We obtain sharp rotation bounds for the subclass of homeomorphisms of finite distortion which have distortion function in , , and for which a Hölder continuous inverse is available. The interest in this class is partially motivated by examples arising from fluid mechanics. Our rotation bounds hereby presented improve the existing ones, for which the Hölder continuity is not assumed. We also present examples proving sharpness.
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http://dx.doi.org/10.1007/s12220-022-00950-y | DOI Listing |
Soft Matter
January 2025
Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia.
We demonstrate the generation of diverse material flow regimes in nematic liquid cells as driven by time-variable active surface anchoring, including no-net flow, oscillatory flow, steady flow, and pulsating flow. Specifically, we numerically simulate a passive nematic fluid inside a cell bounded with two flat solid boundaries at which the time-dependent anchoring is applied with the dynamically variable surface anchoring easy axis. We show that different flow regimes emerge as the result of different anchoring driving directions ( co-rotating or counter-rotating) and relative phase of anchoring driving.
View Article and Find Full Text PDFAnal Chim Acta
January 2025
, Institute for Advanced Studies in Basic Sciences, 45195-1159, Zanjan, Iran. Electronic address:
Background: Multivariate curve resolution methods are usually confronted with non-unique pure component factors. This rotational ambiguity can be represented by ranges of feasible profiles, which are equally compatible with the imposed constraints. Sensor-wise N-BANDS is an effective algorithm for the calculation of the bounds of feasible profiles in the presence of noise, but suffers from high computational cost.
View Article and Find Full Text PDFJ Chem Phys
January 2025
Department of Physics and Astronomy, University of Calgary, 2500 University Drive North West, Calgary, Alberta T2N 1N4, Canada.
Spectra of the weakly bound H2O-O2 dimer are studied in the region of the H2O ν2 band using a tunable quantum cascade laser to probe a pulsed supersonic slit jet expansion. These are the first gas-phase infrared spectra of H2O-O2 and among only a few such results for O2-containing complexes. Almost 100 infrared lines are assigned based on the ground state combination differences from the microwave spectrum of H2O-O2.
View Article and Find Full Text PDFSci Rep
December 2024
Departamento de Física, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911, Leganés, Spain.
Considering a universal deep neural network organized as a series of nested qubit rotations, accomplished by adjustable data re-uploads we analyze its expressivity. This ability to approximate continuous functions in regression tasks is quantified making use of a partial Fourier decomposition of the generated output and systematically benchmarked with the aid of a teacher-student scheme. While the maximal expressive power increases with the depth of the network and the number of qubits, it is fundamentally bounded by the data encoding mechanism.
View Article and Find Full Text PDFJ Biomol Struct Dyn
December 2024
School of Physical Sciences, Swami Ramanand Teerth Marathwada University, Nanded, Maharashtra, India.
The dielectric behavior of Asparagine (CHNO) in water over the frequency range of 10 MHz to 30 GHz in the temperature region of 278.15-303.15 K in a step of 5 K has been carried out using time domain reflectometry (TDR) at various concentrations of asparagine.
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