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Due to its critical importance in engineering applications, this study is motivated by the essential need to understand natural convection over a vertical cylinder with combined heat and mass transfer. Lie group symmetry transformations are used to analyze the thermal and velocity boundary layers of steady, naturally convective laminar fluid flow over the surface of a vertical cylinder. The one-parameter Lie group symmetry technique converts the system of governing equations into ordinary differential equations, which are then solved numerically using the implicit Runge–Kutta method. The effect of the Prandtl number, Schmidt number, and combined buoyancy ratio parameter on axial velocity, temperature, and concentration profiles are illustrated graphically. A specific range of parameter values was chosen to compare the obtained results with previous studies, demonstrating the accuracy of this method relative to others. The average Nusselt number and average Sherwood number are computed for various values of the Prandtl number Pr and Schmidt number Sc and presented in tables. It was found that the time required to reach a steady state for velocity and concentration profiles decreases as the Schmidt number Sc increases. Additionally, both temperature and concentration profiles decrease with an increase in the combined buoyancy ratio parameter N. Flow reversal and temperature defect with varying Prandtl numbers are also shown and discussed in detail. [ABSTRACT FROM AUTHOR]

The investigation is about the effect of heat and mass transportation over a dragging out cylinder for Cross fluid flow in addition to free stream. This research is a notable effort to measure heat and mass transportation of the flow over an expanding cylinder with the imposition of the external flow. The system of complex partial differential equations is converted into highly nonlinear ordinary differential equations. The solution of the nonlinear system of equations is made with the numerical technique Runge‐Kutta fifth order just after the implementation of the shooting technique with suitable conditions. MATLAB solver bvp4c has solved the problem of the flow over stretching cylinder very efficiently and presents the facts in the form of the graphs and numerical values. The results claim that for the values of gamma parameter from 0.1 to 0.5 the rate of heat transfer increases by 14% on the other lambda with values from 0.1 to 0.3 the heat transfer rate declines 11%. For the growing values of Schmidt number from 1.0 to 5.0 the rate of mass transfer decreases by 85%. The rate of heat transfer has fallen by 86% for the improving values of the Prandtl number from 1, 2, and 3. [ABSTRACT FROM AUTHOR]

In engineering and technology, particularly in designing structures like ships, it can be difficult to allow fluids (like water) to flow smoothly around them. This is called a ''fluid combination problem.'' It is especially important when designing the hull (the bottom part) of ships. Engineers need to calculate the impact of water pressure on the hull and how the water's surface changes. These calculations help make sure that the hull is strong enough to handle different conditions, like waves or fast-moving water. In many engineering problems, geometries like wedges are used to model flow around objects. Studying flow over a wedge helps in understanding how fluids behave near sharp edges. This investigation represents the effect of thermal radiation, viscous dissipation on MHD of a chemically reacting flow of the Casson nanofluid across the moving wedge by the convective boundary conditions with internal heat generation/absorption. Silicon Dioxide (SiO₂) nanofluids are considered. The basic governing partial differential equations are converting into nonlinear ordinary differential equations with employing suitable similarity transformations. The resultant coupled non-linear ordinary differential equations are effectively solved numerically by the aid of MATLAB software. The variations of the relevant parameters on the velocity, temperature and concentration are investigated through graphs. The numeral quantities of skin friction coefficients, Nussult number and Sherwood numbers exhibited for the several sets of values of the physical parameters using graphical profiles. To vindicate the current analysis, the computational outputs are comparing by the previous available works which is accessible in the literature and they determined to be in the good concurrence. The main findings are the nanoparticle concentration profile decrease by increasing the values of the chemical reaction, Brownian motion and Schmidt parameter, and increases with enhance in the thermophoresis parameter.

Simulations of the processes contributing to the deposition of trace gases and small particles from the air to natural surfaces routinely describe the consequences of changing molecular diffusivity in terms of the Schmidt number, Sc ≡ ν/D, where ν is kinematic viscosity and D the molecular diffusivity of the constituent in question. Using well-verified results of pipe flow experiments, early workers proposed that the relevant property entering dry deposition and other models of similar kind should be Sc−2/3 rather than Sc−1 as would be expected from historic flat plate experiments. Upon reconsideration, it is now proposed that no universal power-law dependence on Sc can be expected; the corresponding role of molecular diffusivity is likely to be site-specific. Relevant experimental evidence remains elusive. [ABSTRACT FROM AUTHOR]

In this paper, we present a new application of group theory to develop a systematical approach to efficiently compute the Schmidt numbers. The Schmidt number is a natural quantification of entanglement in quantum information theory, but computing its exact value is generally a challenging task even for very concrete examples. We exhibit a complete characterization of all orthogonally covariant k-positive maps. This result generalizes earlier results by Tomiyama (Linear Algebra Appl 69:169–177, 1985). Furthermore, we optimize duality relations between k-positivity and Schmidt numbers under group symmetries. This new approach enables us to transfer the results of k-positivity to the computation of the Schmidt numbers of all orthogonally invariant quantum states. [ABSTRACT FROM AUTHOR]

