Cauchy-Type Problem for Diffusion-Wave Equation with the Riemann-Liouville Partial Derivative

2000 Mathematics Subject Classification: 35A15, 44A15, 26A33

On a Hypersingular Equation of a Problem, for a Crack in Elastic Media

Mathematics Subject Classification 2010: 45DB05, 45E05, 78A45.

An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative

Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.

On a 3D-Hypersingular Equation of a Problem for a Crack

MSC 2010: 45DB05, 45E05, 78A45

Inverse Problem for Fractional Diffusion Equation

MSC 2010: 26A33, 33E12, 34K29, 34L15, 35K57, 35R30

Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations

A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.

A desalination system with efficiency approaching the theoretical limits

The objective of this project is to design a new desalination system with energy efficiency approaching the theoretical thermodynamic limit—even at high recovery ratio. The system uses reverse osmosis (RO) and a batch principle of operation to overcome the problem of concentration factor which prevents continuous-flow RO systems from ever reaching this limit and thus achieving the minimum possible specific energy consumption, SEC. Batch operation comprises a cycle in three phases: pressurisation, purge, and refill. Energy recovery is inherent to the design. Unlike in closed-circuit desalination (CCD), no feedwater is added to the pressure circuit during the pressurisation phase. The batch configuration is compared to standard configurations such as continuous single-stage RO (with energy recovery) and CCD. Theoretical analysis has shown that the new system is able to use 33% less energy than CCD at a recovery ratio of 80%. A prototype has been constructed using readily available parts and tested with feedwater salinities and recovery ratios ranging from 2,000 to 5,000 ppm and 17.2–70.6%, respectively. Results compare very well against the standard configurations. For example, with feedwater containing 5,000 ppm NaCl and recovery ratio of 69%, a hydraulic SEC of 0.31 kWh/m3 was obtained—better than the minimum theoretically possible with a single-stage continuous flow system with energy recovery device.

Achieving zero accidents—A strategic framework for continuous safety improvement in the construction industry

In the U.S., construction accidents remain a significant economic and social problem. Despite recent improvement, the Construction industry, generally, has lagged behind other industries in implementing safety as a total management process for achieving zero accidents and developing a high-performance safety culture. One aspect of this total approach to safety that has frustrated the construction industry the most has been “measurement”, which involves identifying and quantifying the factors that critically influence safe work behaviors. The basic problem attributed is the difficulty in assessing what to measure and how to measure it—particularly the intangible aspects of safety. Without measurement, the notion of continuous improvement is hard to follow. This research was undertaken to develop a strategic framework for the measurement and continuous improvement of total safety in order to achieve and sustain the goal of zero accidents, while improving the quality, productivity and the competitiveness of the construction industry as it moves forward. The research based itself on an integral model of total safety that allowed decomposition of safety into interior and exterior characteristics using a multiattribute analysis technique. Statistical relationships between total safety dimensions and safety performance (measured by safe work behavior) were revealed through a series of latent variables (factors) that describe the total safety environment of a construction organization. A structural equation model (SEM) was estimated for the latent variables to quantify relationships among them and between these total safety determinants and safety performance of a construction organization. The developed SEM constituted a strategic framework for identifying, measuring, and continuously improving safety as a total concern for achieving and sustaining the goal of zero accidents.

A quantitative approach to the organizational design problem

The span of control is the most discussed single concept in classical and modern management theory. In specifying conditions for organizational effectiveness, the span of control has generally been regarded as a critical factor. Existing research work has focused mainly on qualitative methods to analyze this concept, for example heuristic rules based on experiences and/or intuition. This research takes a quantitative approach to this problem and formulates it as a binary integer model, which is used as a tool to study the organizational design issue. This model considers a range of requirements affecting management and supervision of a given set of jobs in a company. These decision variables include allocation of jobs to workers, considering complexity and compatibility of each job with respect to workers, and the requirement of management for planning, execution, training, and control activities in a hierarchical organization. The objective of the model is minimal operations cost, which is the sum of supervision costs at each level of the hierarchy, and the costs of workers assigned to jobs. The model is intended for application in the make-to-order industries as a design tool. It could also be applied to make-to-stock companies as an evaluation tool, to assess the optimality of their current organizational structure. Extensive experiments were conducted to validate the model, to study its behavior, and to evaluate the impact of changing parameters with practical problems. This research proposes a meta-heuristic approach to solving large-size problems, based on the concept of greedy algorithms and the Meta-RaPS algorithm. The proposed heuristic was evaluated with two measures of performance: solution quality and computational speed. The quality is assessed by comparing the obtained objective function value to the one achieved by the optimal solution. The computational efficiency is assessed by comparing the computer time used by the proposed heuristic to the time taken by a commercial software system. Test results show the proposed heuristic procedure generates good solutions in a time-efficient manner.

