Show newer

Advanced Mathematical Techniques in Renormalization of Elastic Models: A Comprehensive Analysis arxiv.org/abs/2409.13775

Advanced Mathematical Techniques in Renormalization of Elastic Models: A Comprehensive Analysis

In this study, we delve into the intricate mathematical frameworks essential for the renormalization of effective elastic models within complex physical systems. By integrating advanced tools such as Laurent series, residue theorem, winding numbers, and path integrals, we systematically address divergent loop integrals encountered in renormalization group analyses. Furthermore, we extend our analysis to higher-order physical models, incorporating techniques from quantum field theory and exploring quantum coherent states in complex systems. This comprehensive approach not only enhances the precision of calculating elastic anomalous exponents but also provides deeper insights into the topological structures underlying phase transitions and fixed-point behaviors. The methodologies developed herein pave the way for future explorations into more intricate many-body systems.This paper presents an extensive mathematical framework aimed at enhancing the complexity and extending the theory of Fermi condensates to high-temperature regimes. By incorporating a range of mathematical formulations from thermodynamics, statistical physics, and quantum field theory, we derive key equations and their high-temperature modifications. The study encompasses corrections to the Fermi-Dirac distribution, thermodynamic quantities of Fermi condensates, pairing gap equations within the BCS theory, correlation functions, modified Hamiltonians, path integral representations, and hydrodynamic equations.

arxiv.org

Simple lipids form stable higher-order structures in concentrated sulfuric acid arxiv.org/abs/2409.12982

Simple lipids form stable higher-order structures in concentrated sulfuric acid

Venus has become a target of astrobiological interest because it is physically accessible to direct exploration, unlike exoplanets. So far this interest has been motivated not by the explicit expectation of finding life, but rather a desire to understand the limits of biology. The Venusian surface is sterilizing, but the cloud deck includes regions with temperatures and pressures conventionally considered compatible with life. However, the Venusian clouds are thought to consist of concentrated sulfuric acid. To determine if any fundamental features of life as we understand them here on Earth could in principle exist in these extreme solvent conditions, we have tested several simple lipids for resistance to solvolysis and their ability to form structures in concentrated sulfuric acid. We find that single-chain saturated lipids with sulfate, alcohol, trimethylamine, and phosphonate head groups are resistant to sulfuric acid degradation at room temperature. Furthermore, we find that they form stable higher-order structures typically associated with lipid membranes, micelles, and vesicles. Finally, results from molecular dynamics simulations suggest a molecular explanation for the observed robustness of the lipid structures formed in concentrated sulfuric acid. We conclude with implications for the study of Venus as a target of experimental astrobiology.

arxiv.org

Universal cascade and relaxation of strong anisotropic turbulence in fusion plasmas arxiv.org/abs/2409.12988

Universal cascade and relaxation of strong anisotropic turbulence in fusion plasmas

Starting from the governing equations, exact relations have been derived for three-dimensional reduced magnetohydrodynamic turbulence corresponding to the inertial range cascade of energy and cross-helicity. Justifications are provided for not attempting to recover the said exact relations as a limit of the exact relations previously derived for incompressible magnetohydrodynamic turbulence. Assuming axial symmetry, anisotropic energy spectrum has been predicted from the exact relation and is found to be consistent with the critical balance thus leading to a -5/3 perpendicular energy spectrum. In the case of a strong alignment between the velocity and the magnetic field fluctuations, the derived exact relation implies a generalized anisotropic spectrum with a -3/2 power-law dependence in the direction of alignment. Using the alternative form of the exact relations, it is shown that the flow naturally relaxes towards a state of dynamic alignment in the limit of negligible kinetic and magnetic pressure. Finally, despite having different equations of dynamics, the exact relations for energy and cross-helicity and the relaxed states of a two-dimensional MHD are found to be identical to those in reduced magnetohydrodynamic flow.

arxiv.org

Metamorphosis of transition to periodic oscillations in a turbulent reactive flow system arxiv.org/abs/2409.13044

Metamorphosis of transition to periodic oscillations in a turbulent reactive flow system

The emergence of periodic oscillations is observed in various complex systems in nature and engineering. Thermoacoustic oscillations in systems comprising turbulent reactive flow exemplify such complexity in the engineering context, where the emergence of oscillatory dynamics is often undesirable. In this work, we experimentally study the transition to periodic oscillations within a turbulent flow reactive system, with varying fuel-to-air ratio, represented by equivalence ratio as a bifurcation parameter. Further, we explore the change in the nature of the transition by varying a secondary parameter. In our system, we vary the thermal power input and the location of the flame stabilizer position individually as a secondary parameter. Our findings reveal five qualitatively distinct types of transitions to periodic oscillations. Two types of these transitions exhibit a continuous nature. Another two types of transitions involve multiple shifts in the dynamical states consisting of both continuous and discontinuous bifurcations. The last type of transition is characterized by an abrupt bifurcation to high-amplitude periodic oscillations. Understanding this metamorphosis of the transition - from continuous to discontinuous nature - is critical for advancing our comprehension of the dynamic behavior in turbulent reactive flow systems. The insights gained from this study have the potential to inform the design and control of similar engineering systems where managing oscillatory behavior is crucial.