Let E denote the set of all unital entanglement breaking (UEB) linear maps defined on an operator system S ⊂ M d and, mapping into M n. As it turns out, the set E is not only convex in the classical sense but also in a quantum sense, namely it is C ⁎ -convex. The main objective of this article is to describe the C ⁎ -extreme points of this set E. By observing that every EB map defined on the operator system S dilates to a positive map with commutative range and also extends to an EB map on M d , we show that the C ⁎ -extreme points of the set E are precisely the UEB maps that are maximal in the sense of Arveson ([1] and [2]) and that they are also exactly the linear extreme points of the set E with commutative range. We also determine their explicit structure, thereby obtaining operator system generalizations of the analogous structure theorem and the Krein-Milman type theorem given in [8]. As a consequence, we show that C ⁎ -extreme (UEB) maps in E extend to C ⁎ -extreme UEB maps on the full algebra. Finally, we obtain an improved version of the main result in [8] , which contains various characterizations of C ⁎ -extreme UEB maps between the algebras M d and M n. [ABSTRACT FROM AUTHOR]

Micro-seismic monitoring technology has become a fundamental method for deep-ground pressure research and management. Based on the IMS micro-seismic monitoring system, the micro-fractures of rock mass caused by the mining process of Chifeng NFC Baiyinnuoer lead-zinc mine are monitored, it can accurately reflect the stability of the goafs and production operation stopes in the target areas. Data analysis shows that; 1) By analyzing the spatiotemporal distribution of micro-seismic events, using b-value method and the methods of relationships between energy index(EI) and cumulative apparent volume(CAV), as well as Schmidt number(Scs) and CAV, combined with on-site construction conditions, micro-seismic data can be more accurately analyze and the overall stability of underground mining sites can be evaluate effectively to draw reasonable conclusions; 2) On the premise of El decreases, the slip in slope of the CAV curve at the inflection points corresponds to an decrease in the probability of occurrence of micro-seismic events or the number of micro-seismic events compared to the last previous values, and vice versa; On the premise of Scs decreases, regardless of the rise or fall in the slope of the CAV curve at the inflection points, the probability of occurrence of micro-seismic events or the number of micro-seismic events compared to the last previous values both decrease; 3)The frequency of occurrence of aftershock events caused by large explosions in the underground mining area of this nonferrous metal mine has significantly decreased, a good stability of the production site could be demonstrated. The application of this system will play a positive role in earthquake prevention, disaster reduction, and safety production in the underground mining of Chifeng NFC Baiyinnuoer lead-zinc mine. [ABSTRACT FROM AUTHOR]

An approximate analytical solution is obtained for the system of equations describing the high-temperature dissociating boundary layer at the lateral surfaces of blunt nose cones in high-speed aircraft, so as to determine the heat fluxes and surface temperatures in aerodynamic heating. Significant use is made of the Reynolds analogy regarding the velocity, temperature, and concentration profiles of the atomic component in a binary gas. To determine the surface temperature of a high-speed aircraft, radiant and conductive heat transfer within the structure is taken into account. [ABSTRACT FROM AUTHOR]

Some target refrigerants used in refrigeration systems have various flammability. Once the flammable refrigerants leak into a confined space, it is easy to pose safety hazards. Moreover, the leakage refrigerants undergo continuous expansion and compression processes in the near field of the confined space, and the field strength of the refrigerants changes dramatically, which has an impact on the diffusion and the concentration distribution of the refrigerant in the far field of the confined space. The differences in the field strength and the flammable area for different refrigerants are largely determined by the thermophysical parameters of the refrigerants. Therefore, to better assess the hazards of refrigerant leakage, R717, R290, R161, R32, R152a and R1234yf were selected as the targeted leakage refrigerants in this paper, R744 and R134a were selected as the referenced refrigerants, the temperature, velocity and concentration fields of the refrigerants leaking into a confined space were studied, the influence of thermophysical parameters on the field strength of the refrigerants in the near field was further analyzed, and the flammable area formed in the space was explored. The results found that the temperature field was mainly affected by the density and the specific heat of the refrigerant. The velocity field was mainly affected by the density and viscosity of the refrigerant. The concentration field was mainly influenced by the density, viscosity and diffusion coefficient of the refrigerant. When the density was close, Schmidt number could be used to assess the influence of the viscosity and the diffusion coefficient on the concentration field. Under the same leakage pressure, the range of the flammable area formed by the leakage of R290 was the largest, followed by R161 and R152a, the flammable areas of R1234yf and R717 were very close, and the flammable area formed by R32 was the smallest. [ABSTRACT FROM AUTHOR]

Considering pure quantum states, entanglement concentration is the procedure where, from N copies of a partially entangled state, a single state with higher entanglement can be obtained. Obtaining a maximally entangled state is possible for N = 1 . However, the associated success probability can be extremely low when increasing the system's dimensionality. In this work, we study two methods to achieve a probabilistic entanglement concentration for bipartite quantum systems with a large dimensionality for N = 1 , regarding a reasonably good probability of success at the expense of having a non-maximal entanglement. Firstly, we define an efficiency function Q considering a tradeoff between the amount of entanglement (quantified by the I-Concurrence) of the final state after the concentration procedure and its success probability, which leads to solving a quadratic optimization problem. We found an analytical solution, ensuring that an optimal scheme for entanglement concentration can always be found in terms of Q. Finally, a second method was explored, which is based on fixing the success probability and searching for the maximum amount of entanglement attainable. Both ways resemble the Procrustean method applied to a subset of the most significant Schmidt coefficients but obtaining non-maximally entangled states. [ABSTRACT FROM AUTHOR]

