Power allocations in an interference-limited wireless network for global maximization of the weighted sum throughput or global optimization of the minimum weighted rate among network links are not ...only important but also very hard optimization problems due to their nonconvexity nature. Recently developed methods are either unable to locate the global optimal solutions or prohibitively complex for practical applications. This paper exploits the d.c. (difference of two convex functions/sets) structure of either the objective function or constraints of these global optimization problems to develop efficient iterative algorithms with very low complexity. Numerical results demonstrate that the developed algorithms are able to locate the global optimal solutions by only a few iterations and they are superior to the previously-proposed methods in both performance and computation complexity.
Current analytical models for sessile droplet evaporation do not consider the nonuniform temperature field within the droplet and can overpredict the evaporation by 20%. This deviation can be ...attributed to a significant temperature drop due to the release of the latent heat of evaporation along the air–liquid interface. We report, for the first time, an analytical solution of the sessile droplet evaporation coupled with this interfacial cooling effect. The two-way coupling model of the quasi-steady thermal diffusion within the droplet and the quasi-steady diffusion-controlled droplet evaporation is conveniently solved in the toroidal coordinate system by applying the method of separation of variables. Our new analytical model for the coupled vapor concentration and temperature fields is in the closed form and is applicable for a full range of spherical-cap shape droplets of different contact angles and types of fluids. Our analytical results are uniquely quantified by a dimensionless evaporative cooling number E o whose magnitude is determined only by the thermophysical properties of the liquid and the atmosphere. Accordingly, the larger the magnitude of E o, the more significant the effect of the evaporative cooling, which results in stronger suppression on the evaporation rate. The classical isothermal model is recovered if the temperature gradient along the air–liquid interface is negligible (E o = 0). For substrates with very high thermal conductivities (isothermal substrates), our analytical model predicts a reversal of temperature gradient along the droplet-free surface at a contact angle of 119°. Our findings pose interesting challenges but also guidance for experimental investigations.
The formation of water-stable aggregates in finely textured and polymineral magnetite Fe ore tailings is one of the critical processes in eco-engineering tailings into soil-like substrates as a new ...way to rehabilitate the tailings. Organic matter (OM) amendment and plant colonization are considered to be effective in enhancing water-stable aggregation, but the underlying mechanisms have not yet been elucidated. The present study aimed to characterize detailed changes in physicochemistry, Fe-bearing mineralogy, and organo-mineral interactions in magnetite Fe ore tailings subject to the combined treatments of OM amendment and plant colonization, by employing various microspectroscopic methods, including synchrotron-based X-ray absorption fine structure spectroscopy and nanoscale secondary ion mass spectroscopy. The results indicated that OM amendment and plant colonization neutralized the tailings’ alkaline pH and facilitated water-stable aggregate formation. The resultant aggregates were consequences of ligand-promoted bioweathering of primary Fe-bearing minerals (mainly biotite-like minerals) and the formation of secondary Fe-rich mineral gels. Especially, the sequestration of OM (rich in carboxyl, aromatic, and/or carbonyl C) by Fe-rich minerals via ligand-exchange and/or hydrophobic interactions contributed to the aggregation. These findings have uncovered the processes and mechanisms of water-stable aggregate formation driven by OM amendment and plant colonization in alkaline Fe ore tailings, thus providing important basis for eco-engineered pedogenesis in the tailings.
Providing ultra reliable and low-latency communication (URLLC) is considered one of the major challenges for wireless communication networks. This article considers a downlink URLLC system in which a ...base station (BS) serves multiple single-antenna users in the short blocklength regime. With the objective of maximizing the users' minimum rate, three different optimization problems are considered: (i) joint design of bandwidth and power allocation for the case of a single-antenna BS; (ii) beamforming design for the case of a multiple-antenna BS; and (iii) design of power allocation with regularized zero-forcing beamforming for the case of a multiple-antenna BS. In the short blocklength regime, the achievable rate is a complicated function of bandwidth and power allocation coefficients or beamforming vectors, which makes these max-min rate optimization problems challenging to solve. This work develops path-following algorithms, which generate a sequence of improved feasible points and converge at least to a locally optimal solution, to solve these three optimization problems. Performance of the proposed algorithms is analyzed through extensive simulations under various settings of transmit power budget, number of users, total bandwidth, transmission time, and number of transmit antennas at the BS. Simulation results clearly demonstrate the merits of the proposed algorithms.
This paper considers joint linear processing at multi-antenna sources and one multiple-input multiple-output (MIMO) relay station for both one-way and two-way relay-assisted wireless communications. ...The one-way relaying is applicable in the scenario of downlink transmission by a multi-antenna base station to multiple single-antenna users with the help of one MIMO relay. In such a scenario, the objective of join linear processing is to maximize the information throughput to users. The design problem is equivalently formulated as the maximization of the worst signal-to-interference-plus-noise ratio (SINR) among all users subject to various transmission power constraints. Such a program of nonconvex objective minimization under nonconvex constraints is transformed to a canonical d.c. (difference of convex functions/sets) program of d.c. function optimization under convex constraints through nonconvex duality with zero duality gap. An efficient iterative algorithm is then applied to solve this canonical d.c program. For the scenario of using one MIMO relay to assist two sources exchanging their information in two-way relying manner, the joint linear processing aims at either minimizing the maximum mean square error (MSE) or maximizing the total information throughput of the two sources. By applying tractable optimization for the linear minimum MSE estimator and d.c. programming, an iterative algorithm is developed to solve these two optimization problems. Extensive simulation results demonstrate that the proposed methods substantially outperform previously-known joint optimization methods.
