Strong Mixing Research Articles

New a Priori estimate for stochastic 2D Navier–Stokes equations with applications to invariant measure

AbstractThe paper deals with the stochastic two-dimensional Navier–Stokes equations for homogeneous and incompressible fluids, set in a bounded domain with Dirichlet boundary conditions. We consider additive noise in the form $$G\,\textrm{d}W$$ G d W , where W is a cylindrical Wiener process and G a bounded linear operator with range dense in the domain of $$A^\gamma $$ A γ , A being the Stokes operator. While it is known that existence of invariant measure holds for $$\gamma >1/4$$ γ > 1 / 4 , previous results show its uniqueness only for $$\gamma > 3/8$$ γ > 3 / 8 . We fill this gap and prove uniqueness and strong mixing property in the range $$\gamma \in (1/4, 3/8]$$ γ ∈ ( 1 / 4 , 3 / 8 ] by adapting the so-called Sobolevskiĭ-Kato-Fujita approach to the stochastic N–S equations. This method provides new a priori estimates, which entail both better regularity in space for the solution and strong Feller and irreducibility properties for the associated Markov semigroup.

Analisis Pengaruh Penerapan Strategi Bauran Pemasaran terhadap Keputusan Pembelian pada UMKM Serba Nanas Alam Sari Subang Jawa Barat

UMKM One of the producers in Subang offering processed pineapples is Serba Nanas Alam Sari. Processed pineapple sales are erratic. Businesses must create a strong marketing mix strategy in order to overcome consumer preferences and market rivalry. The purpose of this study is to examine how purchase decisions at Serba Nanas Alam Sari UMKM in Subang, West Java, are affected by the application of a marketing mix approach. In order to collect data for this study, 100 UMKM customers were given questionnaires. Mixed methods were used in this research. The techniques employed for gathering data included surveys, interviews, documentation, and observation. A Likert scale is used for variable measurement, and MSI is used to alter it. Multiple linear regression data analysis was used to ascertain the impact of place, promotion, price, and product variables on consumer purchase decisions. The study's findings indicate that the significant value is less than 0.05, indicating that purchase decisions are influenced by product, price, place, and promotion all at the same time. With a result of 1,042, the product variable has the biggest impact. This is due to the product's variety, good taste, and guaranteed product quality. The variables that affect promotion, pricing, and location are next in line. Based on the study's findings, Serba Nanas Alam Sari UMKM can benefit from an efficient marketing plan that combines quality products, competitive pricing, effective distribution, and eye-catching promotions to influence more customers' purchases.

Particle-Hole Asymmetric Ferromagnetism and Spin Textures in the Triangular Hubbard-Hofstadter Model

In a lattice model subject to a perpendicular magnetic field, when the lattice constant is comparable to the magnetic length, one enters the “Hofstadter regime,” where continuum Landau levels become fractal magnetic Bloch bands. Strong mixing between bands alters the nature of the resulting quantum phases compared to the continuum limit; lattice potential, magnetic field, and Coulomb interaction must be treated on equal footing. Using determinant quantum Monte Carlo and density matrix renormalization group techniques, we study this regime numerically in the context of the Hubbard-Hofstadter model on a triangular lattice. In the field-filling phase diagram, we find a broad wedge-shaped region of ferromagnetic ground states for filling factor ν≤1, bounded below by filling factor ν=1 and bounded above by half filling the lowest Hofstadter subband. We observe signatures of SU(2) quantum Hall ferromagnetism at filling factors ν=1 and ν=3. The phases near ν=1 are particle-hole asymmetric, and we observe a rapid decrease in ground-state spin polarization consistent with the formation of skyrmions only on the electron doped side. At large fields, above the ferromagnetic wedge, we observe a low-spin metallic region with spin correlations peaked at small momenta. We argue that the phenomenology of this region likely results from exchange interaction mixing fractal Hofstadter subbands. The phase diagram derived beyond the continuum limit points to a rich landscape to explore interaction effects in magnetic Bloch bands. Published by the American Physical Society 2024