Design and development of a diagonal-airflow batch dryer for spatial drying homogeneity

Das Verfahren der Lebensmitteltrocknung wird häufig angewendet, um ein Produkt für längere Zeit haltbar zu machen. Obst und Gemüse sind aufgrund ihres hohen Wassergehalts leicht verderblich durch biochemische Vorgänge innerhalb des Produktes, nicht sachgemäße Lagerung und unzureichende Transportmöglichkeiten. Um solche Verluste zu vermeiden wird die direkte Trocknung eingesetzt, welche die älteste Methode zum langfristigen haltbarmachen ist. Diese Methode ist jedoch veraltet und kann den heutigen Herausforderungen nicht gerecht werden. In der vorliegenden Arbeit wurde ein neuer Chargentrockner, mit diagonalem Luftstömungskanal entlang der Länge des Trocknungsraumes und ohne Leitbleche entwickelt. Neben dem unbestreitbaren Nutzen der Verwendung von Leitblechen, erhöhen diese jedoch die Konstruktionskosten und führen auch zu einer Erhöhung des Druckverlustes. Dadurch wird im Trocknungsprozess mehr Energie verbraucht. Um eine räumlich gleichmäßige Trocknung ohne Leitbleche zu erreichen, wurden die Lebensmittelbehälter diagonal entlang der Länge des Trockners platziert. Das vorrangige Ziel des diagonalen Kanals war, die einströmende, warme Luft gleichmäßig auf das gesamte Produkt auszurichten. Die Simulation des Luftstroms wurde mit ANSYS-Fluent in der ANSYS Workbench Plattform durchgeführt. Zwei verschiedene Geometrien der Trocknungskammer, diagonal und nicht diagonal, wurden modelliert und die Ergebnisse für eine gleichmäßige Luftverteilung aus dem diagonalen Luftströmungsdesign erhalten. Es wurde eine Reihe von Experimenten durchgeführt, um das Design zu bewerten. Kartoffelscheiben dienten als Trocknungsgut. Die statistischen Ergebnisse zeigen einen guten Korrelationskoeffizienten für die Luftstromverteilung (87,09%) zwischen dem durchschnittlich vorhergesagten und der durchschnittlichen gemessenen Strömungsgeschwindigkeit. Um den Effekt der gleichmäßigen Luftverteilung auf die Veränderung der Qualität zu bewerten, wurde die Farbe des Produktes, entlang der gesamten Länge der Trocknungskammer kontaktfrei im on-line-Verfahren bestimmt. Zu diesem Zweck wurde eine Imaging-Box, bestehend aus Kamera und Beleuchtung entwickelt. Räumliche Unterschiede dieses Qualitätsparameters wurden als Kriterium gewählt, um die gleichmäßige Trocknungsqualität in der Trocknungskammer zu bewerten. Entscheidend beim Lebensmittel-Chargentrockner ist sein Energieverbrauch. Dafür wurden thermodynamische Analysen des Trockners durchgeführt. Die Energieeffizienz des Systems wurde unter den gewählten Trocknungsbedingungen mit 50,16% kalkuliert. Die durchschnittlich genutzten Energie in Form von Elektrizität zur Herstellung von 1kg getrockneter Kartoffeln wurde mit weniger als 16,24 MJ/kg und weniger als 4,78 MJ/kg Wasser zum verdampfen bei einer sehr hohen Temperatur von jeweils 65°C und Scheibendicken von 5mm kalkuliert. Die Energie- und Exergieanalysen für diagonale Chargentrockner wurden zudem mit denen anderer Chargentrockner verglichen. Die Auswahl von Trocknungstemperatur, Massenflussrate der Trocknungsluft, Trocknerkapazität und Heiztyp sind die wichtigen Parameter zur Bewertung der genutzten Energie von Chargentrocknern. Die Entwicklung des diagonalen Chargentrockners ist eine nützliche und effektive Möglichkeit um dei Trocknungshomogenität zu erhöhen. Das Design erlaubt es, das gesamte Produkt in der Trocknungskammer gleichmäßigen Luftverhältnissen auszusetzen, statt die Luft von einer Horde zur nächsten zu leiten.

