Dual Solutions Research Articles

Targeted alpha therapy with the 224Ra/212Pb-TCMC-TP-3 dual alpha solution in a multicellular tumor spheroid model of osteosarcoma.

Osteosarcoma patients with overt metastases at primary diagnosis have a 5-year survival rate of less than 20%. TP-3 is a murine IgG2b monoclonal antibody with high affinity for an epitope residing on the p80 osteosarcoma cell surface membrane antigen. The tumor-associated antigen p80 is overexpressed in osteosarcomas, and has very low normal tissue expression. We propose a novel dual alpha targeting solution containing two radionuclides from the same decay chain, including the bone-seeking 224Ra, and cancer cell-surface seeking 212Pb-TCMC-TP-3 for the treatment of osteoblastic bone cancers, circulating cancer cells and micrometastases. In this in vitro study, the cytotoxic effects of 212Pb-TCMC-TP-3 (single alpha solution) and 224Ra/212Pb-TCMC-TP-3 (dual alpha solution) were investigated in a multicellular spheroid model mimicking micrometastatic disease in osteosarcoma. OHS spheroids with diameters of 253 ± 98 μm treated with 4.5, 2.7, and 3.3 kBq/ml of 212Pb-TCMC-TP-3 for 1, 4, and 24 h, respectively, were disintegrated within 3 weeks. The 212Pb-TCMC-TP-3 induced a 7-fold delay in spheroid doubling time compared to a 28-times higher dose with the non-specific 212Pb-TCMC-rituximab. The 224Ra/212Pb-TCMC-TP-3 completely disintegrated spheroids with diameters of 218-476 μm within 3 and 2 weeks after 4 and 24 h incubation with 5 kBq/ml, respectively. Treatment with 1 kBq/ml of 224Ra/212Pb-TCMC-TP-3 for 24 h caused an 11.4-fold reduction in spheroid viability compared with unconjugated 224Ra/212Pb. The single and dual alpha solutions with TP-3 showed cytotoxicity in spheroids of clinically relevant size, which warrant further testing of the dual alpha solution using in vivo osteosarcoma models.

MHD Mixed Convection of Hybrid Ferrofluid Flow over an Exponentially Stretching/Shrinking Surface with Heat Source/Sink and Velocity Slip

This paper investigates the mixed convection flow related to Fe3O4-CoFe2O4/water hybrid ferrofluids on stagnation point over an exponentially stretching/shrinking surface with the influence of magnetohydrodynamic (MHD), velocity slip, and heat source/sink. The proposed system of differential equations is reduced using the similarity transformation procedure that is numerically solvable using MATLAB. Dual solutions are obtained for various governing parameters, in which the first solution is found to be in a stable state via the stability analysis. The CoFe2O4 nanoparticles volume fraction increases the heat transfer rate and the skin friction coefficient while delaying the separation of the boundary layer at the bifurcation point. Adding CoFe2O4 nanoparticles in hybrid ferrofluids gives a better heat transfer rate than that obtained with ferrofluids. The presence of a magnetic field enhances the fluid flow velocity. The increased strengths of the heat sink and stretching parameters give better results on the heat transfer, while the results are reversed for the heat source and shrinking parameters. The presence of velocity slip does influence the skin friction and the fluid flow.

Mixed convection flow of a hybrid nanofluid towards a permeable wedge

Flow and heat transfer involving hybrid nanofluids has been applied in a variety of technological and engineering applications. Thus, this work deeply features the mixed convection flow behavior and thermal characteristics of water based Cu-Al2O3 hybrid nanofluid towards a vertical and permeable wedge. The governing model is developed based on the physical and theoretical assumptions which are then, simplified into a set of ordinary differential equations (ODEs). The dual steady flow solutions are obtained using the bvp4c solver in the Matlab software. The opposing flow admits dual (first and second) solutions, while the assisting flow and pure force convection only produce a unique solution. The validity of the first solution is justified by the stability analysis. Besides, the wedge and suction parameters are the main factors that influence the flow and thermal progress of the hybrid nanofluid. Meanwhile, the Cu-Al2O3/water has a greater skin friction coefficient and heat transfer rate as compared to the Cu-water and Al2O3/water nanofluids which shows the significant role of hybrid nanofluid in the flow progress and thermal growth under the vertical wedge geometry case.