Effects of the internal temperature on vertical mixing and on cloud structures in ultra-hot Jupiters

The vertical mixing in hot-Jupiter atmospheres plays a critical role in the formation and spacial distribution of cloud particles in their atmospheres. This affects the observed spectra of a planet through cloud opacity, which can be influenced by the degree of cold trapping of refractory species in the deep atmosphere. We aim to isolate the effects of the internal temperature on the mixing efficiency in the atmospheres of ultra-hot Jupiters (UHJs) and the spacial distribution of cloud particles across the planet. We combined a simplified tracer-based cloud model, a picket fence radiative-transfer scheme, and a mixing length theory to the Exo-FMS general circulation model. We ran the model for five different internal temperatures at typical UHJ atmosphere system parameters. Our results show the convective eddy diffusion coefficient remains low throughout the vast majority of the atmosphere, with mixing dominated by advective flows. However, some regions can show convective mixing in the upper atmosphere for colder interior temperatures. The vertical extent of the clouds is reduced as the internal temperature is increased. Additionally, a global cloud layer gets formed below the radiative--convective boundary (RCB) in the cooler cases. Convection is generally strongly inhibited in UHJ atmospheres above the RCB due to their strong irradiation. Convective mixing plays a minor role compared to advective mixing in keeping cloud particles aloft in UHJs with warm interiors. Higher vertical turbulent heat fluxes and the advection of potential temperature inhibit convection in warmer interiors. Our results suggest that isolated upper atmosphere regions above cold interiors may exhibit strong convective mixing in isolated regions around Rossby gyres, allowing aerosols to be better retained in these areas.

Design, experimental optimization, and flow analysis of a novel bioreactor for dynamic mammalian cell culture at laboratory scale using Box-Behnken design

Improving the quality of dynamic cell culture in laboratories is an important field in bioengineering. In this study, a novel lab-scale bioreactor using a vibrating agitator and a modified flask has been introduced to create a strong mixing at low shear stress. This bioreactor has been optimized using Box-Behnken design based on three dimensionless important structural factors including disc diameter, vibration amplitude, and the height of the disc placement. Three growth indicators including the specific growth rate, the natural logarithm of the maximum cell density, and productivity have been considered as biological responses. The results show that the disc diameter has the most important role in these indicators. If the disc diameter, vibration amplitude, and the height of disc placement are set to 0.24, 0.02, and 0.4 of the flask diameter, respectively, the values of the specific growth rate, the maximum cell density, and productivity at this optimum settings are 0.033 (h−1), 13.11, and 5133 (cells/(mL.h)), respectively. These values of the indicators are high and indicate the better performance of this bioreactor than other lab-scale bioreactors. In addition, investigating Reynolds number in the fluid flow indicates that in the range of 780 up to 1150, growth indices are high.

Cosmological Flow of Primordial Correlators.

Correlation functions of primordial density fluctuations provide an exciting probe of the physics governing the earliest moments of our Universe. However, the standard approach to compute them is technically challenging. Theoretical predictions are therefore available only in restricted classes of theories. In this Letter, we present a complete method to systematically compute tree-level inflationary correlators. This method is based on following the time evolution of equal-time correlators and it accurately captures all physical effects in any theory. These theories are conveniently formulated at the level of inflationary fluctuations, and can feature any number of degrees of freedom with arbitrary dispersion relations and masses, coupled through any type of time-dependent interactions. We demonstrate the power of this approach by exploring the properties of the cosmological collider signal, a discovery channel for new high-energy physics, in theories with strong mixing and in the presence of features. This work lays the foundation for a universal program to assist our theoretical understanding of inflationary physics and generate theoretical data for an unbiased interpretation of upcoming cosmological observations.

