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The constitutive relation for an initially stressed reference is often determined using the response of a virtual stress-free reference. However, it is usually difficult to identify the constitutive relation of the associated stress-free reference, without performing a destructive testing. In this paper, we introduce three approaches to determine the response of the stress-free, or any arbitrary initially stressed reference, using the response of a given initially stressed reference. The first and third approaches directly find out the constitutive relations for one stressed reference from another. The second approach uses the response of a given stressed reference, to identify the stress-free material, and thereafter determines the response of any stressed reference. Quite interestingly, it appears that the stress-free material, or the arbitrarily stressed references, can be implicit, although the given (known) initially stressed state is Green elastic. We also obtain a few simple cases of explicit constitutive relations. These approaches of changing the reference configuration do not begin from the stress-free state. Using the present framework and the concept of symmetry, we also explore the dependence or independence of constitutive relation on the choice of reference. The present work also develops the universal relations for stress-free isotropic implicit elastic materials.

Akin to the traditional quasi-classical trajectory method for investigating the dynamics on a single adiabatic potential energy surface for an elementary chemical reaction, we carry out the dynamics on a 2-state ab initio potential energy surface including nonadiabatic coupling terms as friction terms for D+ + H2 collisions. It is shown that the resulting dynamics correctly accounts for nonreactive charge transfer, reactive non charge transfer and reactive charge transfer processes. In addition, it leads to the formation of triatomic DH2+ species as well., Comment: 31 pages, 7 figures

MnBi$_{2}$Te$_{4}$, the first topological insulator with inherent magnetic ordering, has attracted significant attention recently for providing a platform to realize several exotic quantum phenomena at relatively higher temperatures. In this work, we have carried out an exhaustive investigation of MnBi$_{2}$Te$_{4}$ and Sb doped MnBi$_{2}$Te$_{4}$ thin films using THz time-domain spectroscopy. The extracted real THz conductivity displays a strong IR active E$_u$ phonon absorption peak (at $\sim$1.5 THz) merged on top of the Drude-like contributions from bulk and surface electrons. The extracted parameters from the THz conductivity data fitted to the Drude-Fano-Lorentz model, show significant changes in their temperature dependence around the magnetic ordering N\'eel temperature of $\sim$ 25K, which is suggestive of the coupling between magnetic ordering and electronic band structure. The frequency of the E$_u$ phonon displays an anomalous blue-shift with increasing temperatures by $\sim$ 0.1 THz ($\sim$7 %) for MnBi$_{2}$Te$_{4}$ and $\sim$0.2 THz ($\sim$13 %) for Sb doped MnBi$_{2}$Te$_{4}$ between 7K and 250K. The line-shape of the E$_u$ phonon mode in Sb doped MnBi$_{2}$Te$_{4}$ shows significant Fano asymmetry compared to that of MnBi$_{2}$Te$_{4}$, indicating that Sb doping plays an important role in the Fano interference between the phonons and the electrons, in this system. These results indicate that the anomalous phonon behaviour seen in MBT arise mainly from positive cubic anharmonicity induced self energy parameter, whereas both anharmonicity and the electron phonon coupling are at play in making the relatively higher anomalous blue shift of phonons in MBST. Our studies provide the first comprehensive understanding of the phonon and electron dynamics of MnBi$_{2}$Te$_{4}$ and Sb doped MnBi$_{2}$Te$_{4}$ in the THz range using time-domain THz spectroscopy.

Elucidating the emergence of long-range magnetic ordering from its precursor short-range magnetic ordering (SRMO) in two-dimensional van der Waals materials holds profound implications for fundamental research and technological advancements. However, directly observing the intricate stages of this magnetic dimensional crossover (MDC) remains a significant experimental challenge. While magneto-elastic coupling offers a promising avenue, detecting the minute lattice response to SRMO proves challenging. Recent investigations utilizing second harmonic generation have unveiled a two-step MDC in a van der Waals ferromagnetic insulator. However, an unambiguous detection of MDC through the time-resolved techniques remains elusive. To meet this goal, we have executed an alternative approach by employing picosecond acoustic strain pulses generated by femtosecond lasers to probe the various stages of MDC through the magneto-elastic coupling for the first time. By analyzing the shape of the strain pulse in both the time and frequency domains as a function of temperature, we clearly demonstrate the detection of the subtle influence of spin fluctuations on the lattice. Additionally, the ultrafast carrier dynamics also show signatures of MDC. Our measurements pave the way towards characterizing magnetic materials in time-resolved experiments that are crucial in designing a new generation of spin-based optoelectronic devices., Comment: Manuscript contains 12 pages with 3 figures + Supplementary Material