Radiative Hybrid Ferrofluid Flow Over a Permeable Shrinking Sheet in a Three-Dimensional System

Due to the significance of magnetic nanofluids in environmental and biomedical sectors, this study is designed to analyze the available solutions alongside with the flow and thermal behaviours of radiative hybrid ferrofluid flow in a three-dimensional system subjected to the shrinking surface. The case of Fe3O4-CoFe2O4/water is considered in this work. The initial procedure is conducted by reducing the complex model into a system of nonlinear differential equations using similarity transformation technique. The results are generated using the bvp4c package in the Matlab software and graphically presented. The existence of dual solutions leads to the treatment of stability analysis where the first solution is affirmed as the physical solution. Meanwhile, the impact of thermal radiation, magnetic field and suction are also observed for the distributions of thermal rate and skin friction coefficients. These distributions boost with the imposition of magnetic field and suction while a deterioration in thermal rate is observed with the rise of thermal radiation.

Higher form symmetries TFT in 6d

Symmetries and anomalies of a d-dimensional quantum field theory are often encoded in a (d + 1)-dimensional topological action, called symmetry topological field theory (TFT). We derive the symmetry TFT for the 2-form and 1-form symmetries of 6d (1, 0) field theories, focusing on theories with a single tensor multiplet (rank 1). We implement this by coupling the low-energy tensor branch action to the background fields for the higher-form symmetries and by looking at the symmetry transformation rules on dynamical and background fields. These transformation rules also imply a mixing of the higher-form symmetries in a 3-group structure. For some specific and related higher rank cases, we also derive the symmetry TFT from the holographic dual IIA supergravity solutions. The symmetry TFT action contains a coupling between the 2-form symmetry and the 1-form symmetry backgrounds, which leads to a mixed anomaly between the 1-form symmetries of the 5d KK-theory obtained by circle compactification. We confirm this by a pure 5d analysis provided by the 5d effective low-energy Coulomb branch Lagrangian coupled to background fields. We also derive the symmetry TFT for 5d SU(p) supersymmetric gauge theories with Chern-Simons level q and for 5d theories without non-abelian gauge theory description at low-energy. Finally, we discuss the fate of the 2-form and 1-form symmetry of rank 1 6d field theories when coupled to gravity.

MHD Casson fluid flow with Navier's and second order slip due to a perforated stretching or shrinking sheet.

The present work discusses the laminar boundary layer flow of an electrically conducting Casson fluid due to a horizontal perforated sheet undergoing linear shrinking/stretching with mass transpiration. Navier's slip and second-order slip conditions are also imposed on the flow. The system is subjected to a transverse magnetic field. The non-Newtonian flow under consideration obeys the rheological equation of state due to the Casson model. The PDEs governing the bounder layer flow is reduced to a nonlinear boundary value problem in ODEs by utilizing appropriate similarity transformations and are expressed analytically. The similarity solution is found to be a function of the Casson parameter, magnetic parameter, mass suction/injection parameter, and the first/second-order slip parameters. Such a solution is either unique, or dual solutions exist in a region defined by the mass transfer induced slip parameter. The results of the present work are found to be an increase of the magnetic effects resulting in expansion of the unique solution region and contraction of the dual solution region for the flow due to the induced Lorentz force. In the unique solution region, an increase in magnitudes of mass suction induced slip and the first/second-order slip parameters result in a reduction of the wall shear stress in the shrinking sheet, while the wall shear stress with mass suction increases with the Casson and the magnetic effects. Similar results exist for the stretching sheet case with mass suction. However, only unique similarity solutions exist only for the case of stretching sheets with mass injection. The current work is a generalization of the classical works of Crane (1970) and Pavlov (1974) for a stretching sheet. Mass suction/injection induced slip enhances and achieves a dominant flow driven by reversing the flow direction of the moving sheet, which allows an adjacent flow against the sheet. The findings have possible industrial applications in fluid-based systems including stretchable/shrinkable things, automated cooling systems, power generation, microelectronics, and present new results to the problem.