On the convergence of phase space distributions to microcanonical equilibrium: dynamical isometry and generalized coarse-graining

Abstract This work explores the manner in which classical phase space distribution functions converge to the microcanonical distribution. We first prove a theorem about the lack of convergence, then define a generalization of the coarse-graining procedure that leads to convergence. We prove that the time evolution of phase space distributions is an isometry for a broad class of statistical distance metrics, implying that ensembles do not get any closer to (or farther from) equilibrium, according to these metrics. This extends the known result that strong convergence of phase space distributions to the microcanonical distribution does not occur. However, it has long been known that weak convergence can occur, such that coarse-grained distributions---defined by partitioning phase space into a finite number of cells---converge pointwise to the microcanonical distribution. We define a generalization of coarse-graining that removes the need for partitioning phase space into cells. We prove that our generalized coarse-grained distribution converges pointwise to the microcanonical distribution if the dynamics are strong mixing. As an example, we study an ensemble of triangular billiard systems.

Thermal mixing and structure of the jet in swirling crossflow

The dilution zone in modern aero-engine combustors is characterized by a strong swirling mainstream with weak transverse jets. This characteristic brings new challenges in homogenizing the temperature distribution at the combustor exit. Therefore, it is imperative to understand the temperature penetration and mixing process of the jet in swirling crossflow (JISCF). This investigation provides new insight in the temperature mixing process for a JISCF in nozzle exit diameter (D) at 7.4, 10.7, and 14 mm and jet to mainstream velocity ratio (VR) from 2.0 to 6.6. The temperature mixing process was measured in a specially designed optical assessable three-dome model gas turbine combustor by planar 1-methylnaphthalene (1-MN) tracer laser-induced fluorescence thermometry. A detailed quantitative measurement of temperature distribution is achieved through the spectral red shift in the fluorescence of 1-MN as the temperature increase. This diagnostic was employed to provide the first two-dimensional temperature distribution for the JISCF. The results showed that the swirling crossflows induce strong spanwise thermal advection, forming secondary low-temperature regions downstream. Generally, the flow structure and mixing process are governed by the interaction of jet and swirling flow. The jet flow parameters, including velocity ratio and diameter, changed the flow structures by changing the interaction between jet and swirling flow. Statistical results and proper orthogonal decomposition (POD) analyses showed a strong anisotropic mixing process in the downstream of the jet.

A comparative study on aquatic environment of two mega reservoirs in the mainstream of Yangtze River

With the mega dams being built in large rivers around the world for water resources utilization and flood prevention, their environmental impacts such as algae bloom are increasingly concerned by the professionals and the publics, but the mechanism controlling the occurrence of algae are still unclear. Along the mainstream of the Yangtze River, world-class reservoirs have been put into operation successively. Among these reservoirs, the Three Gorges Reservoir (TGR) and the cascade reservoirs (CRs) are adjacent but the conditions of algae bloom in the tributary bays of them are totally different. To explore the reasons of the distinguished situations and factors relating to the high frequent algae bloom in the tributary bays of the TGR, a comparative study was carried out between the TGR and its neighbored reservoir out of the CRs based on field survey investigation, water quality records and literature review. The result reveals the considerable influences of geological and climatic factors on the hydrodynamic processes and environmental problems happening in the tributary bays of mega reservoirs. The two reservoirs exhibit significant differences in physical properties such as the hydrodynamic condition, terrain characteristics and climate. The field-investigation suggests that the water columns in the tributary bays of the CRs tend to experience weak vertical stratification. The analysis shows that this is the result of the combining result of the local terrain characteristics and the cooler, rainier and cloudier climate in the CRs region which significantly affect the hydro-thermal dynamic processes in the tributary bays. With the low level of nutrient and strong vertical mixing, the growth of the algae is constrained and these should be the significant reasons of the low frequency of algae bloom in the tributary bays of the CRs.