As in the case of enhancing the performance of high-temperature superconductors, the dynamics of colloidal mixes of water and copper-based nanoparticles exposed to an inclined magnetic field owing to free convection is a recognized issue. However, nothing is known about the dynamics mentioned above when the radius and inter-particle spacing of copper nanoparticles grow in the presence of Joule dissipation, mass flux owing to a temperature gradient, internal heating, and heat flux due to concentration gradient. When the ratio of momentum to thermal diffusivities is incorporated into the momentum equation using appropriate models, the governing equation (i.e. Partial Differential Equations) that models the transport mentioned above was scaled, solved numerically, and simulated with a focus on the nanoparticle radius and the spacing between copper nanoparticles. The resultant non-linear coupled Ordinary Differential Equation was solved using the MATLAB integrated (i.e. bvp4c software package) and the shooting approach (i.e. fourth-order Runge–Kutta integration strategy shrk4). Just because of the resulting improvement in the temperature distribution, increasing the ratio of momentum to thermal diffusivities leads to a more pronounced local skin friction within the layers adjacent to the wall and heat transfer. Because buoyancy forces are exclusively associated with the growth of concentration difference, they cause the distance covered by the transport phenomenon in terms of the spatial domain to decrease. Higher ratios of momentum to thermal diffusivities cause the full-fledged sheer stress profile, which is proportional to friction across fluid layers, to rise. [ABSTRACT FROM AUTHOR]

In this article, by using a novel approach, the heat transfer related to the hybrid nanofluid flow containing graphene oxide and copper particles in pure water, which is located in a rotating system, is analyzed. The innovation of this article, using a new approach, explores the heat transfer related to the flow of mixed nanofluid containing graphene oxide and copper particles in pure water, which is in a rotating system, and using the RBF method for the first time Investigates differential equations and simplified coupled equations. The radial basis function methodology was utilized to solve the equations, and the outcomes were compared to those obtained using the Runge –Kutta –Fehlberg numerical method. In this problem, there are much necessary quantities such as the Reynolds number, Nusselt number, Schmidt number, Thermophoretic quantity, Brownian quantity, Injection quantity, and Rotation quantity so that communication between them is investigated. Based on the results, with the increase of Reynolds number, the amount of heat transfer decreases significantly, and with the decrease of heat flows from the surfaces, the flow rate of fluid and nanofluid decreases. However, the concentration of nanomaterials reaches a maximum value as the Reynolds number increases. [ABSTRACT FROM AUTHOR]

Building a computational formula which is expressed by a system of nonlinear partial differential equations in two components was done in this job. The matter of energy transfer by free convection of a dissipative liquid running in a horizontal channel with a porous medium was examined in this study, and we describe the behavior of fluid flow through the channel and the temperature distribution within it. Numerical methods were used as the ODE45 method, one of the Rang-Kutta methods for processing the resulting differential equations. The effect of the Prandtl number, the Schmidt multitude, and the Gratshof amount were also studied. [ABSTRACT FROM AUTHOR]

In Christandl et al. (Ann Henri Poincaré 20(7):2295–2322, 2019), the authors introduced k-entanglement breaking linear maps to understand the entanglement breaking property of completely positive maps on taking composition. In this article, we do a systematic study of k-entanglement breaking maps. We prove many equivalent conditions for a k-positive linear map to be k-entanglement breaking, thereby study the mapping cone structure of k-entanglement breaking maps. We discuss examples of k-entanglement breaking maps and some of their significance. As an application of our study, we characterize the completely positive maps that reduce Schmidt number on taking composition with another completely positive map. Finally, we extend a spectral majorization result for separable states. [ABSTRACT FROM AUTHOR]

The unsteady stagnation-point flow of a hybrid nanofluid over a stretching/shrinking sheet embedded in a porous medium with mass transpiration and chemical reactions is considered. The momentum and mass transfer problems are combined to form a system of partial differential equations, which is converted into a set of ordinary differential equations via similarity transformation. These ordinary differential equations are solved analytically to obtain the solution for velocity and concentration profiles in exponential and hypergeometric forms, respectively. The concentration profile is obtained for four different cases namely constant wall concentration, uniform mass flux, general power law wall concentration and general power law mass flux. The effect of different physical parameters such as Darcy number ðDa-1Þ, mass transpiration parameter VC ð Þ, stretching/shrinking parameter ðdÞ, chemical reaction parameter ð-Þ and Schmidt number ðScÞ on velocity and concentration profile is examined. Results show that, the axial velocity will decreases as the shrinking sheet parameter increases, regardless of whether the suction or injection case is examined. The concentration decreases with an increase in the shrinking sheet parameter and the chemical reaction rate parameter. [ABSTRACT FROM AUTHOR]

A steady, incompressible, and thermo-convective flow of micro-polar fluid over a stretching permeable sheet with heat and mass transfer under effects of radiation, Soret, Schmidt, and Dufour numbers have been analyzed. The modeled governing equations, of the classical Navier-Stokes, are coupled with micro rotation, temperature, and concentration equations, in the form of Partial Differential Equations, along with initial and boundary conditions, are transformed into a system of nonlinear coupled Ordinary Differential Equations by using an appropriate transformation. The numerical solution is obtained by using the Parametric Continuation Method. For the validity of the scheme, the results are compared with a numerical package bvp4c. It has been observed that both the results are in the best agreement with each other. The effects of associated parameters on the dimensionless velocity, micro-rotation, temperature, and concentration profiles are discussed and depicted graphically. It has been detected that the permeability parameter gives rise to the microrotation profile. [ABSTRACT FROM AUTHOR]