Verification of Dual Solutions for Water and Kerosene-Based Carbon Nanotubes over a Moving Slender Needle

This article focuses on the boundary layer for an axisymmetric flow and heat transfer of a nanofluid past a moving slender needle with single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs). In this study, the streamlines of the flow are symmetrically located along the needle’s surface. Water and kerosene are two types of base fluids that are considered in this study. This analysis is presented with needle thickness, the ratio of velocity, nanoparticle volume fraction, and Prandtl number. The partial differential equations (PDEs) are transformed into dimensionless ordinary differential equations (ODEs) by adopting relevant similarity transformations. The bvp4c package is implemented in MATLAB R2018a to solve the governing dimensionless problems numerically. The behaviors of various sundry variables on the flow and heat transfer are observed and elaborated further. The magnitude of the skin friction, heat transfer rate, as well as velocity and temperature distributions are demonstrated in graphical form and discussed. It is worth mentioning that kerosene-based CNTs have the largest skin friction coefficient and heat transfer rate compared to water-based CNTs. The thin wall of the needle and the single-walled carbon nanotubes also contributes to high drag force and heat transfer rate on the surface. It is revealed from the stability analysis that the first solution exhibits a stable flow. Obtained results are also matched with the present data in the restricting situation, and excellent agreement is noticed.

Error estimates for total-variation regularized minimization problems with singular dual solutions

Recent quasi-optimal error estimates for the finite element approximation of total-variation regularized minimization problems using the Crouzeix–Raviart element require the existence of a Lipschitz continuous dual solution, which is not generally given. We provide analytic proofs showing that the Lipschitz continuity of a dual solution is not necessary, in general. Using the Lipschitz truncation technique, we, in addition, derive error estimates that depend directly on the Sobolev regularity of a given dual solution.

On the Convergence of Overlapping Schwarz Decomposition for Nonlinear Optimal Control

We study the convergence properties of an overlapping Schwarz decomposition algorithm for solving nonlinear optimal control problems (OCPs). The algorithm decomposes the time domain into a set of overlapping subdomains, and solves all subproblems defined over subdomains in parallel. The convergence is attained by updating primal-dual information at the boundaries of overlapping subdomains. We show that the algorithm exhibits local linear convergence, and that the convergence rate improves exponentially with the overlap size. We also establish global convergence results for a general quadratic programming, which enables the application of the Schwarz scheme inside second-order optimization algorithms (e.g., sequential quadratic programming). The theoretical foundation of our convergence analysis is a sensitivity result of nonlinear OCPs, which we call “exponential decay of sensitivity” (EDS). Intuitively, EDS states that the impact of perturbations at domain boundaries (i.e., initial and terminal time) on the solution decays exponentially as one moves into the domain. Here, we expand a previous analysis available in the literature by showing that EDS holds for both primal and dual solutions of nonlinear OCPs, under uniform second-order sufficient condition, controllability condition, and boundedness condition. We conduct experiments with a quadrotor motion planning problem and a partial differential equations (PDE) control problem to validate our theory, and show that the approach is significantly more efficient than alternating direction method of multipliers and as efficient as the centralized interior-point solver.

Numerical simulation on Cu–H2O nanofluid of destructive and generative reactions in a Darcian medium: application of wall suction and blowing

Application of – nanoparticles in a base fluid of water means the growth of thermal conductivity of Nanofluid. This physical behavior recommends the prospect of applying nanofluids in electronic cooling and advanced nuclear systems. The formulated leading equations are transformed to non-dimensional form by appropriate similarity transformations and finally solved numerically through Runge–Kutta Shooting method of 4th order. The novelty of the current investigation is to examine the impact of wall suction/ injection over the dual solutions by numerical simulation for time-independent, two- dimensional nanofluid flow along a semi-infinite porous stretching horizontal wall placed in a Darcian medium under the application of magnetic drag force. The significant outputs are portrayed in dual solutions for suction/injection and deliberated their salient effects of various emerging physical variables on velocity, temperature, and molar concentration of Copper nanoparticles in water base fluid. It is obtained that the nanoparticle concentration grows via larger destructive chemical reaction and lessens when generative chemical reaction is enhanced. This investigation leads to opposite behavior due to endothermic reaction. The significance of such investigation in Darcian porous medium have frequent applications in the major area of industrial and engineering technologies that covers the bio-engineering, rubber technology and material processing.

