Mathematical modeling of falling liquid film evaporation process

A mathematical model of evaporation process from a laminar falling liquid film on a vertical plate of constant temperature is presented. The model is developed with and without interfacial shear stress due to the vapor flow at the liquid film surface. The vapor pressure drop, vapor exit velocity and cooling rate are calculated for different liquid mass flow values. It is shown that lower liquid mass flow produces higher cooling rate. The results also show that the interfacial shear stress has a considerable negative effect on the cooling rate. It is proved that there exists an optimum distance between the plates, which gives the maximum volumetric cooling rate.     

Comparison of stochastic approaches to the transportation problem:a case study

The objective of this case study is to provide insight to practitioners about the methodology of using the space-time autoregressive integrated moving average (STARIMA) class of models to formulate stochastic demand of the transportation problem. While providing insight, two other methods-expected value (EV) and stochastic approximation (SA)-are also employed to formulate demand. A comparative evaluation of the methods using brewery data for the distribution of four products from five production plants to 64 distribution centers is presented. It is shown that the demand characterized by the STARIMA approach results in a lower total cost of transportation. This occurs because the STARIMA approach results in better forecasts. Based upon the case study, the cost analysis indicated that the STARIMA method when used without (with) updating resulted in a 9.49% (10.5%) increase in the Company's net profit as compared with the SA method. Similarly, the STARIMA approach when used without (with) updating resulted in an 11.36% (12.37%) increase in the net profit as compared with the EV method. For the STARIMA approach, computations for a large size problem are shown to be identical to those of the deterministic transportation problem given the demand forecasts. Extra computation effort for producing STARIMA forecasts are easily justified in terms of the increased profit margin     

The controlled rounding problem: Relaxations and complexity issues

Summary Controlled rounding is a procedure that perturbs tabular data collected from respondents in such a way as to preserve the anonymity of the respondents while maintaining the integrity of the data. Controlled rounding techniques are regularly used by the United States Bureau of the Census and its counterparts in other countries. This paper discusses the complexity of the three-dimensional controlled rounding problem. In particular, the three-dimensional, zero-restricted controlled rounding problem is shown to be NP-complete. As zero-restricted controlled roundings may fail to exist, various relaxations of this basic rounding problem have been defined. The paper introduces a sequence of such relaxations and proceeds to address the existence of solutions and complexity issues for the relaxed problems.

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Zusammenfassung Die Technik des kontrollierten Rundens (Controlled Rounding) wird von Behörden wie dem United States Bureau of Census benutzt, um in mehrdimensionalen Tabellen oder Matrizen erfaßte statistische Daten durch Approximation so zu verändern, daß sowohl die Anonymität von Einzeldaten (Matrixeinträgen) als auch die Integrität der Gesamtdaten (Zeilensummen, Spaltensummen etc.) gewährleistet ist. In dieser Arbeit behandeln wir die Komplexität und Lösbarkeit des dreidimensionalen Rundungsproblems und diskutieren eine Hierarchie von Relaxationen, die bei Nichtlösbarkeit des Ausgangsproblems alternative, nahezu zulässige Lösungen liefern.

     

Structural,optical and electrical properties of Cu<Subscript>2</Subscript>Zn<Subscript>1−x</Subscript>Cd<Subscript>x</Subscript>SnS<Subscript>4</Subscript> quinternary alloys nanostructures deposited on porous silicon

The Cu₂Zn_1?xCd_xSnS₄ quinternary alloy nanostructures with different Cd contents were grown using spin coating technique on porous silicon (63.93 %) substrate. The structural properties of Cu₂Zn_1?xCd_xSnS₄/PS were investigated by X-ray diffraction and field emission-scanning electron microscope (FE-SEM). The optical properties studied through photoluminescence technique, indicated that the band gap is shifted as Cd content increases from 1.84 eV at x = 0 to 1.76 eV at x = 1. The electrical characterization of the Ag/n-PS/Cu₂Zn_1?xCd_xSnS₄/Ag diode through current to voltage (I–V) characterization shows the highest photo-response of (value if any) at Cu₂Zn_0.4Cd_0.6SnS₄ composition.     

Solution of the nonlinear elasticity imaging inverse problem: The incompressible case

We have recently developed and tested an efficient algorithm for solving the nonlinear inverse elasticity problem for a compressible hyperelastic material. The data for this problem are the quasi-static deformation fields within the solid measured at two distinct overall strain levels. The main ingredients of our algorithm are a gradient based quasi-Newton minimization strategy, the use of adjoint equations and a novel strategy for continuation in the material parameters. In this paper we present several extensions to this algorithm. First, we extend it to incompressible media thereby extending its applicability to tissues which are nearly incompressible under slow deformation. We achieve this by solving the forward problem using a residual-based, stabilized, mixed finite element formulation which circumvents the Ladyzenskaya-Babuska-Brezzi condition. Second, we demonstrate how the recovery of the spatial distribution of the nonlinear parameter can be improved either by preconditioning the system of equations for the material parameters, or by splitting the problem into two distinct steps. Finally, we present a new strain energy density function with an exponential stress-strain behavior that yields a deviatoric stress tensor, thereby simplifying the interpretation of pressure when compared with other exponential functions. We test the overall approach by solving for the spatial distribution of material parameters from noisy, synthetic deformation fields.     

