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1. Lieb–Thirring Inequality for the 2D Pauli Operator

   https://doi.org/10.1007/s00220-024-05177-2  

   Frank, Rupert_L; Kovařík, Hynek (January 2025, Communications in Mathematical Physics)

   Abstract By the Aharonov–Casher theorem, the Pauli operatorPhas no zero eigenvalue when the normalized magnetic flux$$\alpha $$ $\alpha$satisfies$$|\alpha |<1$$ $\left|\alpha \right|<1$, but it does have a zero energy resonance. We prove that in this case a Lieb–Thirring inequality for the$$\gamma $$ $\gamma$-th moment of the eigenvalues of$$P+V$$ $P+V$is valid under the optimal restrictions$$\gamma \ge |\alpha |$$ $\gamma \ge \left|\alpha \right|$and$$\gamma >0$$ $\gamma >0$. Besides the usual semiclassical integral, the right side of our inequality involves an integral where the zero energy resonance state appears explicitly. Our inequality improves earlier works that were restricted to moments of order$$\gamma \ge 1$$ $\gamma \ge 1$. 

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2. Electrically tunable total reflection of light by oblique helicoidal cholesteric

   https://doi.org/10.1557/s43577-024-00723-8  

   Iadlovska, Olena_S; Thapa, Kamal; Rajabi, Mojtaba; Mrukiewicz, Mateusz; Shiyanovskii, Sergij_V; Lavrentovich, Oleg_D (June 2024, MRS Bulletin)

   AbstractAn oblique helicoidal state of a cholesteric liquid crystal (Ch_OH) is capable of continuous change of the pitch$$P$$ $P$in response to an applied electric field. Such a structure reflects 50% of the unpolarized light incident along the Ch_OHaxis in the electrically tunable band determined by$$P$$ $P$/2. Here, we demonstrate that at an oblique incidence of light, Ch_OHreflects 100% of light of any polarization. This singlet band of total reflection is associated with the full pitch$$P$$ $P$. We also describe the satellite$$P/2$$ $P/2$,$$P/3$$ $P/3$, and$$P/4$$ $P/4$bands. The$$P/2$$ $P/2$and$$P/4$$ $P/4$bands are triplets, whereas$$P/3$$ $P/3$band is a singlet caused by multiple scatterings at$$P$$ $P$and$$P/2$$ $P/2$. A single Ch_OHcell acted upon by an electric field tunes all these bands in a very broad spectral range, from ultraviolet to infrared and beyond, thus representing a structural color device with enormous potential for optical and photonic applications. Impact statementPigments, inks, and dyes produce colors by partially consuming the energy of light. In contrast, structural colors caused by interference and diffraction of light scattered at submicrometer length scales do not involve energy losses, which explains their widespread in Nature and the interest of researchers to develop mimicking materials. The grand challenge is to produce materials in which the structural colors could be dynamically tuned. Among the oldest known materials producing structural colors are cholesteric liquid crystals. Light causes coloration by selective Bragg reflection at the periodic helicoidal structure formed by cholesteric molecules. The cholesteric pitch and thus the color can be altered by chemical composition or by temperature, but, unfortunately, dynamic tuning by electromagnetic field has been elusive. Here, we demonstrate that a cholesteric material in a new oblique helicoidal Ch_OHstate could produce total reflection of an obliquely incident light of any polarization. The material reflects 100% of light within a band that is continuously tunable by the electric field through the entire visible spectrum while preserving its maximum efficiency. Broad electric tunability of total reflection makes the Ch_OHmaterial suitable for applications in energy-saving smart windows, transparent displays, communications, lasers, multispectral imaging, and virtual and augmented reality. Graphical Abstract 

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3. In vivo estimation of anisotropic mechanical properties of the gastrocnemius during functional loading with MR elastography

   https://doi.org/10.1088/1361-6560/acb482  

   Smith, Daniel R; Caban-Rivera, Diego A; Williams, L Tyler; Van_Houten, Elijah_E W; Bayly, Phil V; Paulsen, Keith D; McGarry, Matthew_D J; Johnson, Curtis L (February 2023, Physics in Medicine & Biology)

   Abstract Objective.In vivoimaging assessments of skeletal muscle structure and function allow for longitudinal quantification of tissue health. Magnetic resonance elastography (MRE) non-invasively quantifies tissue mechanical properties, allowing for evaluation of skeletal muscle biomechanics in response to loading, creating a better understanding of muscle functional health.Approach. In this study, we analyze the anisotropic mechanical response of calf muscles using MRE with a transversely isotropic, nonlinear inversion algorithm (TI-NLI) to investigate the role of muscle fiber stiffening under load. We estimate anisotropic material parameters including fiber shear stiffness ( ${\mu }_1$), substrate shear stiffness ( ${\mu }_2$), shear anisotropy ( $\varphi$), and tensile anisotropy ( $\zeta$) of the gastrocnemius muscle in response to both passive and active tension.Main results. In passive tension, we found a significant increase in ${\mu }_1,$ $\varphi ,$and $\zeta$with increasing muscle length. While in active tension, we observed increasing ${\mu }_2$and decreasing $\varphi$and $\zeta$during active dorsiflexion and plantarflexion—indicating less anisotropy—with greater effects when the muscles act as agonist.Significance. The study demonstrates the ability of this anisotropic MRE method to capture the multifaceted mechanical response of skeletal muscle to tissue loading from muscle lengthening and contraction. 