The solid surfaces used in evaporation studies of nanoparticle sessile droplets usually exhibit significant surface roughness, causing significant pinning of the three-phase contact lines and ...producing different types of nanoparticle deposits, from single and multiple coffee rings (formed at the initial pining of triple contact lines) to central bumps. Here we used nanometer-scale smooth hydrophobic surfaces to investigate the evaporation of sessile water droplets containing silica nanoparticles and organic pigment nanoparticles. We observed a new type of coffee ring deposits which were not formed at the initial pinning but at the later pinning. We referred them to as the inner coffee ring deposits (ICRDs). The radius of ICRDs was smaller than the radius of the initially pinned contact area and increased with increasing concentration of added salts and nanoparticles and with increasing contact angle hysteresis of hydrophobic surfaces. We also observed different dendrite deposit patterns inside ICRDs. We argue that all the deposit patterns are due to the second pinning of the three-phase contact lines, which occur when the forces on particles are balanced. The hypothesis is further supported by the transient changes of the dynamic contact angles and contact base area radius. The contact angle hysteresis, the particle concentration, and the colloidal interaction forces such as the electrical double-layer forces play a vital role in determining the size and patterns of ICRDs and the evaporation kinetics of nanoparticle sessile droplets.
Dissolved organic matter (DOM) plays an important role in soil structure and biogeochemical function development, which are fundamental for the eco-engineering of tailings-soil formation to underpin ...sustainable tailings rehabilitation. In the present study, we have characterized the DOM composition and its molecular changes in an alkaline Fe ore tailing primed with organic matter (OM) amendment and plant colonization. The results demonstrated that microbial OM decomposition dramatically increased DOM richness and average molecular weight, as well as its degree of unsaturation, aromaticity, and oxidation in the tailings. Plant colonization drove molecular shifts of DOM by depleting the unsaturated compounds with a high value of nominal oxidation state of carbon (NOSC), such as tannin-like and carboxyl-rich polycyclic-like compounds. This may be partially related to their sequestration by secondary Fe–Si minerals formed from rhizosphere-driven mineral weathering. Furthermore, the molecular shifts of DOM may have also resulted from plant-regulated microbial community changes, which further influenced DOM molecules through microbial–DOM interactions. These findings contribute to the understanding of DOM biogeochemistry and ecofunctionality in the tailings during early pedogenesis driven by OM input and pioneer plant/microbial colonization, providing an important basis for the development of strategies and technologies toward the eco-engineering of tailings-soil formation.
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► Sessile and pendant nanofluid droplet deposits on hydrophobic surfaces compared. ► Coffee ring deposit formed in the sessile configuration. ► Bump deposit formed in the pendant ...position. ► Difference important for foliar fertilizers and cleanliness of building exteriors. ► Flow induced aggregation and orientation dependant accumulation explain results.
The influence of droplet orientation on the flow directed organization of nanoparticles in evaporating nanofluid droplets is important for the efficiency of foliar applied fertilizers and contamination adhesion to the exterior of buildings. The so called “coffee ring” deposit resulting from the evaporation of a sessile nanofluid drop on a hydrophilic surface has received much attention in the literature. Deposits forming on hydrophobic surfaces in the pendant drop position (i.e. hanging drop), which are of importance in foliar fertilizer and exterior building contamination, have received much less attention. In this study, the deposit patterns resulting from the evaporation of water droplets containing silica nanoparticles on hydrophobic surfaces orientated in the sessile or pendant configuration are compared. In the case of a sessile drop the well known coffee ring pattern surrounding a thin nanoparticle layer was formed. A deposit consisting of a thin coffee ring surrounding a bump was formed in the pendant position. A mechanism involving flow induced aggregation at the droplet waist, settling, orientation dependant accumulation within the drop and pinning of the contact line is suggested to explain the findings. Differences in the contact area and adhesion of deposits with surface orientation will affect the efficiency and rainfastness of foliar fertilizers and the cleanliness of building exteriors.
This paper presents a novel smoothing gradient damage model, which goes beyond certain limitations of conventional methods, for accurate prediction of localized failure in quasi-brittle materials. ...The proposed method is particularly tailored to low-order finite elements such as 4-node quadrilateral or 3-node triangular elements. The low-order elements are preferable in practice as they can automatically be generated for problems even with complex geometries at low computational cost. In order to eliminate spurious damage growth and correct wrong prediction of shear band induced by using the constant gradient parameter in terms of conventional models, we thus introduce a novel modified evolving anisotropic nonlocal gradient parameter, which aims to control the behavior of nonlocal interactions of damage microprocess during the entire loading history in a more appropriate manner. Unlike conventional approaches, the novel modified evolving gradient parameter heavily depends on the principal stress and equivalent strain states, which serves to reduce the impact of localized deformation. The stress fields thus play a crucial role in the present formulation as they greatly affect the orientation and intensity of nonlocal interactions. The quality of raw stresses becomes critical (e.g., stress oscillation) once two unknowns (i.e., displacements and nonlocal equivalent strain) are approximated simultaneously using the same orders of interpolation functions (e.g., linear-linear). A smoothing technique is thus adopted to smooth out the raw stresses. The stresses after smoothing are shown adequately in the estimation of the new gradient parameter, providing much better solutions. In addition, to precisely capture the softening in quasi-brittle materials, the original energy norm is decomposed into tensile and compressive parts to form a new bi-energy norm. The scalar equivalent strain is thus estimated through this new bi-energy norm, which is obviously able to distinguish tensile and compressive conditions. To further enhance the capability of the present damage model, the material softening process is also determined through fracture energy in terms of fracture mechanics. Comparison of the present results with reference solutions derived from experimental data and other numerical methods for benchmark applications, regarding the nonlocal equivalent strain, damage profile, structural force-displacement curves, etc., confirms the accuracy and superior performance of the proposed approach for characterizing localized failure in quasi-brittle materials.
