Here, we describe the mathematical background of the code, we lay out the workflow, and we validate the functionality of our package by comparing it to commercial software, as well as to experimental transient reflectivity data recorded in a pump-probe experiment with femtosecond light pulses

NTMpy: An open source package for solving coupled parabolic differential equations in the framework of the three-temperature model

The NTMpy code package allows for simulating the one-dimensional thermal response of multilayer samples after optical excitation, as in a typical pump-probe experiment. Several Python routines are combined and optimized to solve coupled heat diffusion equations in one dimension, on arbitrary piecewise homogeneous material stacks, in the framework of the so-called three-temperature model. The energy source deposited in the material is modelled as a light pulse of arbitrary cross-section and temporal profile. A transfer matrix method enables the calculation of realistic light absorption in presence of scattering interfaces as in multilayer samples. The open source code is fully object-oriented to enable a user-friendly and intuitive interface for adjusting the physically relevant input parameters. Here, we describe the mathematical background of the code, we lay out the workflow, and we validate the functionality of our package by comparing it to commercial software, as well as to experimental transient reflectivity data recorded in a pump-probe experiment with femtosecond light pulses.Program summaryProgram title: NTMpy v.0.1.1CPC Library link to program files: https: //doi.org/10.17632/5czr76gmwr.1Developer's repository link: https://github.com/udcm-su/NTMpyCode Ocean capsule: https://codeocean.com/capsule/5661399Licensing provisions: MIT licenseProgramming language: PythonExternal routines: Python 3.5 or higher, numpy, matplotlib, bsplines, tqdmNature of problem: 1-dimensional coupled non linear partial differential equations; diffusion and relaxation dynamics formultiple systems and multiple layers.Solution method: Simulate the diffusion and relaxation dynamics of up to 3 coupled systems via an object oriented user interface. In order to approximate the solution and its derivatives in space B-Spline interpolation is used. The solution is developed in time via the Explicit Euler method.Additional comments including restrictions and unusual features: A routine to automatically select the ideal time step for stability of the algorithm is implemented. Routines for output of raw data in order to post process and pre- made visualization routines are implemented. (C) 2021 The Author(s). Published by Elsevier B.V

Analysis in k-space of Magnetization Dynamics Driven by Strong Terahertz Fields

Demagnetization in a thin film due to a terahertz pulse of magnetic field is investigated. Linearized LLG equation in the Fourier space to describe the magnetization dynamics is derived, and spin waves time evolution is studied. Finally, the demagnetization due to spin waves dynamics and recent experimental observations on similar magnetic system are compared. As a result of it, the marginal role of spin waves dynamics in loss of magnetization is established.Comment: 5 pages, 6 figure

A Fast Matrix Compression Method for Large Scale Numerical Modelling of Rotationally Symmetric 3D Passive Structures in Fusion Devices

This paper illustrates the development of a recursive QR technique for the analysis of transient events, such as disruptions or scenario evolution, in fusion devices with three-dimensional conducting structures using an integral eddy current formulation. An integral formulation involves the solution, at each time step, of a large full linear system. For this reason, a direct solution is impractical in terms of time and memory consumption. Moreover, typical fusion devices show a symmetric/periodic structure. This can be properly exploited when the plasma and other sources possess the same symmetry/periodicity of the structure. Indeed, in this case, the computation can be reduced to only a single sector of the overall structure. In this work the periodicity and the symmetries are merged in the recursive QR technique, exhibiting a huge decrease in the computational cost. Finally, the proposed technique is applied to a realistic large-scale problem related to the International Thermonuclear Experimental Reactor (ITER)

Inertial spin dynamics in ferromagnets

The understanding of how spins move and can be manipulated at pico- and femtosecond timescales has implications for ultrafast and energy-efficient data-processing and storage applications. However, the possibility of realizing commercial technologies based on ultrafast spin dynamics has been hampered by our limited knowledge of the physics behind processes on this timescale. Recently, it has been suggested that inertial effects should be considered in the full description of the spin dynamics at these ultrafast timescales, but a clear observation of such effects in ferromagnets is still lacking. Here, we report direct experimental evidence of intrinsic inertial spin dynamics in ferromagnetic thin films in the form of a nutation of the magnetization at a frequency of ~0.5 THz. This allows us to reveal that the angular momentum relaxation time in ferromagnets is on the order of 10 ps

Fast and ultrafast nonlinear magnetization dynamics in magnetic storage technologies

The thesis treats the nonlinear magnetization dynamics in nanosystems. Analytical models for uniformly magnetized bodies are derived, in particular it is considered the dynamics induced by harmonic magnetic fields. Numerical and semi-analytical tools for the magnetization dynamics with noise are developed. Data retention and writing process reliability in magnetic storage technologies are analyzed. Models for the ultrafast magnetization dynamics are studied, the theoretical results are compared with experimental data. First direct evidence of inertia in magnetization dynamics is observed in experiments

Robust link functions

In binary and ordinal response models outlying covariates as well as incoherent responses may affect the reliability of the maximum likelihood estimators and that of the derived inferential procedures. However the various link functions, which provide the relationship between the linear predictor and the probabilities of the response categories, differ in terms of sensitivity to anomalous data. The current paper derives conditions useful to evaluate the properties of the link functions with respect to robustness, either when the covariates are outlier free or when extreme design points may occur. The main results show that – by an appropriate choice of the link function – robust estimators, with a bounded influence function, can be easily derived from the usual likelihood function, while preserving the predictive ability of the fitted model

Current-driven hysteretic synchronization in vortex nanopillar spin-transfer oscillators

The synchronization of nanopillar vortex spin-transfer nano-oscillators with external ac injected current is considered. A collective variables description is used to derive an analytical reduced-order model for the vortex core dynamics. This model is able to predict all the possible vortex oscillation regimes as well as the transition mechanisms among them. In particular, it is shown that hysteretic synchronization occurs at moderate ac currents. The analytical results are in good agreement with micromagnetic simulations

Effect of Temperature in Hysteretic Synchronization of Magnetic Vortex Spin-Torque Nano-Oscillators

The synchronization of vortex spin-transfer nano-oscillators (both nanopillar and nanocontact structures) with external microwave excitations is considered. A collective variables description is used to derive an analytical reduced-order model for the vortex core dynamics, which is able to predict all the possible oscillation regimes and hysteretic transitions among them. The influence of thermal fluctuations on hysteretic synchronization is studied by full micromagnetic simulations. The numerical results are in good agreement with the theory