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The MPSDynamics.jl package provides an easy to use interface for performing open quantum systems simulations at zero and finite temperatures. The package has been developed with the aim of studying non-Markovian open system dynamics using the state-of-the-art numerically exact Thermalized-Time Evolving Density operator with Orthonormal Polynomials Algorithm (T-TEDOPA) based on environment chain mapping. The simulations rely on a tensor network representation of the quantum states as matrix product states (MPS) and tree tensor network (TTN) states. Written in the Julia programming language, MPSDynamics.jl is a versatile open-source package providing a choice of several variants of the Time-Dependent Variational Principle (TDVP) method for time evolution (including novel bond-adaptive one-site algorithms). The package also provides strong support for the measurement of single and multi-site observables, as well as the storing and logging of data, which makes it a useful tool for the study of many-body physics. It currently handles long-range interactions, time-dependent Hamiltonians, multiple environments, bosonic and fermionic environments, and joint system-environment observables., Comment: 11 pages, 3 figures

Understanding the local fracture resistance of microstructural features. such as brittle inclusions, coatings, and interfaces at the microscale under complex loading conditions is critical for microstructure-informed design of materials. In this study, a novel approach has been formulated to decompose the J-integral evaluation of the elastic energy release rate to the three-dimensional stress intensity factors directly from experimental measurements of the elastic deformation gradient tensors of the crack field by in situ high (angular) resolution electron backscatter diffraction (HR-EBSD). An exemplar study is presented of a quasi-static crack, inclined to the observed surface, propagating on low index {hkl} planes in a (001) single crystal silicon wafer.

For high (angular) resolution electron backscatter diffraction (HR-EBSD), the selection of a reference diffraction pattern (EBSP0) significantly affects the precision of the calculated strain and rotation maps. This effect was demonstrated in plastically deformed body-centred cubic and face-centred cubic ductile metals (ferrite and austenite grains in duplex stainless steel) and brittle single-crystal silicon, which showed that the effect is not only limited to measurement magnitude but also spatial distribution. An empirical relationship was then identified between the cross-correlation parameter and angular error, which was used in an iterative algorithm to identify the optimal reference pattern that maximises the precision of HR-EBSD.

Component failure due to cold dwell fatigue of titanium and its alloys is a long-standing problem which has significant safety and economic implications to the aviation industry. This can be addressed by understanding the governing mechanisms of time dependent plasticity behaviour of Ti at low temperatures. Here, stress relaxation tests were performed at four different temperatures on three major alloy systems: commercially pure titanium (two alloys with different oxygen content), Ti-6Al-4V (two microstructures with differing beta phase fractions) and Ti-6Al-2Sn-4Zr-xMo (two alloys with different Mo content x= 2 or 6, and portion of beta phase). Key parameters controlling the time dependent plasticity were determined as a function of temperature. Both activation volume and energy were found to increase with temperature in all six alloys. It was found that the dwell fatigue effect is more significant by oxygen alloying but is suppressed by the addition of Mo. The presence of the beta phase did not strongly affect the dwell fatigue, however, it was suppressed at high temperature due to the low strain rate and strain rate sensitivity.

We introduce a weighted ellipse fitting routine to measure Debye Scherrer rings acquired on 2D area detectors and demonstrate its use in strain determination. The method is relatively robust against incomplete rings due to low number of grains in the diffraction volume (spotty rings), or strong texture (intensity depletion in some azimuths). The method works by applying an annular mask around each diffraction ring and fitting an ellipse, using all pixel positions and their diffracted intensity as weights in the minimisation. We compare this method to the more popular cake integration method, and show that the weighted ellipse method works when the cake integration method fails or works poorly. The lattice strain sensitivity from spotty diffraction rings is in the order or 2E-5 or better. The algorithm has been made available for public use and works with 2D diffraction patterns acquired in a laboratory scale XRD equipment, TEM or a synchrotron.