Energy-Aware Cloud-Edge Collaborative Task Offloading with Adjustable Base Station Radii in Smart Cities

In smart cities, the computing power and battery life of terminal devices (TDs) can be effectively enhanced by offloading tasks to nearby base stations (BSs) with richer resources. With the goal of TDs being fully served and achieving low-carbon energy savings for the system, this paper investigates task offloading in cloud-edge collaborative heterogeneous scenarios with multiple BSs and TDs. According to the proportional relationship between the energy and coverage radii of BSs, a complete coverage task offloading model with adjustable BS radii is proposed. The task offloading problem is formulated as an integer linear program with multidimensional resource constraints to minimize the sum of energy consumption of BS coverage, offloading tasks to BSs and the cloud data center (CC). Since this task offloading problem is NP-hard, two approximate algorithms with polynomial time complexity are designed based on the greedy strategy of seeking the most energy-effective disk and the primal–dual method of constructing primal feasible solutions according to dual feasible solutions. Experimental results show that both the greedy and primal–dual algorithms can achieve good approximation performance, but each of them has its own advantages due to different design principles. The former is superior in execution time and energy consumption, while the latter has advantages in balancing loads among BSs and alleviating core network bandwidth pressure.

Thermal analysis of a radiative nanofluid over a stretching/shrinking cylinder with viscous dissipation

This study explores the impact of thermal radiation and viscous dissipation on the stagnation point flow of a copper–water nanofluid across a convective stretching/shrinking cylinder. The copper suspension in the base fluid water enables the fluid to conduct more heat by increasing its thermal conductivity. The mathematical model that governs the flow of Cu-H2O nanofluid is formulated by the system of partial differential equations (PDEs) which are then subjected to transformation by introducing suitable similarity variables so the system is transformed to the Ordinary Differential Equations (ODEs). These equations have been solved numerically via the bvp4c package in MATLAB. The outcomes have been signified graphically in the form of heat transfer rate, temperature, skin friction and velocity which are dependent on the concerning flow parameters. For each of these result, dual solutions have been produced which are conditional on the shrinking of cylinder. These results declare that the skin friction increases for the shrinking cylinder and decreases for the stretching cylinder whereas an opposite trend is seen for the rate of heat transfer. Similarly, heat transfer is found to be decreasing for the increase in both Biot and Eckert number. Meanwhile, the existence of greater values of curvature parameter causes to enhance both first and second solution of velocity as well as the temperature is augmenting with the increase in Eckert number and volume fraction of nano particles.

Heat Transport during Colloidal Mixture of Water with Al2O3-SiO2 Nanoparticles within Porous Medium: Semi-Analytical Solutions.

In recent years, energy consumption has become an essential aspect in the manufacturing industry, and low heat transfer is one of the obstacles that affect the quality of the final product. This situation can be managed by suspending nanoparticles into ordinary heat transferring fluid (the base fluid). This newly prepared colloidal suspension has better heat transport capabilities. Keeping such usage of nanofluids in mind, this research was performed to better understand the heat transport characteristics during flow analysis saturated in porous media subject to Al2O3-SiO2/water hybrid nanofluids. This flow problem was generated by a stretching/shrinking surface. The surface of the sheet was under the influence of mass suction and second-order partial slip. The boundary layer flow was formulated in a system of partial differential equations by utilizing basic conservation laws in conjunction with the Tiwari and Das nanofluid model. Then, the appropriate form of the similarity transformation was adapted to transform the model into a system of ordinary differential equations. The built-in function, i.e., the bvp4c function in the MATLAB software, solved the reduced form of the boundary layer model. The novelty of this study lay in the predicting of two different exact and numerical solutions for both the flow and temperature fields. The computed results showed that the medium porosity as well as the nanoparticle volume fraction widened the existence range of the dual solutions. In addition, the investigational output exposed the fact that the temperature fields were significantly enhanced by the higher nanoparticle volume fraction. Moreover, the outcomes of this study showed a superb correlation with existing works. The present results can be utilized in various branches of science and engineering such as the polymer industry and in the treatment of different diseases.