Cerebrospinal fluid (CSF) is a symmetric flow transport that surrounds brain and central nervous system (CNS). Hydrocephalus is an asymmetric and unusual cerebrospinal fluid flow in the lateral ventricular portions. This dumping impact enhances the elasticity over the ventricle wall. Henceforth, compression change influences the force of brain tissues. Mathematical models of transport in the hydrocephalus, which constitutes an excess of fluid in the cavities deep within the brain, enable a better perspective of how this condition contributes to disturbances of the CSF flow in the hollow places of the brain. Recent approaches to brain phase spaces reinforce the foremost role of symmetries and energy requirements in the assessment of nervous activity. Thermophysical and mass transfer effects are therefore addressed in this paper to quantify the transport phenomena in pulsatile hydrocephalus CSF transport with oscillating pressure variations that characterize general neurological activity and transitions from one functional state to another. A new mathematical model is developed which includes porous media drag for brain tissue and solutal diffusion (concentration) effects. A classical Laplace transform method is deployed to solve the dimensionless model derived with appropriate boundary conditions. The analysis reveals that with increasing permeability of the subarachnoid space, the CSF velocity is increased, and a significant fluid flux enhancement arises through the brain parenchyma as the pressure of the fluid escalates drastically due to hydrocephalus disorder. Stronger thermal buoyancy (Grashof number) also results in deceleration in the flow. CSF temperature is reduced with progression in time. Particle (e.g. ion) concentration is suppressed with increasing Schmidt number. As heat conduction parameter increases, there is a substantial depletion in CSF velocity with respect to time. Increasing Womersley parameter displaces the CSF velocity peaks and troughs. The present effects are beneficial in determining the thermo-fluidic transport mechanism of the pathological disorder hydrocephalus. Also, the present results are compared with those clinical studies for some cases. We have confirmed that our validity provides a decent justification with the neurological studies. [ABSTRACT FROM AUTHOR]

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The consequences of viscous, ohmic, thermal radiation, and chemical reaction on an incompressible, steady, magnetized nanofluid moving through a stretched surface are investigated for choosing two distinct Nanoliquids (Cuo/water and Silver/water). Through the similarity transformations, the controlling dimensional equations of momentum, energy, and concentration were simplified to non-dimensional forms. The solution to the resulting problem is obtained by Bvp4c. The velocity, temperature and concentration are significantly shown for various emerging factors. On both kinds of nanofluids, thermal is grown consistently with an increasing Eckart number. It does, however, lessen as the radiation term values increase. Moreover, if the Schmidt number ranges on the concentration fluid flow indicate that the H(η) profile is going to fall. The tendency for H(η) to boost as the Soret number raises is becoming increasingly noticeable. Ag/water has a higher heat flow rate than Cuo/water when the amounts of Eckart and Radiation numbers are changed. Tables and plots displayed an engineering physical parameter such as coefficient of skin friction, rate of heat transmission and mass transfer. [ABSTRACT FROM AUTHOR]

Considering pure quantum states, entanglement concentration is the procedure where, from N copies of a partially entangled state, a single state with higher entanglement can be obtained. Obtaining a maximally entangled state is possible for N=1. However, the associated success probability can be extremely low when increasing the system’s dimensionality. In this work, we study two methods to achieve a probabilistic entanglement concentration for bipartite quantum systems with a large dimensionality for N=1, regarding a reasonably good probability of success at the expense of having a non-maximal entanglement. Firstly, we define an efficiency function Q considering a tradeoff between the amount of entanglement (quantified by the I-Concurrence) of the final state after the concentration procedure and its success probability, which leads to solving a quadratic optimization problem. We found an analytical solution, ensuring that an optimal scheme for entanglement concentration can always be found in terms of Q. Finally, a second method was explored, which is based on fixing the success probability and searching for the maximum amount of entanglement attainable. Both ways resemble the Procrustean method applied to a subset of the most significant Schmidt coefficients but obtaining non-maximally entangled states.

Double-Tee junctions serve as building blocks of pipe network systems and fluid mixing occurring in them is complex due to excessive eddying of flow. In this paper a LES model with pure advection was used on a double-Tee junction turbulent mixing phenomena problem. This kind of approach does not require the turbulent Schmidt number which is problem specific and needs to be calibrated with experimental data. When applying the LES-WALE turbulence model in conjunction with the pure advection transport of a scalar quantity on the double-Tee mixing problem it is achieved that the resolved turbulent flow field accurately transports the scalar when compared to experimental data from literature. This approach enables accurate mixing predictions in double-Tee junctions for the purpose of correcting simpler 1D numerical mixing models without the need of obtaining new experimental data since no turbulent Schmidt number calibration is needed. The approach can be applied to biological or chemical agent transport in a fluid and the model was tested and shown to be valid for a Reynolds number range of 20,000–400,000 on three different types of double-Tee junction configurations and five double-Tee distances with a constant inlet and outlet pipe diameter.

We systematically study the constructions of unextendible entangled bases with a fixed Schmidt number k (UEBk) in a bipartite system Cd⊗Cd′. Motivated by the methods of [J. Phys. A 52 : 375,303, 2019], we construct (dd’ − v)-member UEBks in Cd⊗Cd′ by using generalized weighing matrices and thus generalize the results of [arXiv: 1909.10043, 2020]. We also present the corresponding expressions of our constructions and graphically illustrate UEB3s in C5⊗C6 and C6⊗C6.

