The Resolvent Problem and $${{H^{\infty}}}$$ -calculus of the Stokes Operator in Unbounded Cylinders with Several Exits to Infinity

It is proved that the Stokes operator in L^q -space on an infinite cylindrical domain of , , with several exits to infinity generates a bounded and exponentially decaying analytic semigroup and admits a bounded -calculus. For the resolvent estimates, the Stokes resolvent system with a prescribed divergence in an infinite straight cylinder with bounded cross-section is studied in L ^q where and is an arbitrary Muckenhoupt weight. The proofs use cut-off techniques and the theory of Schauder decomposition of UMD spaces based on -boundedness of operator families and on square function estimates involving Muckenhoupt weights.     

Single Benzene Green Fluorophore: Solid‐State Emissive,Water‐Soluble,and Solvent‐ and pH‐Independent Fluorescence with Large Stokes Shifts

Benzene is the simplest aromatic hydrocarbon with a six‐membered ring. It is one of the most basic structural units for the construction of π conjugated systems, which are widely used as fluorescent dyes and other luminescent materials for imaging applications and displays because of their enhanced spectroscopic signal. Presented herein is 2,5‐bis(methylsulfonyl)‐1,4‐diaminobenzene as a novel architecture for green fluorophores, established based on an effective push–pull system supported by intramolecular hydrogen bonding. This compound demonstrates high fluorescence emission and photostability and is solid‐state emissive, water‐soluble, and solvent‐ and pH‐independent with quantum yields of Φ=0.67 and Stokes shift of 140 nm (in water). This architecture is a significant departure from conventional extended π‐conjugated systems based on a flat and rigid molecular design and provides a minimum requirement for green fluorophores comprising a single benzene ring.     

Efficient One‐Pot Access to 2,9‐Dihydrothiopyrano[2,3‐b]indole Scaffolds Showing Large Stokes Shifts

A simple, mild and efficient one‐pot approach for the construction of 2‐aryl‐3‐nitro‐2,9‐dihydrothiopyrano[2,3‐b]indole derivatives has been realized in CH₂Cl₂ medium at ambient temperature via three‐component tandem reaction of N‐protected‐2‐chloro‐3‐formylindoles, sodium hydrosulfide and β‐substituted nitroolefins/δ‐substituted nitrodienes using DABCO (10 mol%) as an organocatalyst, followed by dehydration in the presence of activated molecular sieves (4 Å). The significant advantages of this protocol are simple operation, shorter reaction time, high atom economy, good to high yields (73% –89%) and wider substrate scope. In addition, all the synthesized compounds have shown the large positive Stokes shift values (5632–6081 cm^?1).     

Reynolds-averaged Navier–Stokes initialization and benchmarking in shock-driven turbulent mixing

We investigate a strategy for benchmarking Reynolds-averaged Navier–Stokes (RANS) models by comparing moments extracted from averaged large eddy simulation (LES) data and those predicted directly by RANS. We consider the Besnard–Harlow–Rauenzahn (BHR) RANS approach designed for variable-density compressible flows, which has been previously applied to a wide variety of turbulence problems of interest. We focus on the model's ability to predict moments relevant to shock-driven material mixing. A prototypical inverse chevron shock tube configuration is considered, for which laboratory and previous LES studies are available for comparison and validation. We show that when appropriately initialized, BHR is capable of accurately capturing various characteristic integral measures of the flow; strategies for initialization are demonstrated while addressing sensitivity of BHR predictions to closure and initialization specifics, initial material interface conditions, and grid resolution. The reference simulations are performed using implicit LES based on the Los Alamos National Laboratory RAGE hydrodynamics code.     

Fiber optic probes for linear and nonlinear Raman applications – Current trends and future development

This review focuses on fiber optic probes for linear and nonlinear Raman spectroscopy, especially for medical applications. It aims at providing an overview over contemporary technology, recent first clinical trials, and helps identifying future developments necessary to bring the emerging technology to clinical end users. After a short introduction to linear and nonlinear Raman spectroscopic modalities, general design considerations will be discussed and compared to common fiber probe setups. Subsequently, examples for medical applications of fiber optic Raman probes will be given concentrating on probes for linear Raman spectroscopy as these devices are technologically more mature compared to their counterparts based on nonlinear Raman spectroscopy. The review also includes a brief summary of first multimodal fiber optic probes and highlights their benefits for clinical applications. Finally, probes are introduced which employ either nonlinear Raman spectroscopy or surface enhanced spectroscopy.     