A study on dual solutions for water-based hybrid nanofluids flowing through convergent channel with dissipative heat transport

Over the years, the fluid flows in conjunction with thermal transport between non-parallel surfaces having converging nature is of great significance due to their broad spectrum of applications, which include fluid flows through nozzles in petroleum engineering, blood flow in arteries, lubrication systems, automobile radiators, thermal pumps, and water purification processes. Additionally, hybrid nanofluid is a prolific topic because of its thermal properties and potentials which provide a better performance even compared with common nanofluid in optimizing heat transfer. Therefore, this article presents a numerical simulation to investigate the heat transport characteristics of hybrid nanofluids in Jeffery-Hamel flow through a convergent channel. The considered hybrid nanofluids are composed of Copper (Cu) and Graphene-oxide (Go) as suspended nanoparticles and water as base fluid. This analysis further includes the impacts of viscous dissipation and magnetic field. A mathematical model for fluid flow and heat transfer are constructed with the help of cylindrical polar coordinates. The governing equations are converted into a system of ordinary differential equations (ODEs) by Lie symmetry group transformation. A MATLAB code is exercise to get the numerical solutions for flow and thermal distributions. An interesting phenomenon is that dual solutions are obtained in the computation. Thus, a comprehensive discussion is included on the dual solutions for various involved variables. The current findings may be employed in petroleum science, r biomedical scientists, polymer industry, etc.

Significance of multiple solutions on the dynamics of ethylene glycol conveying gold and copper nanoparticles on a shrinking surface

All previously published data on the dynamics of ethylene glycol conveying copper and gold nanoparticles over a convective surface, nothing is known about the importance of dual branch solutions. Hybrid nanofluids improve the thermal conductivity of the fluid. The nanoparticles copper and gold having ethylene glycol as a base fluid are used here. The flow problem is described over a stretching/shrinking surface with the influence of Ohmic heating, non-linear radiation, and a convectively heated surface. Furthermore, the magnetic field strength is applied perpendicular to the direction of the flow. To control the fluid, flow-governing equations are numerically solved by using bvp4c, a built-in approach in MATLAB. For hybrid nanomaterials, the consequence of different physical parameters is discussed graphically and with tabular data. A comparison with previous findings reveals that the present findings are in good agreement. The results revealed that the coefficient of skin friction for the physically stable branch declines over a certain range of shrinking parameters; nonetheless, for the unstable branch, the reverse pattern is discovered. The magnetic force diminishes the flow field and energy dispersion in the upper branch but improves it in the lower branch.

Maximum A Posteriori Inference of Random Dot Product Graphs via Conic Programming

We present a convex cone program to infer the latent probability matrix of a random dot product graph (RDPG). The optimization problem maximizes the Bernoulli maximum likelihood function with an added nuclear norm regularization term. The dual problem has a particularly nice form, related to the well-known semidefinite program relaxation of the maxcut problem. Using the primal-dual optimality conditions, we bound the entries and rank of the primal and dual solutions. Furthermore, we bound the optimal objective value and prove asymptotic consistency of the probability estimates of a slightly modified model under mild technical assumptions. Our experiments on synthetic RDPGs not only recover natural clusters, but also reveal the underlying low-dimensional geometry of the original data. We also demonstrate that the method recovers latent structure in the Karate Club Graph and synthetic U.S. Senate vote graphs and is scalable to graphs with up to a few hundred nodes.