Unextendible product basis (UPB), a set of incomplete orthonormal product states whose complementary space has no product state, is very useful for constructing bound entangled states. Naturally, instead of considering the set of product states, Bravyi and Smolin considered the set of maximally entangled states. They introduced the concept of unextendible maximally entangled basis (UMEB), a set of incomplete orthonormal maximally entangled states whose complementary space contains no maximally entangled state [Phys. Rev. A 84, 042,306 (2011)]. An entangled state whose nonzero Schmidt coefficients are all equal to 1/k is called a special entangled state of “type k”. In this paper, we introduce a concept named special unextendible entangled basis of “type k” which generalizes both UPB and UMEB. A special unextendible entangled basis of “type k” (SUEBk) is a set of incomplete orthonormal special entangled states of “type k” whose complementary space has no special entangled state of “type k”. We present an efficient method to construct sets of SUEBk. The main strategy here is to decompose the whole space into two subspaces such that the rank of each element in one subspace can be easily upper bounded by k while the other one can be generated by two kinds of the special entangled states of “type k”. This method is very effective when k = pm ≥ 3 where p is a prime number. For these cases, we can obtain sets of SUEBk with continuous integer cardinality when the local dimensions are large.

In the present study, the lattice Boltzmann method (LBM) is employed to study the diffusion phenomenon in solid oxide fuel cell (SOFC) with direct internal reforming (DIR). The main focus of this work is to correlate and estimate the diffusion coefficient through dimensionless numbers, i.e., Schmidt and Prandtl. This work tries to reveal the importance of reforming and electrochemical reactions on these dimensionless numbers in active and inactive zones. In addition, the effects of inlet velocity (Re number), steam-to-carbon ratio (S/C) of inlet flow, current density, and porosity were investigated to disclose their importance on diffusion phenomena. A lattice Boltzmann method is used for numerical simulation of diffusion phenomenon in porous media of anode. Our results show that the Schmidt and the Prandtl numbers could be used for high precision estimation of the diffusion process in SOFC. It is also found that the molar ratio variation in hydrogen and water is highly effective since their diffusion characteristics are significantly different from other gases. By changing in operating parameters, the variation in the Prandtl number is much greater than the reforming reactions due to electrochemical reactions. Our results indicate that the Schmidt number of hydrogen increases by 53%, and the Prandtl number decreases about 45% at the center of SOFC when the porosity decreases about 25%. [ABSTRACT FROM AUTHOR]

The impact of a variety of physical variables on Casson flow fluid through a vertical plate is investigated and, in this research, heat source/sink, radiation, diffusion thermo and chemical reaction has been included. Perturbation procedure is accustomed to solve non-dimensional multivariable governing equations. Graphical representations are habituated to explain the behaviour of concentration, temperature, and velocity for many characteristics and physical constants such as the Casson parameter (γ), Magnetic parameter (M), Grashof number (Gr), Prandtl number (Pr), modified Grashof number (Gm), Radiation parameter (R), heat sink parameter (Q), Dufour parameter (Du), influence of concentration, temperature, and velocity. The most important finding of the study is that when Dufour values rises, velocity and temperature rises as well. Tables are also used to compute the skin friction, Nusselt and Sherwood numbers. [ABSTRACT FROM AUTHOR]

Can vectors with low Schmidt rank form mutually unbiased bases? Can vectors with high Schmidt rank form positive under partial transpose states? In this work, we address these questions by presenting several new results related to Schmidt rank constraints and their compatibility with other properties. We provide an upper bound on the number of mutually unbiased bases of C m ⊗ C n (m ≤ n) formed by vectors with low Schmidt rank. In particular, the number of mutually unbiased product bases of C m ⊗ C n cannot exceed m + 1 , which solves a conjecture proposed by McNulty et al. Then, we show how to create a positive under partial transpose entangled state from any state supported on the antisymmetric space and how their Schmidt numbers are exactly related. Finally, we show that the Schmidt number of operator Schmidt rank 3 states of M m ⊗ M n (m ≤ n) that are invariant under left partial transpose cannot exceed m - 2 . [ABSTRACT FROM AUTHOR]

The tracer gas method is one of the common ways to evaluate the air exchange rate in a naturally ventilated barn. One crucial condition for the accuracy of the method is that both considered gases (pollutant and tracer) are perfectly mixed at the points where the measurements are done. In the present study, by means of computational fluids dynamics (CFD), the mixing ratio NH 3 /CO 2 is evaluated inside a barn in order to assess under which flow conditions the common height recommendation guidelines for sampling points (sampling line and sampling net) of the tracer gas method are most valuable. Our CFD model considered a barn with a rectangular layout and four animal-occupied zones modeled as a porous medium representing pressure drop and heat entry from lying and standing cows. We studied three inflow angles and six combinations of air inlet wind speed and temperatures gradients covering the three types of convection, i.e., natural, mixed, and forced. Our results showed that few cases corresponded to a nearly perfect gas mixing ratio at the currently common recommendation of at least a 3 m measurement height, while the best height in fact lied between 1.5 m and 2.5 m for most cases. [ABSTRACT FROM AUTHOR]