Hybrid spin-orbit exciton-magnon excitations in FePS3

FePS3 is a layered van der Waals (vdW) Ising antiferromagnet that has recently been studied in the context of true 2D magnetism and emerged as an ideal material platform for investigating strong spin-phonon coupling, and non-linear magneto-optical phenomena. In this work, we demonstrate an important unresolved role of spin-orbit coupling (SOC) in the ground state and excitations of this compound. Combining first-principles calculations with linear flavor wave theory (LFWT), we find strong mixing and spectral overlap of different spin-orbital single-ion states. Low-lying excitations form hybrid spin-orbit exciton/magnon modes. Complete parameterization of the low-energy model requires nearly half a million coupling constants. Despite this complexity, such a model can be inexpensively derived using local many-body-based approaches, which yield quantitative agreement with recent experiments. The results highlight the importance of SOC even in first-row transition metals and provide essential insight into the properties of 2D magnets with unquenched orbital moments.

Simulation of a cold spell in Guangdong-Hong Kong-Macao Greater Bay Area with WRF: Sensitivity to PBL schemes

The selection of the planetary boundary layer (PBL) parameterisation schemes is crucial for the simulation of local meteorology, especially under extreme weather events. A suitable PBL scheme is one of the key conditions to accurately reproduce the real weather conditions. In this study, the performance of all the three available PBL schemes that can be coupled with the multi-layer urban canopy model in the Weather Research and Forecasting (WRF) model: Yonsei University (YSU), Mellor-Yamada-Janjic (MYJ), and Bougeault-Lacarrere (BL), is evaluated for a cold spell event with Guangdong-Hong Kong-Macao Greater Bay Area (GBA) as the study region. It is found that accurate prediction of the strength of the vertical mixing and the change in wind speeds over the upper atmosphere is critical for reproducing the nighttime temperatures during the cold spell. The simulations of the BL scheme are consistent with observations that wind speeds do not vary much during daytime and nighttime, thus exhibiting strong vertical mixing and slowing down the near-surface temperature decrease during nighttime. The MYJ and YSU schemes cause significant underestimation of the nighttime 2-m temperature due to significant overestimation of the nighttime upper-air wind speeds, which leads to more heat transport through horizontal advection and hinders vertical mixing and convective activities. The results confirm that selection of a suitable PBL scheme can effectively reduce the uncertainty of the simulation results, and the coupling of the BL scheme with the multi-layer urban canopy model can better simulate the cold spell events occurring in the GBA, which also provides valuable references for the simulation of other similar coastal cities.

Characteristics and Mechanisms of Spring Tidal Mixing and Sediment Transport in a Microtidal Funnel-Shaped Estuary

Information about estuarine mixing and its control of sediment transport is crucial to elucidating the dynamics and evolution of estuaries. Here, the microtidal and funnel-shaped Zhenhai Estuary, located in the southwestern Pearl River Delta of China, is used to investigate the characteristics and mechanisms of water mixing and sediment transport based on observations from three spring tides. The results reveal that the studied estuary remains well mixed during spring tides from 2013–2022 despite its microtidal regime. Tidal stirring, which is enhanced by tidal energy convergence and benefits from the funnel-shaped geometry and shallow bathymetry, favors vertical mixing, contributing to the formation of strong mixing in the estuary. Due to the well-mixed regime, sediment transport in the estuary is dominated by the advective term, followed by a moderate tidal pumping term and minor estuarine circulation term. Accordingly, sediments within the estuary tend to be transported landward owing to the regulation of the funnel-shaped geometry, and a gradual but slow infilling trend is predictable. This paper deepens our understanding of hydrodynamics and sediment transport in microtidal estuaries.