Modeling linear absorption spectra of solvated chromophores is highly challenging as contributions are present both from coupling of the electronic states to nuclear vibrations and solute-solvent interactions. In systems where excited states intersect in the Condon region, significant non-adiabatic contributions to absorption lineshapes can also be observed. Here, we introduce a robust approach to model linear absorption spectra accounting for both environmental and non-adiabatic effects from first principles. This model parameterizes a linear vibronic coupling (LVC) Hamiltonian directly from energy gap fluctuations calculated along molecular dynamics (MD) trajectories of the chromophore in solution, accounting for both anharmonicity in the potential and direct solute-solvent interactions. The resulting system dynamics described by the LVC Hamiltonian are solved exactly using the thermalized time-evolving density operator with orthogonal polynomials algorithm (T-TEDOPA). The approach is applied to the linear absorption spectrum of methylene blue (MB) in water. We show that the strong shoulder in the experimental spectrum is caused by vibrationally driven population transfer between the bright S1 and the dark S2 state. The treatment of the solvent environment is one of many factors which strongly influences the population transfer and lineshape; accurate modeling can only be achieved through the use of explicit quantum mechanical solvation. The efficiency of T-TEDOPA, combined with LVC Hamiltonian parameterizations from MD, leads to an attractive method for describing a large variety of systems in complex environments from first principles., Comment: 16 pages, 7 figures

A statistical framework is presented enabling optimal sampling and analysis of constant life fatigue data. Protocols using Bayesian maximum entropy sampling are built based on conventional staircase and stress step methods, reducing the requirement of prior knowledge for data collection. The Bayesian Staircase method shows improved parameter estimation efficiency, and the Bayesian Stress Step method shows equal accuracy to the standard method at larger step size allowing experimentalists to lessen concerns of loading history. Statistical methods for determining model suitability are shown, highlighting the influence of protocol. Experimental validation is performed, showing the applicability of the methods in laboratory testing., Comment: 27 pages, 12 figures + 1 SI figure

Digital image correlation (DIC) and crystal plasticity simulation were utilised to study cold dwell behaviour in a coarse grain Ti-6Al alloy at 3 different temperatures up to 230 C. Strains extracted from large volume grains were measured during creep by DIC and were used to calibrate the crystal plasticity model. The values of critical resolved shear stresses (CRSS) of the two main slip systems (basal and prismatic) were determined as a function of temperature. Stress along paths across the boundaries of two grain pairs, (1) a `rogue' grain pair and (2) a `non-rogue' grain pair, were determined at different temperatures. Load shedding was observed in the `rogue' grain pair, where a stress increment during the creep period was found in the `hard' grain. At elevated temperatures, 120 C was found to be the worst-case scenario as the stress difference at the grain boundaries of these two grain pairs were found to be the largest among the three temperatures. This can be attributed to the fact that the strain rate sensitivity of both prismatic and basal slip systems is at its greatest in this worst-case scenario temperature.

For complex molecules, nuclear degrees of freedom can act as an environment for the electronic `system' variables, allowing the theory and concepts of open quantum systems to be applied. However, when molecular system-environment interactions are non-perturbative and non-Markovian, numerical simulations of the complete system-environment wave function become necessary. These many body dynamics can be very expensive to simulate, and extracting finite-temperature results - which require running and averaging over many such simulations - becomes especially challenging. Here, we present numerical simulations that exploit a recent theoretical result that allows dissipative environmental effects at finite temperature to be extracted efficiently from a single, zero-temperature wave function simulation. Using numerically exact time-dependent variational matrix product states, we verify that this approach can be applied to vibronic tunneling systems and provide insight into the practical problems lurking behind the elegance of the theory, such as the rapidly growing numerical demands that can appear for high temperatures over the length of computations., Comment: 12 pages, 8 figures

The spatial variation in martensite tetragonality (c/a ratio) in Fe-0.77C (wt.%) alloy was investigated by means of pattern matching of electron backscatter diffraction patterns combined with high angular resolution electron backscatter diffraction analysis. It was found that the c/a ratio varies within a martensite block and between blocks. The c/a variation within a block is particularly evident in the vicinity of grain boundaries and shear strains are also present in addition to tetragonal distortion. The c/a variation between blocks is more apparent than that within a block. The lattice parameter frequency profile predicted by our approach well matches with the X-ray diffraction profile from the same material by assuming reasonable residual strain acting on a- and b-axes. The heterogeneities of the crystal distortion are brought by a decrease and scatter in solid solution carbon and in carbon ordering as a result of the martensite transformation sequence as well as heterogeneous residual strain.