Modelling and Verification of a Correction Factor to Evaluate the Efficiency of Solar Thermal Collectors with the Rapid Test Method

A new method for the evaluation of the efficiency of parabolic trough collectors, called Rapid Test Method, is investigated at the Solar Institut Jülich. The basic concept is to carry out measurements under stagnation conditions. This allows a fast and inexpensive process due to the fact that no working fluid is required. With this approach, the temperature reached by the inner wall of the receiver is assumed to be the stagnation temperature and hence the average temperature inside the collector. This leads to a systematic error which can be rectified through the introduction of a correction factor. A model of the collector is simulated with COMSOL Multipyisics to study the size of the correction factor depending on collector geometry and working conditions. The resulting values are compared with experimental data obtained at a test rig at the Solar Institut Jülich. These results do not match with the simulated ones. Consequentially, it was not pos-sible to verify the model. The reliability of both the model with COMSOL Multiphysics and of the measurements are analysed. The influence of the correction factor on the rapid test method is also studied, as well as the possibility of neglecting it by measuring the receiver’s inner wall temperature where it receives the least amount of solar rays. The last two chapters analyse the specific heat capacity as a function of pressure and tem-perature and present some considerations about the uncertainties on the efficiency curve obtained with the Rapid Test Method.

Thermodynamic efficiency of carbon capture and utilisation in anaerobic batch digestion process

Carbon capture and storage (CCS) in the oil and water industries is becoming common and a significant consumer of energy typically requiring 150–450 °C and or several hundred bar pressure [1] particularly in geological deposition. A biological carbon capture and conversion has been considered in conventional anaerobic digestion processes. The process has been utilised in biological mixed culture, where acetoclastic bacteria and hydrogenophilic methanogens play a major key role in the utilisation of carbon dioxide. However, the bio catalytic microorganisms, hydrogenophilic methanogens are reported to be unstable with acetoclastic bacteria. In this work the biochemical thermodynamic efficiency was investigated for the stabilisation of the microbial process in carbon capture and utilisation. The authors observed that a thermodynamic efficiency of biological carbon capture and utilisation (BCCU) had 32% of overall reduction in yield of carbon dioxide with complimentary increase of 30% in yield of methane, while the process was overall endothermic. Total consumption of energy (≈0.33 MJ l−1) was estimated for the carbonate solubility (0.1 mol l−1) in batched BCCU. This has a major influence on microbial composition in the bioreactor. This thermodynamic study is an essential tool to aid the understanding of the interactions between operating parameters and the mixed microbial culture.