Dispersion of particles in a sessile droplet evaporating on a heated substrate

A coupled volume-of-fluid (VOF) and discrete element model (DEM) is developed and used to study the dispersion of particles in an evaporating pinned sessile droplet on a heated substrate. Fully resolved simulations of evaporating droplets are performed to study the effects of substrate temperature and the Marangoni stresses to study the fluid flow and temperature distribution within the droplet. The fluid flow inside the evaporating droplets is used to predict the behavior of particles, studying the effect of relative particle density and the aforementioned effects on the particle dispersion within the droplet. This study shows that the presence of Marangoni stresses significantly affects the flow and temperature distribution inside the droplet, which, in turn, influences the dispersion of particles in the droplet. The fluid velocity induced by the Marangoni stresses is nearly two orders of magnitude larger than the velocity generated by capillary flow as a result of evaporation, promoting a strong convective mixing within the droplet, while working to equilibrate the temperature distribution at the interface. In the absence of Marangoni stresses, the dispersion of particles is governed by the competing effects of adsorption by the downward-moving interface as a result of evaporation, and particle sedimentation under the influence of gravity. However, both these effects become less dominant in the presence of a flow induced by the Marangoni stresses, causing the particles to initially move toward the apex of the droplet along the interface and, subsequently, toward a stagnation point on the interface.

Leadership for AI Transformation in Health Care Organization: Scoping Review.

The leaders of health care organizations are grappling with rising expenses and surging demands for health services. In response, they are increasingly embracing artificial intelligence (AI) technologies to improve patient care delivery, alleviate operational burdens, and efficiently improve health care safety and quality. In this paper, we map the current literature and synthesize insights on the role of leadership in driving AI transformation within health care organizations. We conducted a comprehensive search across several databases, including MEDLINE (via Ovid), PsycINFO (via Ovid), CINAHL (via EBSCO), Business Source Premier (via EBSCO), and Canadian Business & Current Affairs (via ProQuest), spanning articles published from 2015 to June 2023 discussing AI transformation within the health care sector. Specifically, we focused on empirical studies with a particular emphasis on leadership. We used an inductive, thematic analysis approach to qualitatively map the evidence. The findings were reported in accordance with the PRISMA-ScR (Preferred Reporting Items for Systematic Reviews and Meta-Analysis extension for Scoping Reviews) guidelines. A comprehensive review of 2813 unique abstracts led to the retrieval of 97 full-text articles, with 22 included for detailed assessment. Our literature mapping reveals that successful AI integration within healthcare organizations requires leadership engagement across technological, strategic, operational, and organizational domains. Leaders must demonstrate a blend of technical expertise, adaptive strategies, and strong interpersonal skills to navigate the dynamic healthcare landscape shaped by complex regulatory, technological, and organizational factors. In conclusion, leading AI transformation in healthcare requires a multidimensional approach, with leadership across technological, strategic, operational, and organizational domains. Organizations should implement a comprehensive leadership development strategy, including targeted training and cross-functional collaboration, to equip leaders with the skills needed for AI integration. Additionally, when upskilling or recruiting AI talent, priority should be given to individuals with a strong mix of technical expertise, adaptive capacity, and interpersonal acumen, enabling them to navigate the unique complexities of the healthcare environment.

Validated DNA isolation method ensuring successful long-read sequencing of cattle semen genome.

Obtaining high-quality DNA suitable for long-read sequencing can be difficult for many types of tissues and cells, and it is a key step in current genomic studies. The challenge is even greater when it comes to isolating genomic DNA from mammalian spermatozoa, as DNA is tightly packed into a cell with a robust membrane rich in disulfide bonds. Here we describe a method for isolating high molecular weight DNA from Bovine commercial semen straws. This protocol includes a cleaning step to remove diluents and preservatives used for the long-term storage of the semen, which may affect long read sequencing. It is based on a simple salting-out method and avoid the use of spin columns, strong mixing or intensive centrifugation, in order to limit DNA fragmentation. However, we have adapted this protocol to facilitate the disruption of cell membranes and disulfide bonds with strong chaotropic and reducing agents. The average size of the fragments produced was approximately 49 kb, ranging from 25 to 85 kb, according to the femto pulse profiles.This method was used to isolate DNA from semen straws, more than 80 of them were successfully sequenced using the Continuous Long-Read (CLR) sequencing mode on the PacBio SequelII platform to study genome diversity and notably to detect large structural variations within genomes.