Randomized control trials, RCTs, have become a powerful tool for assessing the impact of interventions and policies in many contexts. They are considered the gold-standard for inference in the biomedical fields and in many social sciences. Researchers have published an increasing number of studies that rely on RCTs for at least part of the inference, and these studies typically include the response data collected, de-identified and sometimes protected through traditional disclosure limitation methods. In this paper, we empirically assess the impact of strong privacy-preservation methodology (with \ac{DP} guarantees), on published analyses from RCTs, leveraging the availability of replication packages (research compendia) in economics and policy analysis. We provide simulations studies and demonstrate how we can replicate the analysis in a published economics article on privacy-protected data under various parametrizations. We find that relatively straightforward DP-based methods allow for inference-valid protection of the published data, though computational issues may limit more complex analyses from using these methods. The results have applicability to researchers wishing to share RCT data, especially in the context of low- and middle-income countries, with strong privacy protection., Comment: Submitted

By going beyond the Born-Oppenheimer approximation and treating the non-adiabatic coupling terms (NACTs) as equivalent to a frictional force in a molecular system, the classical equations of motion are solved for a test case of H3+. Using an ab initio potential energy surface for the ground electronic state and its NACTs with the first excited state of H3+, it is shown that (D+, H2) collisions are slowed enough to result in trapping and formation of a stable DH2+., Comment: 16 pages, 2 figures

Real-world solids, such as rocks, soft tissues, and engineering materials, are often under some form of stress. Most real materials are also, to some degree, anisotropic due to their microstructure, a characteristic often called the `texture anisotropy'. This anisotropy can stem from preferential grain alignment in polycrystalline materials, aligned micro-cracks, or structural reinforcement, such as collagen bundles in biological tissues, steel rods in prestressed concrete and reinforcing fibres in composites. Here we establish a framework for initially stressed solids with transverse texture anisotropy. We consider that the strain energy per unit mass of the reference is an explicit function of the elastic deformation gradient, the initial stress tensor, and the texture anisotropy. We determine the corresponding constitutive relations and develop examples of nonlinear strain energies which depend explicitly on the initial stress and direction of texture anisotropy. As an application, we then employ these models to analyse the stress distribution of an inflated initially stressed cylinder with texture anisotropy, and the tension of a welded metal plate. We also deduce the elastic moduli needed to describe linear elasticity from stress reference with transverse texture anisotropy. As an example we show how to measure the stress with small-amplitude shear waves.

This paper applies a symmetry-adapted method to examine the influence of deformation and defects on the electronic structure and band structure in carbon nanotubes. First, the symmetry-adapted approach is used to develop the analog of Bloch waves. Building on this, the technique of perfectly-matched layers is applied to develop a method to truncate the computational domain of electronic structure calculations without spurious size effects. This provides an efficient and accurate numerical approach to compute the electronic structure and electromechanics of defects in nanotubes. The computational method is applied to study the effect of twist, stretch, and bending, with and without various types of defects, on the band structure of nanotubes. Specifically, the effect of stretch and twist on band structure in defect-free conducting and semiconducting nanotubes is examined, and the interaction with vacancy defects is elucidated. Next, the effect of localized bending or kinking on the electronic structure is studied. Finally, the paper examines the effect of 5-8-5 Stone-Wales defects. In all of these settings, the perfectly-matched layer method enables the calculation of localized non-propagating defect modes with energies in the bandgap of the defect-free nanotube., Comment: To appear in Mathematics and Mechanics of Solids

In the early universe, following the nucleosynthesis, conditions were right for recombination processes to take place yielding neutral atoms H, He and Li. The understanding so far in astrophysics is that the first molecule to be formed was HeH+ by radiative association (He + H+ -> HeH+ + h(nu) and He+ + H -> HeH+ + h(nu). The recent report by Guesten et al (Nature, 568, 357, 2019) of detection of HeH+ in planetary Nebula NGC 7027 confirms its presence, but it does not conclusively prove the origin of this species. To create molecules from free moving quasi-ions surrounded by an electronic cloud, the Born-Oppenheimer-Huang (BOH) theory furnishes two kinds of forces, namely, one that results from the Potential Energy Surfaces (PESs) and the other from Non-Adiabatic Coupling Terms (NACTs). Whereas the PESs are known to manage slow moving quasi-ions the NACTs, with their, frequently, infinitely large values at the vicinity of the singularities can control the fast moving quasi-ions. To achieve that the BOH equation indicates that the NACTs are affecting the fast moving quasi-ions directly and if they are attributed with dissipative features or in other words to behave as a Friction Force they indeed could serve (like any other ordinary friction) as moderators for the fast atomic(ionic) species. It is proposed in the present paper that the triatomic HeH2+ was the precursor to HeH+ and it could have been formed by the (He, H, H)+ nuclei coming together under the electron cloud, facilitated by the NACTs between different electronic states acting as an astronomical friction force. This is possible because of the singularities in the NACTs for triatomic systems and NOT for diatomic systems. Although the existence of HeH2+ was established in the laboratory in 1996, it has not been detected in the interstellar media so far. But, there is no reason why it cannot be detected in near future., Comment: 25 pages, 4 figures