arxiv.org

Machine Learning Model for Complete Reconstruction of Diagnostic Polarimetric Images from partial Mueller polarimetry data arxiv.org/abs/2409.13073

Machine Learning Model for Complete Reconstruction of Diagnostic Polarimetric Images from partial Mueller polarimetry data

The translation of imaging Mueller polarimetry to clinical practice is often hindered by large footprint and relatively slow acquisition speed of the existing instruments. Using polarization-sensitive camera as a detector may reduce instrument dimensions and allow data streaming at video rate. However, only the first three rows of a complete 4x4 Mueller matrix can be measured. To overcome this hurdle we developed a machine learning approach using sequential neural network algorithm for the reconstruction of missing elements of a Mueller matrix from the measured elements of the first three rows. The algorithm was trained and tested on the dataset of polarimetric images of various excised human tissues (uterine cervix, colon, skin, brain) acquired with two different imaging Mueller polarimeters operating in either reflection (wide-field imaging system) or transmission (microscope) configurations at different wavelengths of 550 nm and 385 nm, respectively. The reconstruction performance was evaluated using various error metrics, all of which confirmed low error values. The execution time of the trained neural network algorithm was about 300 microseconds for a single image pixel. It suggests that a machine learning approach with parallel processing of all image pixels combined with the partial Mueller polarimeter operating at video rate can effectively substitute for the complete Mueller polarimeter and produce accurate maps of depolarization, linear retardance and orientation of the optical axis of biological tissues, which can be used for medical diagnosis in clinical settings.

arxiv.org

Ortho-positronium Lifetime For Soft-tissue Classification arxiv.org/abs/2409.13102

Ortho-positronium Lifetime For Soft-tissue Classification

The objective of this work is to showcase the ortho-positronium lifetime as a probe for soft-tissue characterization. We employed positron annihilation lifetime spectroscopy to experimentally measure the three components of the positron annihilation lifetime para-positronium (p-Ps), positron, and ortho-positronium (o-Ps) for three types of porcine, non-fixated soft tissues ex vivo: adipose, hepatic, and muscle.Then, we benchmarked our measurements with X-ray phase-contrast imaging, which is the current state-of-the-art for soft-tissue analysis. We found that the o-Ps lifetime in adipose tissues (2.54+/-0.12) ns was approximately 20\% longer than in hepatic (2.04+/-0.09 ns) and muscle (2.03+/-0.12 ns) tissues .In addition, the separation between the measurements for adipose tissue and the other tissues was better from o-Ps lifetime measurement than from X-ray phase-contrast imaging. This experimental study proved that the o-Ps lifetime is a viable non-invasive probe for characterizing and classifying the different soft tissues. Specifically, o-Ps lifetime as a soft-tissue characterization probe had a strong sensitivity to the lipid content that can be potentially implemented in commercial positron emission tomography scanners that feature list-mode data acquisition.

arxiv.org

A Ray Tracing Survey of Asymmetric Operation of the X-ray Rowland Circle Using Spherically Bent Crystal Analyzers arxiv.org/abs/2409.13119

A Ray Tracing Survey of Asymmetric Operation of the X-ray Rowland Circle Using Spherically Bent Crystal Analyzers

The spherically bent crystal analyzer (SBCA) is a widely-adopted hard x-ray optic, renowned for its good energy resolution and large collection solid angle. It is frequently employed in synchrotron-based techniques like Resonant Inelastic X-ray Scattering (RIXS) and X-ray Emission Spectroscopy, as well as in the rebirth of laboratory-based X-ray Absorption Fine Strucure (XAFS) and XES, and its predominant use has been in 'symmetric' operation on the Rowland circle. The recent study of Gironda et al. (J. Anal. At. Spectrom., 2024, 39, 1375) emphasizes the benefits of 'asymmetric' SBCA operation, demonstrating the use of multiple crystal reflections from a single SBCA to broaden its accessible energy range. Furthermore, Gironda et al. demonstrate that asymmetric operation frequently mitigates energy broadening intrinsic to Johann optics and propose that under a specific Rowland circle configuration, designated here the Johann Normal Alignment (JNA), such broadening is eradicated altogether. We report extensive ray tracing simulations to scrutinize the impact of asymmetric configurations on energy broadening and detector plane defocusing. We find that the performance of asymmetric SBCA operation generally exceeds its symmetric counterpart in energy resolution when no analyzer masking is used and, with strategic detector placement, the decrease in detection efficiency due to defocusing can be minimized. Spectroscopic imaging is adversely affected by the detector plane blurring, but rejection of scattering from special environment windows in x-ray Raman imaging is still feasible. These results help inform future, more common implementation of asymmetric reflections with SBCA.

arxiv.org
Show older
Qoto Mastodon

QOTO: Question Others to Teach Ourselves
An inclusive, Academic Freedom, instance
All cultures welcome.
Hate speech and harassment strictly forbidden.