There is a long-standing technological problem in which a stress dwell during cyclic loading at room temperature in Ti causes a significant fatigue life reduction. It is thought that localised time dependent plasticity in soft grains favourably oriented for easy plastic slip leads to load shedding and an increase in stress within a neighbouring hard grain poorly oriented for easy slip. Quantifying this time dependent plasticity process is key to understand the complex cold dwell fatigue problem. Knowing the effect of operating temperature and oxygen content on cold dwell fatigue will be beneficial for future alloy design to address this problem. In this work, synchrotron X-ray diffraction during stress relaxation experiments was used to characterise the time dependent plastic behaviour of two commercially pure titanium samples (grade 1 and grade 4) with different oxygen content at 4 different temperatures (room temperature, 75C, 145C and 250C). Lattice strains were measured by tracking the diffraction peak shift from multiple crystallographic plane families (21 diffraction rings) as a function of their orientation with respect to the loading direction. Critical resolved shear stress, activation energy and activation volume were established for both prismatic and basal slip as a function of temperature and oxygen content by fitting a crystal plasticity finite element model to the lattice strain relaxation responses measured along the loading axis for five strong reflections. Higher strain rate sensitivity was found to lead to higher plasticity during cold dwell.

Axisymmetric ($m=0$) gyrokinetic and extended-MHD simulations of sheared-flow Z-pinch plasma are performed with the high-order finite volume code COGENT. The present gyrokinetic model solves the long-wavelength limit of the gyrokinetic equation for both ion and electron species coupled to the electrostatic gyro-Poisson equation for the electrostatic potential. The electromagnetic MHD model includes the effects of the gyro-viscous pressure tensor, diamagnetic electron and ion heat fluxes, and generalized Ohm's law. A prominent feature of this work is that the radial profiles for the plasma density and temperature are taken from the FuZE experiment and the magnetic field profile is obtained as a solution of the MHD force balance equation. Such an approach allows to address realistic plasma parameters and provide insights into the current and planned experiments. In particular, it is demonstrated that the radial profiles play an important role in stabilization, as the embedded guiding center ($E{\times} B$) drift has a strong radial shear, which can contribute to the Z-pinch stabilization even in the absence of the fluid flow shear. The results of simulations for the FuZE plasma parameters show a decrease of the linear growth rate with an increase in the flow shear, however full stabilization in the linear regime is not observed even for large (comparable to the Alfv\'en velocity) radial variations of the axial flow. Nonlinear stability properties of the FuZE plasmas are also studied and it is found that profile broadening can have a pronounced stabilizing effect in the nonlinear regime.

The fracture properties of as-cast TiVNbTa, a refractory high-entropy alloy (RHEA), were investigated using four-point bending tests from -139C to 20C under a strain-rate of 10-3 s-1. From those tests and fractography, the conditional fracture toughness values and the brittle-to-ductile transition temperature were obtained. The brittle-to-ductile transition temperature was between -47C to -27C, which gives an estimated activation energy value of 0.52+-0.09 eV for the alloy. This study provides a preliminary understanding of the nature of dislocation motion in a relatively ductile RHEA.

Understanding the emergent system-bath correlations in non-Markovian and non-perturbative open systems is a theoretical challenge that has benefited greatly from the application of Matrix Product State (MPS) methods. Here, we propose an autonmously adapative variant of the one-site Time-Dependent-Variational-Principle (1TDVP) method for many-body MPS wave-functions in which the local bond-dimensions can evolve to capture growing entanglement 'on the fly'. We achieve this by efficiently examining the effect of increasing each MPS bond-dimension in advance of each dynamic timestep, resulting in an MPS that can dynamically and inhomogeneously restructure itself as the complexity of the dynamics grows across time and space. This naturally leads to more efficient simulations, oviates the need for multiple convergence runs, and, as we demonstrate, is ideally suited to the typical, finite-temperature 'impurity' problems that describe open quantum system connected to multiple environments., Comment: 8 pages, 3 figures

Changes in stress applied to mantle rocks, such as those imposed by earthquakes, induce a period of evolution in viscosity and microstructure. This transient creep is often modelled based on stress transfer among slip systems due to grain interactions. However, recent experiments have demonstrated that the intragranular accumulation of stresses among dislocations is the dominant cause of strain hardening in olivine at low temperatures, raising the question of whether the same process contributes to transient creep at higher temperatures. Here, we demonstrate that olivine samples deformed at 25{\deg}C or 1150 to 1250{\deg}C both contain stress heterogeneities of ~1 GPa that are imparted by dislocations and have correlation lengths of ~1 micrometre. The similar stress distributions formed in both temperature regimes indicate that accumulation of stresses among dislocations also provides a contribution to transient creep at high temperatures. The results motivate a new generation of models that capture these intragranular processes and may refine predictions of evolving mantle viscosity over the earthquake cycle., Comment: 17 pages, 5 figures, 2 tables