Scrutinisation of Chebyshev collocation method for mass transfer on a continuous flat plate moving in parallel to a free stream in the presence of a chemical reaction

The paper presents the boundary layer flow of mass transfer on a continuous flat plate moving in parallel or reversely to a free stream with a chemical reaction. By using suitable similarity transformations, the boundary-layer equations are transformed into coupled nonlinear ordinary differential equations (NODEs) over semi-infinite interval. These equations have been analysed using a novel semi-numerical method, viz. spectral method. The dual solutions for velocity and concentration distributions are determined using Chebyshev collocation method (CCM) and the results are presented in the form of tables and graphs. The obtained spectral solutions are compared with previously published results and are comparable. Many interesting physical properties of the problem are observed and verified through both theoretical as well as semi-numerical approach. The derived quantities show that the mass transfer rate is established to be increased as the Schmidt number increases for the solution of the upper branch and reduces for the solution of lower branch.

Stability analysis of inclined MHD and Joule effects in Ti-alloy and MWCNT/water hybrid nanofluid: Flow separation

This research article explains the Joule heating and inclined magnetic field effects on Ti6Al4V-MWCNT/[Formula: see text] hybrid nanofluids toward an exponentially shrinking surface. The system of flow governing equations, which is a coupled system of non-linear PDE’s, are transformed into a system of non-dimensional ODE’s by using suitable similarity transformations. The shooting method along with a fourth order Runge-Kutta approach is used to solve the system of resultant ODE’s. As a result, the dual solutions are identified for this problem. By utilizing the least eigenvalue approach, the first solution is found to be realistic and stable whereas the second solution is not stable. In order to verify the accuracy of outcomes, it is compared with the previously published results, and it is found that the present analysis is accurate upto four decimal places. Further, the streamline profiles are also provided in addition to the least eigenvalue profiles to understand the flow patterns. Finally, the flow separation point is identified. The velocity profiles improves in the case of first solution but it declines in the case of second solution with a rise in the shrinking strength parameter, however the temperature profiles behave in opposite manner. The skin friction coefficient and heat transfer rate of Ti6Al4V-MWCNT/[Formula: see text] based hybrid nanofluids are found to be better with higher values of inclined MHD [Formula: see text] and incline angle [Formula: see text].

Exact solutions for MHD and radiative wall jet hybrid nanofluid flow over a permeable surface with velocity slip and convective boundary conditions

AbstractIn this research, we investigated the wall jet problem for a hybrid nanofluid with MHD, thermal radiation, velocity slip, and convective boundary conditions. After converting the governing partial differential equations into nonlinear ordinary ones, by using the proper similarity transformations, they were theoretically solved in view of the hypergeometric function. Comparing the present results with those in the literature, a very good agreement was obtained for fixed values of the included parameters. For some included parameters, regions of physical solutions were presented. By deducing the critical and terminated values of the suction/injection parameter, dual solutions for the reduced skin friction coefficient have been determined. It was found that the hybrid nanofluid temperature is efficiently heated by increasing values of the moving wall, absolute value of the Biot number, and thermal radiation parameters. However, it is cooled by enlarging values of the velocity slip and suction parameters.

Numerical and asymptotic solutions of the unsteady mixed convection boundary-layer flow over an expanding/contracting vertical cylinder

PurposeThe purpose of this study is to obtain both the numerical and asymptotic solutions of the unsteady mixed convection flow and heat transfer over an expanding or contracting cylinder which is placed vertically.Design/methodology/approachSolutions of the governing ordinary (similarity) differential equations for the fluid flow and temperature field are obtained using the function bvp4c from MATLAB. The problem involves the Prandtl number σ, the mixed convection parameter λ and unsteadiness parameter S that characterize an expanding or contracting cylinder. This solution approach is capable of producing multiple solutions once the necessary assumptions are provided.FindingsIt is found that solutions exist for all negative values of S, expanding cylinder, and only for small positive values of S, contracting cylinder. Further, more than one solution is observed; numerical computation shows that the critical point of S becomes singular as λ approaching zero. For the case of expanding cylinder, the mixed convection parameter has a significant effect on both the flow and heat transfer characteristics. Asymptotic analysis also shows that when σ is large, dual solutions exist for some values of S and λ.Originality/valueThe present results are new and original for the study of the unsteady mixed convection flow and heat transfer over an expanding/contracting cylinder where numerical solutions are obtained for representative values of the involved parameters. Asymptotic solutions for large λ and large σ are derived.