Cerussite,PbCO3 – a new Stimulated Raman Scattering (SRS)‐active crystal with high‐order Stokes and anti‐Stokes lasing

Orthorhombic PbCO₃, known as natural crystal cerussite, is presented as a new Stimulated Raman Scattering (SRS)‐active crystal. With picosecond laser pumping high‐order Raman‐induced χ⁽³⁾ generation is observed. All registered Stokes and anti‐Stokes sidebands in the visible and near‐IR are identified and attributed to the SRS‐promoting phonon mode A_1g of the carbonate group, with ω_SRS ≈ 1054 cm⁻¹. The first Stokes steady‐state Raman gain coefficient in the visible spectral range is estimated as well to a value not less than 4.6 cm·GW⁻¹.     

A local lagrangian analysis of passive particle advection in a gas flow field

A local analysis is performed to study the departure from passive advection by small inertial particles based on a Lagrangian framework. The analysis considers heavy particles immersed in a gaseous flow and is restricted to short times, making it relevant to the PIV technique. A necessary (but not sufficient condition) for passive particle advection of inertial particles is that the quantity Λ_maxτ_p be much smaller than one, where Λ_max is the largest modulus of the eigenvalues corresponding to the velocity gradient tensor. This allows for the inertial and passive time scales to match beyond the initial transient, and consequently for the respective trajectories to remain relatively close. Due to this important role regarding advection behavior, Λ_maxτ_p is offered as a definition of a local Stokes number, St_Λ. Since this quantity is a field quantity, it directly provides indication of when and where passive advection by particles can be expected. A departure equation is obtained in one-dimension, where the influence of initial velocity and gravity are explicitly shown. If the flow is irrotational, the higher dimensional analysis reduces to a set of decoupled one-dimensional equations acting along each respective eigenvector of the velocity gradient tensor. A similar expression is found for the case of a purely temporal flow field.     

Linear differential equations and multiple zeta values. II. A generalization of the WKB method

For linear differential equations x(n)+a₁x(n−1)+?+anx=0 (and corresponding linear differential systems) with large complex parameter λ and meromorphic coefficients aj=aj(t;λ) we prove existence of analogues of Stokes matrices for the asymptotic WKB solutions. These matrices may depend on the parameter, but under some natural assumptions such dependence does not take place. We also discuss a generalization of the Hukuhara-Levelt-Turritin theorem about formal reduction of a linear differential system near an irregular singular point t=0 to a normal form with ramified change of time to the case of systems with large parameter. These results are applied to some hypergeometric equations related with generating functions for multiple zeta values.     

Reduced finite difference scheme and error estimates based on POD method for non-stationary Stokes equation

The proper orthogonal decomposition (POD) is a model reduction technique for the simulation of physical processes governed by partial differential equations (e.g.,fluid flows). It has been successfully used in the reduced-order modeling of complex systems. In this paper, the applications of the POD method are extended, i.e., the POD method is applied to a classical finite difference (FD) scheme for the non-stationary Stokes equation with a real practical applied background. A reduced FD scheme is established with lower dimensions and sufficiently high accuracy, and the error estimates are provided between the reduced and the classical FD solutions. Some numerical examples illustrate that the numerical results are consistent with theoretical conclusions. Moreover, it is shown that the reduced FD scheme based on the POD method is feasible and efficient in solving the FD scheme for the non-stationary Stokes equation.     

Fundamental solution of rotating generalized stokes problem in ℝ<Superscript>3</Superscript>

In this paper,the fundamental solution of rotating generalized Stokes problem in R 3 is established.To obtain it,some fundamental solutions of other problems also are established,such as generalized Laplace problem,generalized Stokes problem and rotating Stokes problem.