The serration of grain boundaries in Inconel 600 caused by heat treatment is studied systematically. A new method based on Fourier transforms is used to analyse the multiple wave-like character of the serrated grain boundaries. A new metric -- the serration index -- is devised and utilised to quantify the degree of serration and more generally to distinguish objectively between serrated and non-serrated boundaries. By considering the variation of the serration index with processing parameters, a causal relationship between degree of serration and solution treatment/cooling rate is elucidated. Processing maps for the degree of serration are presented. Two distinct formation mechanisms arise which rely upon grain boundary interaction with carbides: (i) Zener-type dragging which hinders grain boundary migration and (ii) a faceted carbide growth-induced serration.

There is a long standing technological problem in which a stress dwell during cyclic loading at room temperature in Ti causes a significant fatigue life reduction. It is thought that localised time dependent plasticity in soft grains oriented for easy plastic slip leads to load shedding and an increase in stress within a neighbouring hard grain poorly oriented for easy slip. Quantifying this time dependent plasticity process is key to successfully predicting the complex cold dwell fatigue problem. This work uses a novel approach of in situ synchrotron X-ray diffraction during stress relaxation tests, to quantify the time dependent plasticity. Measured lattice strains from multiple lattice families (21 diffraction rings) were compared with simulated lattice strains from crystal plasticity finite element (CPFE) simulations. The prism slip parameters were found to show stronger strain rate sensitivity compared to basal slip, and this has a significant effect on stress redistribution to hard grain orientations during cold creep.

We use the classical Ax-Kochen-Ershov analysis of the model theory of Henselian fields to bring out some model-theoretical aspects of the structure sheaf of the spectrum of Z^ and the ring of finite ad\`eles over Q. We show that various structures associated to a prime ideal, such as quotients and localizations, are well understood model-theoretically, and they are closely connected to ultrafilters on the set of standard primes., Comment: 17 pages

Measurements of the local tetragonality in Fe-C martensite at microstructural length-scale through pattern matching of electron backscatter diffraction patterns (EBSPs) and careful calibration of detector geometry are presented. It is found that the local tetragonality varies within the complex microstructure by several per cent at largest and that the scatter in the axial ratio is increased at higher nominal carbon content. At some analysis points the local crystal structure can be regarded as lower symmetry than simple body centred tetragonal. A linear relation between the nominal carbon content and averaged local tetragonality measured by EBSD is also obtained, although the averaged axial ratio is slightly below that obtained from more classical X-ray diffraction measurements., Comment: 33 pages, 12 figures, 2 Tables

The strength of the lithosphere is typically modelled based on constitutive equations for steady-state flow. However, models of lithospheric flexure reveal differences in lithospheric strength that are difficult to reconcile based on such flow laws. Recent rheological data from low-temperature deformation experiments on olivine suggest that this discrepancy may be largely explained by strain hardening. Details of the mechanical data, specifically the effects of temperature-independent back stresses stored in the samples, indicate that strain hardening in olivine occurs primarily due to long-range elastic interactions between dislocations. These interpretations provided the basis for a new flow law that incorporates hardening by development of back stress. Here, we test this hypothesis by examining the microstructures of olivine samples deformed plastically at room temperature either in a deformation-DIA apparatus at differential stresses of < 4.3 GPa or in a nanoindenter at applied contact stresses of > 10.2 GPa. High-angular resolution electron backscatter diffraction maps reveal the presence of geometrically necessary dislocations with densities commonly above 10$^{14}$ m$^{-2}$ and intragranular heterogeneities in residual stress on the order of 1 GPa in both sets of samples. Scanning transmission electron micrographs reveal straight dislocations aligned along slip bands and interacting with dislocations of other types that act as obstacles. The stress heterogeneities and accumulations of dislocations along their slip planes are consistent with strain hardening resulting from long-range back-stresses acting between dislocations. These results corroborate the mechanical data in supporting the form of the new flow law for low-temperature plasticity and provide new microstructural criteria for identifying the operation of this deformation mechanism in natural samples.

