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Brzeźniak, Z., Rana, N.: Low regularity solutions to the stochastic geometric wave equation driven by a fractional Brownian sheet. arXiv:2006.07740 (2020) Burq, N., Tzvetkov, N.: Random data Cauchy theory for supercritical wave equations. I. Local theory. Invent. Math. 173(3), 449–...
In the FUS condensates the proteins in the shell exhibit a higher cross-β-sheet content than the proteins in the core. Conclusion The physical model developed in this work lays the foundation to obtain the rheological properties of bursting shell-forming condensates. We hypothesize that shell ...
Consider the general stochastic partial differential equation given by where the meaning of the symbols is identical to Eq. (9) and is a d-dimensional random vector having sample space Ω. We now aim to solve the PCE Numerical algorithms In this section, we present computationally efficient ...
Smith, Probing current sheet instabilities from flare ribbon dynamics. ApJ 922, 117 (2021) ADS Google Scholar K. Galsgaard, A. Nordlund, Heating and activity of the solar corona. 3. Dynamics of a low beta plasma with three-dimensional null points. J. Geophys. Res. 102, 231 (1997) ...
His theory on multiphonon transition in semiconductors and insulators, the Huang-Rhys theory, which dealt with both the multiphonon optical and non-radiative transitions, laid the foundation of this important field. He pointed out the possibility of observing X-ray diffuse scattering in crystals due...
The leading order of the operational cost is the same as that for a single equation. The shift invariance of the Krylov subspace is the mathematical foundation of the shifted Krylov subspace methods. Applications in materials science are presented to demonstrate the advantages of the algorithm over...
Sinceuis the solution of the forward problem, it is clear that the forward equation must be solved before the adjoint equation, which, however, remains strictly linear. A useful interpretation of the adjoint equation is that it solves the original PDE but with the mismatch between observations an...
By analyzing this equation in the limit of n = 1, we precisely resolve the dynamics of initial crumpling of a smooth sheet into a ball, a well-studied problem. Results Evolution of the crease patterns in thin sheets The development of damage networks is investigated by repeatedly ...
{\mathrm{M}} - \gamma _{\mathrm{M}} - i\omega _{\mathrm{M}} - i\omega _{\mathrm{M}}^\prime } \right)b - D\), where the parameters\(\omega _{\mathrm{M}}^\prime\)andDcan be obtained by comparing this motion equation with equation (7). The effective mechanical gain is ...