Optimal structure for heat and cold protection under transient heat conduction

A suitable combination of materials for sheltering a system from a sudden change of environmental temperature has been theoretically studied. The protective composite wall consists of two materials. An insulating material is placed on the outer surface, while, for the inner surface, materials that have good heat storage properties but negligible heat transfer resistance are chosen. The results show that by replacing some of the insulation material with a heat storage material, the temperature of the protected system can be maintained at a considerably lower level. Although the optimal thickness ratio X depends on the Biot number, Fourier number, and on the heat capacity ratio K _C, for a large number of thermal protection cases, the approximation X = 0.45 yields practically the minimum progress of the transient. If the Biot number is sufficiently small, it is better to replace all of the insulation material with a good heat storage material.     

Spatial distribution and habitat characterization of schistosomiasis host snails in lake and land habitats of western Kenya

Intermediate host snails of schistosomiasis were surveyed in this study to determine their abundance and distribution in the lake and land aquatic habitats of Lake Victoria basin of Kenya. Several sites were sampled at eight locations, both in the lake and on the land. The habitat and/or vegetation type (i.e. open water, hippo grass, hyacinth, ambatch trees, other vegetation, stream, swamp, pond, dam) of the sampled aquatic sites within the locations were also differentiated, water physicochemical parameters were determined, and the abundance of different species or taxa of phytoplankton and zooplankton were enumerated and correlated with the abundance of schistosomiasis snails in the sites. The results indicated significantly more Biomphalaria sudanica snails than Bulinus africanus snails in different physical habitats on land (Student's t‐test, P < 0.05), as well as in different locations on land (Student's t‐test, P = 0.026). Regression analyses revealed that several physicochemical parameters, including dissolved oxygen (R² = ?0.659; n = 8; P = 0.014), pH (R² = 0.728; n = 8; P = 0.007) and turbulence (R² = ?0.616; n = 8; P = 0.02), were predictive of Biomphalaria spp. abundance, while pH (R² = 0.610; n = 8; P = 0.02) and turbulence (R² = ?0.578; n = 8; P = 0.028) were predictive of Bulinus spp. abundance in different locations in the lake. Cyanobacteria (R² = 0.638; n = 8; P = 0.02) and chlorophyceae (R² = ?0.50; n = 8; P = 0.05) were shown to be predictive of both Biomphalaria spp. and Bulinus spp. abundance in different locations in the lake. Zooplankton abundance varied significantly between different locations in the lake (One‐way anova , P < 0.001). Bosmina spp. were found to be predictive of both Biomphalaria spp. (R² = ?0.627; n = 8; P = 0.01) and Bulinus spp. (R² = ?0.50; n = 8; P = 0.05) in different locations in the lake. The results from this study will help inform policy regarding control measures for schistosomias and intermediate snail hosts in Lake Victoria waters, as well as in adjacent terrestrial aquatic habitats and even beyond.     

Storage and permeation of hydrogen molecule,atom and ions (H+ and H−) through silicon carbide nanotube; a DFT approach

The barriers for the encapsulation and decapsulation of hydrogen ions (cationic hydrogen and hydride), atom, and molecule through silicon carbide nanotube are thoroughly studied. DFT method is selected to measure the kinetic barriers for the passage of hydrogen atom, ions and molecule through nanotube via scanning potential energy surface. The kinetic barriers for the passage (encapsulation and decapsulation) of hydrogen are very important to understand the mechanism of hydrogen storage and release. The barriers for the permeation of H, H⁺ and H^? across SiC nanosheet are lower compared to hydrogen molecule (H₂). The exohedral and endohedral adsorption of hydrogen ions (cation and anion), atom and exohedral hydrogen molecule on silicon carbide are exothermic in nature. Whereas the encapsulation of hydrogen molecule in silicon carbide is endothermic. Electronic properties are analyzed through measurement of energy gap between highest occupied and lowest unoccupied molecular orbitals gap (G_H-L) and the density of state (DOS) spectra. The G_H-L analysis reveals that endohedral complexes have more pronounced effect on electronic properties compared to exohedral complexes. The SiC nanotube has highly favorable properties for storage and release of hydrogen ions, and atom.     

Formal probabilistic analysis of a surgical robot control algorithm with different virtual fixtures

Surgical robots are increasingly being used in operation theaters involving normal or laparoscopic surgeries. The working of these surgical robots is highly dependent on their control algorithms, which require very rigorous analysis to ensure their correct functionality due to the safety-critical nature of surgeries. Traditionally, safety of control algorithms is ensured by simulations, but they provide incomplete and approximate analysis results due to their inherent sampling-based nature. We propose to use probabilistic model checking, which is a formal verification method, for quantitative analysis, to verify the control algorithms of surgical robots in this paper. As an illustrative example, the paper provides a formal analysis of a virtual fixture control algorithm, implemented in a neuro-surgical robot, using the PRISM model checker. In particular, we provide a formal discrete-time Markov chain-based model of the given control algorithm and its environment. This formal model is then analyzed for multiple virtual fixtures, like cubic, hexagonal and irregular shapes. This verification allowed us to discover new insights about the considered algorithm that allow us to design safer control algorithms.