A direct numerical simulation (DNS) of a planar jet with a second-order chemical reaction is performed using four different Schmidt number (Sc = 1, 2, 4, 8). Reactant A is contained in the jet flow and reactant B is contained in the ambient flow. The chemical reaction ( A + B → P ) proceeds by molecular mixing of the two reactants in the jet. The results show that the higher Sc becomes, the finer the structure of the product concentration becomes. The region where the reaction occurs changes depending on the Sc. Mean concentration and mean production rate conditioned on the distance from the T/NT (Turbulent/Non-Turbulent) interface is calculeted. The change in the conditional mean concentration of the reactive species near the T/NT interface occurs within the order of Taylor’s microscale regardless of the difference in Sc. In the chemical reaction field, the slope of the concentration change at T/NT does not differ much depending on the Sc. When the Sc is high, the mean production rate decreases. This is because the molecular diffusion is weak and small-scale concentration fluctuation occurs at high Sc. It also found that the thickness of the reaction layer becomes thinner as the Sc increases and the thickness of the reaction layer is scaled on the Bachelor scale ηB.

Scalar mixing is under the joint control of convection and diffusion. The ratio of the dissipative scale of velocity field to that of the scalar field depends on the Schmidt number. In the high Schmidt number limit, the scalar scale is much smaller than that of the momentum, which then requires either special treatment or ad hoc models for the scalar quantity in numerical simulations. In order to avoid model uncertainty or unnecessary numerical complexity, the direct numerical simulation is performed for studying the scalar mixing process in a confined rotating mixer tank. It has been found that in the range of negligible numerical diffusivity, the characteristic scalar mixing time is inversely proportional to the scalar diffusivity. Analysis based on the dimensional argument justifies such scaling relation as well, from which the unaccepted computational time of the mixing process in the high Schmidt number limit can be efficiently determined, without the use of ad hoc models. This scaling idea is also of practical meaningfulness for other similar problems. [ABSTRACT FROM AUTHOR]

Double-Tee junctions serve as building blocks of pipe network systems and fluid mixing occurring in them is complex due to excessive eddying of flow. In this paper a LES model with pure advection was used on a double-Tee junction turbulent mixing phenomena problem. This kind of approach does not require the turbulent Schmidt number which is problem specific and needs to be calibrated with experimental data. When applying the LES-WALE turbulence model in conjunction with the pure advection transport of a scalar quantity on the double-Tee mixing problem it is achieved that the resolved turbulent flow field accurately transports the scalar when compared to experimental data from literature. This approach enables accurate mixing predictions in double-Tee junctions for the purpose of correcting simpler 1D numerical mixing models without the need of obtaining new experimental data since no turbulent Schmidt number calibration is needed. The approach can be applied to biological or chemical agent transport in a fluid and the model was tested and shown to be valid for a Reynolds number range of 20,000–400,000 on three different types of double-Tee junction configurations and five double-Tee distances with a constant inlet and outlet pipe diameter. [ABSTRACT FROM AUTHOR]

The cleaning or regeneration of fouled membrane modules is an essential procedure in the membrane equipment operation. Despite the development of some successful cleaning techniques, the predictions of the membrane separation process operation parameters after regeneration is still an unsolved problem. In our previous works, the attempt to develop the methodology of estimating the membrane productivity after the regeneration of the fouled spiral wound membrane modules by cleaning the subatmospheric pressure has been made. However, this methodology requires some improvement, including the correction of the dimensionless equation to calculate the mass transfer coefficient. In this work, a set of additional experiments was carried out, and the corrections of the mass transfer correlation were done using both new and previously obtained experimental data. As a result, the improved dimensionless equation was contained as Sh = 0.00045Re0.8Sc0.33(de/l). This equation is valid in the range of Reynolds number variation of 0.4–60.0 for the case of the regeneration of spiral wound modules and can be used for the prediction of the permeate flux after the regeneration procedure.

Finding and quantifying unknown (fugitive) releases of gases such as methane from downstream concentration data is a critical environmental problem. Many proposed solutions involve wind and gas dispersion modelling for which an assumed value of the turbulent Schmidt number (Sct), the ratio of the eddy kinematic viscosity to the turbulent diffusivity, is used to scale the estimated diffusivity. This model constant has a range of physically reasonable values. Numerical simulations were performed on multiple test cases to quantify the impact of Sct uncertainty on the ability to locate and quantify fugitive emissions sources using data from a network of gas concentration sensors. The analysis further considers ways to reduce quantification uncertainty, by either specifying detected source locations based on ancillary knowledge, or by using a two-step optimization in which the presented adjoint approach is used to locate sources and simulated annealing is subsequently used to quantify emissions for these specified locations. Multiple test cases considered both real and numerically generated controlled releases using an open-field geometry and a complex bluff-body dominated geometry based on an actual gas plant in the Alberta, Canada oil and gas sector. Results suggest that correct prediction of unknown source locations is minimally affected by Sct, but emission rate quantification can be heavily influenced. The presence of bluff-bodies was found to partially mitigate these effects, such that, if repeated analyses over a range of Sct is not tractable, open field release results (including those presented here) can be used to estimate conservative error bounds on predicted emission rates. Ultimately this paper demonstrates the under-appreciated importance of considering Sct uncertainty when seeking to quantify unknown fugitive sources from downstream concentration data.