We study the mechanisms of slip transfer at a grain boundary, in titanium, using Differential Aperture X-ray Laue Micro-diffraction (DAXM). This 3D characterization tool enables measurement of the full (9-component) Nye lattice curvature tensor and calculation of the density of geometrically necessary dislocations (GNDs). We observe dislocation pile-ups at a grain boundary, as the neighbor grain prohibits easy passage for dislocation transmission. This incompatibility results in local micro-plasticity within the slipping grain, near to where the slip planes intersect the grain boundary, and we observe bands of GNDs lying near the grain boundary. We observe that the distribution of GNDs can be significantly influenced by the formation of grain boundary ledges that serve as secondary dislocation sources. This observation highlights the non-continuum nature of polycrystal deformation and helps us understand the higher order complexity of grain boundary characteristics., Comment: 30 pages, 9 figures, 2 tables

The well known Warren-Averbach theory of diffraction line profile broadening is shown to be applicable to time of flight data obtained from a neutron spallation source. Without modification, the method is applied to two very different examples; a cold worked ferritic steel and a thermally stressed alumina-30% SiC composite. Values of root mean square strains averaged over a range of lengths for the ferritic steel were used to estimate dislocation densities; values were found to be in good agreement with geometrically necessary dislocation densities independently measured from similarly orientated grains measured from electron backscatter diffraction analysis. An analytical model for the ceramic is described to validate the estimate of root mean square strain., Comment: Preprint under review

Analysis of distortions of the crystal lattice within individual mineral grains is central to the investigation of microscale processes that control and record tectonic events. These distortions are generally combinations of lattice rotations and elastic strains, but a lack of suitable observational techniques has prevented these components being mapped simultaneously and routinely in earth science laboratories. However, the technique of high-angular resolution electron backscatter diffraction (HR-EBSD) provides the opportunity to simultaneously map lattice rotations and elastic strains with exceptional precision, on the order of 0.01 degree for rotations and 10-4 in strain, using a scanning electron microscope. Importantly, these rotations and lattice strains relate to densities of geometrically necessary dislocations and residual stresses. Recent works have begun to apply and adapt HR-EBSD to geological minerals, highlighting the potential of the technique to provide new insights into the microphysics of rock deformation. Therefore, the purpose of this overview is to provide a summary of the technique, to identify caveats and targets for further development, and to suggest areas where it offers potential for major advances. In particular, HREBSD is well suited to characterising the roles of different dislocation types during crystal plastic deformation and to mapping heterogeneous internal stress fields associated with specific deformation mechanisms/microstructures or changes in temperature, confining pressure, or applied deviatoric stress. These capabilities make HR-EBSD a particularly powerful new technique for analysing the microstructures of deformed geological materials., Comment: resubmitted article

Pattern matching between target electron backscatter patterns (EBSPs) and dynamically simulated EBSPs was used to determine the pattern centre (PC) and crystal orientation, using a global optimisation algorithm. Systematic analysis of error and precision with this approach was carried out using dynamically simulated target EBSPs with known PC positions and orientations. Results showed that the error in determining the PC and orientation was < 10$^{-5}$ of pattern width and < 0.01{\deg} respectively for the undistorted full resolution images (956x956 pixels). The introduction of noise, optical distortion and image binning was shown to have some influence on the error although better angular resolution was achieved with the pattern matching than using conventional Hough transform-based analysis. The accuracy of PC determination for the experimental case was explored using the High Resolution (HR-) EBSD method but using dynamically simulated EBSP as the reference pattern. This was demonstrated through a sample rotation experiment and strain analysis around an indent in interstitial free steel.

In this study, we have used a Zr-Nb alloy containing well-defined nano-precipitates as a model material in which to study imaging contrast inversions (atomic number or diffraction contrast) observed with the forescattered electron imaging system, ARGUSTM, in a scanning electron microscope (SEM) when imaging a thin foil in a transmission geometry. The study is based on Monte Carlo simulations and analysis of micrographs experimentally acquired under different imaging conditions. Based on the results, imaging conditions that enhance atomic number or diffraction contrast have been proposed. Data acquired from the ARGUSTM imaging system in SEM has also been compared with results from standard transmission electron microscopy and scanning transmission electron microscopy imaging of the same material. These results demonstrate the capability of the ARGUSTM system to investigate microstructures in nano-scale materials.