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4. Exploring Jahn-Teller distortions: a local vibrational mode perspective

   https://doi.org/10.1007/s00894-024-05882-8  

   Quintano, Mateus; Moura, Renaldo T; Kraka, Elfi (April 2024, Journal of Molecular Modeling)

   AbstractThe characterization of normal mode (CNM) procedure coupled with an adiabatic connection scheme (ACS) between local and normal vibrational modes, both being a part of the Local Vibrational Mode theory developed in our group, can identify spectral changes as structural fingerprints that monitor symmetry alterations, such as those caused by Jahn-Teller (JT) distortions. Employing the PBE0/Def2-TZVP level of theory, we investigated in this proof-of-concept study the hexaaquachromium cation case,$$\mathrm {[Cr{(OH_2)}_6]^{3+}}$$ ${\left[\mathrm{Cr}{\left({\mathrm{OH}}_2\right)}_6\right]}^{3+}$/$$\mathrm {[Cr{(OH_2)}_6]^{2+}}$$ ${\left[\mathrm{Cr}{\left({\mathrm{OH}}_2\right)}_6\right]}^{2+}$, as a commonly known example for a JT distortion, followed by the more difficult ferrous and ferric hexacyanide anion case,$$\mathrm {[Fe{(CN)}_6]^{4-}}$$ ${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_6\right]}^{4-}$/$$\mathrm {[Fe{(CN)}_6]^{3-}}$$ ${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_6\right]}^{3-}$. We found that in both cases CNM of the characteristic normal vibrational modes reflects delocalization consistent with high symmetry and ACS confirms symmetry breaking, as evidenced by the separation of axial and equatorial group frequencies. As underlined by the Cremer-Kraka criterion for covalent bonding, from$$\mathrm {[Cr{(OH_2)}_6]^{3+}}$$ ${\left[\mathrm{Cr}{\left({\mathrm{OH}}_2\right)}_6\right]}^{3+}$to$$\mathrm {[Cr{(OH_2)}_6]^{2+}}$$ ${\left[\mathrm{Cr}{\left({\mathrm{OH}}_2\right)}_6\right]}^{2+}$there is an increase in axial covalency whereas the equatorial bonds shift toward electrostatic character. From$$\mathrm {[Fe{(CN)}_6]^{4-}}$$ ${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_6\right]}^{4-}$to$$\mathrm {[Fe{(CN)}_6]^{3-}}$$ ${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_6\right]}^{3-}$we observed an increase in covalency without altering the bond nature. Distinct$$\pi $$ $\pi$back-donation disparity could be confirmed by comparison with the isolated CN$$^-$$ ${}^{-}$system. In summary, our study positions the CNM/ACS protocol as a robust tool for investigating less-explored JT distortions, paving the way for future applications. Graphical abstractThe adiabatic connection scheme relates local to normal modes, with symmetry breaking giving rise to axial and equatorial group local frequencies 

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5. A multiple-timing analysis of temporal ratcheting

   https://doi.org/10.1140/epje/s10189-024-00421-y  

   Hashemi, Aref; Gilman, Edward T.; Khair, Aditya S. (April 2024, The European Physical Journal E)

   AbstractWe develop a two-timing perturbation analysis to provide quantitative insights on the existence of temporal ratchets in an exemplary system of a particle moving in a tank of fluid in response to an external vibration of the tank. We consider two-mode vibrations with angular frequencies$$\omega $$ $\omega$and$$\alpha \omega $$ $\alpha \omega$, where$$\alpha $$ $\alpha$is a rational number. If$$\alpha $$ $\alpha$is a ratio of odd and even integers (e.g.,$$\tfrac{2}{1},\,\tfrac{3}{2},\,\tfrac{4}{3}$$ $\frac{2}{1},\frac{3}{2},\frac{4}{3}$), the system yields a net response: here, a nonzero time-average particle velocity. Our first-order perturbation solution predicts the existence of temporal ratchets for$$\alpha =2$$ $\alpha =2$. Furthermore, we demonstrate, for a reduced model, that the temporal ratcheting effect for$$\alpha =\tfrac{3}{2}$$ $\alpha =\frac{3}{2}$and$$\tfrac{4}{3}$$ $\frac{4}{3}$appears at the third-order perturbation solution. More importantly, we find closed-form formulas for the magnitude and direction of the induced net velocities for these$$\alpha $$ $\alpha$values. On a broader scale, our methodology offers a new mathematical approach to study the complicated nature of temporal ratchets in physical systems. Graphic abstract 

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