We investigate the entanglement of the ground state in the quantum cyclic graphs whose nodes are considered as quantum harmonic oscillators. To this end, the Schmidt numbers and entanglement entropy between two arbitrary partitions with equal nodes of a cyclic graphs, are calculated. For that, the local operation is used to build singular value decomposition of potential matrix of cyclic graphs. Then the maximum value of entanglement entropy among all bipartite cyclic graphs is obtained. [ABSTRACT FROM AUTHOR]

We introduce the notion of one-sided mapping cones of positive linear maps between matrix algebras. These are convex cones of maps that are invariant under compositions by completely positive maps from either the left or right side. The duals of such convex cones can be characterized in terms of ampliation maps, which can also be used to characterize many notions from quantum information theory—such as separability, entanglement-breaking maps, Schmidt numbers, as well as decomposable maps and k -positive maps in functional analysis. In fact, such characterizations hold if and only if the involved cone is a one-sided mapping cone. Through this analysis, we obtain mapping properties for compositions of cones from which we also obtain several equivalent statements of the PPT (positive partial transpose) square conjecture. [ABSTRACT FROM AUTHOR]

Currently, researchers across the world achieved theoretical and experimental works to investigate the significance of nanofluid due to their diverse application in heat transport phenomena. Nanofluids are actually the suspension of nanoparticles in the base liquid. Embedding nanoparticles in the base fluid enhances thermal conductivity and heat transfer rate. The present article shed light on the influence of gold nanoparticles along with oxytactic microorganisms on radiative Reiner–philippoff fluid due to extendable sheet. Suitable transformation convert the partial differential equations (PDEs) are renovated into nonlinear ordinary differential equations (ODEs) and furthermore tackled these equations numerically via bvp4c Matlab builtin scheme. Further the investigations are carried out in the presence of molecular diffusivity, oxytactic microorganisms and nonlinear thermal radiation. The effect of influential parameters on heat transfer, mass transfer, motile density of microorganisms profile are investigated with the assistance of tables and graphs. Embedding the nanoparticles and nonlinear thermal radiation amplifies the heat transfer process and motile density profile depreciates owing to an augmentation in Peclet number. The novel outcomes of this investigation will advance the field of nanomaterials. [ABSTRACT FROM AUTHOR]

We determine sufficient conditions for certain classes of (n + k) × n matrices E to have all order- n minors to be nonzero. For a special class of (n + 1) × n matrices E , we give the formula for the order- n minors. As an application we construct subspaces of C m ⊗ C n of maximal dimension, which do not contain any vector of Schmidt rank less than k and each of which has a basis of Schmidt rank k for k = 2 , 3 , 4. [ABSTRACT FROM AUTHOR]

The concept of an edge flame structure has been adopted to explain the laminar lifted flames in a non-premixed jet. Two similarity solutions of velocity and fuel concentration have been used to explain flame stability. Recently, it was shown that the experimental results from studies of jet velocities and lift-off heights could be converted to a relationship between the edge flame speed and the fuel concentration gradient. However, this was not sufficient to explain actual structures and behaviors of lifted flames. In this study, related theories and their similarity solutions were improved to get more realistic results through an efficient process. Experiments were conducted with various parameters such as jet velocity, fuel type, tube diameter, air-premixing ratio, and fuel dilution. Effective mass diffusivities and effective Schmidt numbers were estimated based on the experimental results. Using these values, the theoretical basis for a new relationship between the edge flame speed and the fuel concentration gradient was obtained. It was conclusively found that non-monotonic variation in the edge flame speed occurs. From this, flame structures were classified into three regimes based on flame structures and heights: ordinary edge flame in a lower-regime, merged edge flame in a middle-regime, and premixed flame in a higher-regime. Flame speeds of the ordinary edge flames in the lower-regime were selected for comparison with the results of previous studies. From this work, the relationship between the similarity solutions and the experimental results can now be understood in greater detail, and the deviations due to the flame structure can be distinguished. [ABSTRACT FROM AUTHOR]

In this short note, we show two completely opposite methods of constructing bipartite entangled states. Given a bipartite state γ ∈ M k ⊗ M k , define γ S = (I d + F) γ (I d + F) , γ A = (I d - F) γ (I d - F) , where F ∈ M k ⊗ M k is the flip operator. In the first method, entanglement is a consequence of the inequality rank (γ S) < rank (γ A) . In the second method, there is no correlation between γ S and γ A . These two methods show how diverse is quantum entanglement. We show that any bipartite state γ ∈ M k ⊗ M k satisfies SN (γ) ≥ max rank (γ L) rank (γ) , rank (γ R) rank (γ) , SN (γ S) 2 , SN (γ A) 2 , where SN (γ) stands for the Schmidt number of γ and γ L and γ R are the marginal states of γ . These inequalities are useful to compute the Schmidt number of many bipartite states. We prove that SN (γ) = min { rank (γ L) , rank (γ R) } , if rank (γ) = max { rank (γ L) , rank (γ R) } min { rank (γ L) , rank (γ R) } . We also present a family of PPT states in M k ⊗ M k , whose members have Schmidt number equal to n, for any given 1 ≤ n ≤ k 2 . This is a new contribution to the open problem of finding the best possible Schmidt number for PPT states. [ABSTRACT FROM AUTHOR]