Dispersive estimates for the Schrödinger equation

In this document we explore the issue of $L^1\to L^\infty$ estimates for the solution operator of the linear Schr\"{o}dinger equation, \begin{align*} iu_t-\Delta u+Vu&=0 &u(x,0)=f(x)\in \mathcal S(\R^n). \end{align*} We focus particularly on the five and seven dimensional cases. We prove that the solution operator precomposed with projection onto the absolutely continuous spectrum of $H=-\Delta+V$ satisfies the following estimate $\|e^{itH} P_{ac}(H)\|_{L^1\to L^\infty} \lesssim |t|^{-\frac{n}{2}}$ under certain conditions on the potential $V$. Specifically, we prove the dispersive estimate is satisfied with optimal assumptions on smoothness, that is $V\in C^{\frac{n-3}{2}}(\R^n)$ for $n=5,7$ assuming that zero is regular, $|V(x)|\lesssim \langle x\rangle^{-\beta}$ and $|\nabla^j V(x)|\lesssim \langle x\rangle^{-\alpha}$, $1\leq j\leq \frac{n-3}{2}$ for some $\beta>\frac{3n+5}{2}$ and $\alpha>3,8$ in dimensions five and seven respectively. We also show that for the five dimensional result one only needs that $|V(x)|\lesssim \langle x\rangle^{-4-}$ in addition to the assumptions on the derivative and regularity of the potential. This more than cuts in half the required decay rate in the first chapter. Finally we consider a problem involving the non-linear Schr\"{o}dinger equation. In particular, we consider the following equation that arises in fiber optic communication systems, \begin{align*} iu_t+d(t) u_{xx}+|u|^2 u=0. \end{align*} We can reduce this to a non-linear, non-local eigenvalue equation that describes the so-called dispersion management solitons. We prove that the dispersion management solitons decay exponentially in $x$ and in the Fourier transform of $x$.

Adsorção de corantes têxteis aniônicos e catiônicos em resíduos do processamento de fios de algodão modificados quimicamente

The textile industry generates a large volume of high organic effluent loading whoseintense color arises from residual dyes. Due to the environmental implications caused by this category of contaminant there is a permanent search for methods to remove these compounds from industrial waste waters. The adsorption alternative is one of the most efficient ways for such a purpose of sequestering/remediation and the use of inexpensive materials such as agricultural residues (e.g., sugarcane bagasse) and cotton dust waste (CDW) from weaving in their natural or chemically modified forms. The inclusion of quaternary amino groups (DEAE+) and methylcarboxylic (CM-) in the CDW cellulosic structure generates an ion exchange capacity in these formerly inert matrix and, consequently, consolidates its ability for electrovalent adsorption of residual textile dyes. The obtained ionic matrices were evaluated for pHpcz, the retention efficiency for various textile dyes in different experimental conditions, such as initial concentration , temperature, contact time in order to determine the kinetic and thermodynamic parameters of adsorption in batch, turning comprehensive how does occur the process, then understood from the respective isotherms. It was observed a change in the pHpcz for CM--CDW (6.07) and DEAE+-CDW (9.66) as compared to the native CDW (6.46), confirming changes in the total surface charge. The ionized matrices were effective for removing all evaluated pure or residual textile dyes under various tested experimental conditions. The kinetics of the adsorption process data had best fitted to the model a pseudosecond order and an intraparticle diffusion model suggested that the process takes place in more than one step. The time required for the system to reach equilibrium varied according to the initial concentration of dye, being faster in diluted solutions. The isotherm model of Langmuir was the best fit to the experimental data. The maximum adsorption capacity varied differently for each tested dye and it is closely related to the interaction adsorbent/adsorbate and dye chemical structure. Few dyes obtained a linear variation of the balance ka constant due to the inversion of temperature and might have influence form their thermodynamic behavior. Dyes that could be evaluated such as BR 18: 1 and AzL, showed features of an endothermic adsorption process (ΔH° positive) and the dye VmL presented exothermic process characteristics (ΔH° negative). ΔG° values suggested that adsorption occurred spontaneously, except for the BY 28 dye, and the values of ΔH° indicated that adsorption occurred by a chemisorption process. The reduction of 31 to 51% in the biodegradability of the matrix after the dye adsorption means that they must go through a cleaning process before being discarded or recycled, and the regeneration test indicates that matrices can be reused up to five times without loss of performance. The DEAE+-CDW matrix was efficient for the removal of color from a real textile effluent reaching an UV-Visible spectral area decrease of 93% when applied in a proportion of 15 g ion exchanger matrix L-1 of colored wastewater, even in the case of the parallel presence of 50 g L-1 of mordant salts in the waste water. The wide range of colored matter removal by the synthesized matrices varied from 40.27 to 98.65 mg g-1 of ionized matrix, obviously depending in each particular chemical structure of the dye upon adsorption.