Strong Consistency of Wavelet Estimator for Biased Nonparametric Regression Function Under Strong Mixing

Strong Consistency of Wavelet Estimator for Biased Nonparametric Regression Function Under Strong Mixing

Perfect sampling of $q$-spin systems on $\mathbb{Z}^{2}$ via weak spatial mixing

We present a perfect marginal sampler of the unique Gibbs measure of a spin system on \mathbb{Z}^{2} . The algorithm is an adaptation of a previous “lazy depth-first” approach by the authors, but relaxes the requirement of strong spatial mixing to weak. Our result is a step towards methods of efficient sampling using only weak spatial mixing. The work exploits a classical result in statistical physics relating weak spatial mixing on \mathbb{Z}^{2} to strong spatial mixing on squares. When the spin system exhibits weak spatial mixing, the run-time of our sampler is linear in the size of sample. Applications of note are the ferromagnetic Potts model at supercritical temperatures and the ferromagnetic Ising model with consistent non-zero external field at any non-zero temperature.

Lateral Transport Controls the Tidally Averaged Gravitationally Driven Estuarine Circulation: Tidal Mixing Effects

Abstract In classic models of the tidally averaged gravitationally driven estuarine circulation, denser salty oceanic water moves up the estuary near the bottom, while less dense riverine water flows toward the ocean near the surface. Traditionally, it is assumed that the associated pressure gradient forces and salt advection are balanced by vertical mixing. This study, however, demonstrates that lateral (across the estuary width) transport processes are essential for maintaining the estuarine circulation. This is because for realistic estuarine bathymetry, the depth-integrated salt transport up the estuary is enhanced in the deeper estuary channel. A closed salt budget then requires the lateral transport of this excess salt in the deeper channel toward the estuarine flanks. To understand how such lateral transport affects the estuarine salt and momentum balances, we devise an idealized model with explicit lateral transport focusing on tidally averaged lateral mixing effects. Solutions for the along-estuary velocity and salinity are nondimensionalized to depend only on one single nondimensional parameter, referred to as the Fischer number, which describes the relative importance of lateral to vertical tidal mixing. For relatively strong lateral tidal mixing (greater Fischer number), salinity and velocity variations are predominantly vertical. For relatively weak lateral tidal mixing (smaller Fischer number), salinity and velocity variations are predominantly lateral. Overall, lateral transport greatly affects the estuarine circulation and controls the estuarine salinity intrusion length, which is demonstrated to scale inversely with the Fischer number.

Adaptive rank-based tests for high dimensional mean problems

The Wilcoxon signed-rank test and the Wilcoxon–Mann–Whitney test are commonly employed in one sample and two sample mean tests for one-dimensional hypothesis problems. For high-dimensional mean test problems, we calculate the asymptotic distribution of the maximum of rank statistics for each variable and suggest a max-type test. This max-type test is then merged with a sum-type test, based on their asymptotic independence offered by stationary and strong mixing assumptions. Our numerical studies reveal that this combined test demonstrates robustness and superiority over other methods, especially for heavy-tailed distributions.

On non parametric kernel estimation of the mode of the regression function in the strong mixing random design model with censored data

. This study delves into the conditional mode estimation of a randomly censored scalar response variable operating within the framework of strong mixing conditions. We introduce a kernel-based estimator for the conditional mode function. The principal contribution of this investigation lies in the derivation of the asymptotic distribution and the strong rate of convergence of the newly proposed estimators. These findings are established under a set of fairly comprehensive structural assumptions governing the underlying models. Additionally, we conduct a series of simulation studies to showcase the finite sample performance characteristics of the proposed estimator.