Stabilization characteristics of laminar lifted jet flames in a coflow were investigated experimentally to elucidate the effect of Schmidt number in methane and ethylene fuels diluted with N 2 , He, and Ar. A non-monotonic (decreasing and then increasing) liftoff height (H L) behavior with jet velocity (U 0) was observed previously for methane fuel diluted with N 2. To further elucidate the fuel Schmidt number (Sc F) effect in exhibiting such a non-monotonic (U-shaped) behavior, various diluents (N 2 , He, and Ar) were added to the fuel streams and methane and/or ethylene fuels were used. The result showed three flame types in terms of Sc F and fuel density; nozzle-attached flame, stationary lifted flame, and oscillating flame. Among stationary lifted flames, two distinct H L behaviors with U 0 were observed; monotonic and non-monotonic H L behaviors. A critical Schmidt number (Sc F,cr1) existed over which monotonically increasing behavior was observed. A second critical Schmidt number (Sc F,cr2) also existed such that U-shaped behavior was observed for Sc F,cr2

In this paper, an entanglement measure for multipartite quantum states with respect to k-partition was introduced, which is called Schmidt number entanglement measure for multipartite k-nonseparable states, it is simply denoted by k-ME SN. We show that this measure is well-defined, i.e., it satisfies some basic properties as an entanglement measure. In addition, we give a super bound and lower bound of k-ME SN for multipartite pure states according to the definition of joint k-Schmidt number with respect to k-partition. Furthermore, we give some examples to show that Schmidt number entanglement measure can quantify the strength of entanglement for multipartite quantum states. [ABSTRACT FROM AUTHOR]

In the present study, the combination of the Concentration Lattice Boltzmann Method and the Smoothed Profile Method (CLBM–SPM) was used to simulate the dissolution of circular particles between parallel plates moving in opposite directions. The hydrodynamics and fluid concentration simulation were performed based on the single relaxation time Lattice Boltzmann Method. LBM convection–diffusion equation was then used to solve the concentration of the solute in the fluid phase. Additionally, SPM was employed to apply the no-slip boundary condition at the solid–fluid interface and to calculate the concentration forces. Initially, the results of the numerical solution were compared with the ones presented in the literature. Then the effects of the initial solid volume fraction, the Schmidt number, the Reynolds number, and particle size were studied to examine the behavior of particles dissolution. The results showed that the smallest dissolution time in the systems with different volume fractions was in a one with the least solid volume fraction. As the volume fraction was increased, the solid–fluid mass transfer driving force was decreased in the system. Also, with the rise of the Schmidt number, the dissolution time was increased, due to the decrease of the diffusion coefficient of the fluid flow. Moreover, by increasing the Reynolds number, the time required for the volume fraction ratio to reach 0.05 of its initial value was reduced. Finally, the particle size in this system was studied. The results indicated that with the decrease in particle size (or increase in the surface area), we could significantly alter the dissolution time. [ABSTRACT FROM AUTHOR]

Polymer electrolyte membrane fuel cells were analyzed to investigate changes in the structure of the flow field and operating conditions. The cell performance, which was controlled by adjusting the width of the cathodic channel, improved as the backpressure increases. With the anodic and cathodic flow channels mismatched, the maximum power densities at 3.0 bar for a narrow cathodic channel were 1115 and 1024 mW/cm2, and those for a wide cathodic channel were 959 and 868 mW/cm2, respectively. The diffusion characteristics were investigated using the non-dimensional numbers Re (Reynolds), Sc (Schmidt), and Sh (Sherwood) to confirm the improvement of mass transport. The narrower the channel or the higher the operating pressure, the larger Re was and the smaller Sc and Sh became. In particular, the wider the anodic channel, the larger the value of Sh.

The experimental determination of concentration polarization layer resistance during reverse osmosis of mineral salts solutions was carried out with the aim to estimate the influence of solution composition on the value of mentioned resistance. In experimental conditions, the membrane resistance remains constant (the mean value was 0.534·1014 m-1) which means that the membrane compaction was not observed. Moreover, under experimental conditions, the hypothesis about linear dependence between the concentration polarization layer and applied pressure was confirmed for all solutions under investigations. It was defined that value of concentration polarization layer resistance different salt solutions was varied less than 10 % although under experimental conditions the diffusion coefficient values of magnesium sulfate were more than three times higher than corresponded values for other salts. The increasing of solutions concertation determines the increasing of concentration polarization layer resistance. At the same time, in previous study it was defined that changes in hydrodynamic regime in membrane module under similar conditions could determine the change in concentration polarization layer resistance in 3–5 times, while in both studies the trends of impact of hydrodynamic conditions still similar to the value of considered resistance decrease with Reynolds number increasing. Such results showed that in considered range of concentrations the hydrodynamic conditions have a lower influence on concentration polarization layer resistance than solution composition. The obtained results are in agreement with the film theory of concentration polarization.

The tracer gas method is one of the common ways to evaluate the air exchange rate in a naturally ventilated barn. One crucial condition for the accuracy of the method is that both considered gases (pollutant and tracer) are perfectly mixed at the points where the measurements are done. In the present study, by means of computational fluids dynamics (CFD), the mixing ratio NH3/CO2 is evaluated inside a barn in order to assess under which flow conditions the common height recommendation guidelines for sampling points (sampling line and sampling net) of the tracer gas method are most valuable. Our CFD model considered a barn with a rectangular layout and four animal-occupied zones modeled as a porous medium representing pressure drop and heat entry from lying and standing cows. We studied three inflow angles and six combinations of air inlet wind speed and temperatures gradients covering the three types of convection, i.e., natural, mixed, and forced. Our results showed that few cases corresponded to a nearly perfect gas mixing ratio at the currently common recommendation of at least a 3 m measurement height, while the best height in fact lied between 1.5 m and 2.5 m for most cases.