Protein-DNA interactions are critical for the successful functioning of all natural systems. The key role in these interactions is played by processes of protein search for specific sites on DNA. Although it has been studied for many years, only recently microscopic aspects of these processes became more clear. In this work, we present a review on current theoretical understanding of the molecular mechanisms of the protein target search. A comprehensive discrete-state stochastic method to explain the dynamics of the protein search phenomena is introduced and explained. Our theoretical approach utilizes a first-passage analysis and it takes into account the most relevant physical-chemical processes. It is able to describe many fascinating features of the protein search, including unusually high effective association rates, high selectivity and specificity, and the robustness in the presence of crowders and sequence heterogeneity.

The transmission of light is one of the key optical processes in the terrestrial environment (the atmosphere and underlying surfaces). The dependence of light transmittance on the illumination/observation conditions and optical properties of the atmosphere–underlying system can be studied using the integro-differential radiative transfer equation. However, for numerous applications a set of analytical equations is needed to describe the transmitted light intensity and flux. In this paper, we describe various analytical techniques to study light transmittance through light scattering and absorbing media. A physical significance and improved mathematical accuracy of approximations are provided using the analytical models for the diffusion exponent, average cosine of the light field, spherical and plane albedos. The accuracy of various approximations is studied using exact radiative transfer calculations with various scattering phase functions, single-scattering albedos, observational conditions, and optical depths.

FRAP technique have been used for decades to measure movements of molecules in 2D. Data obtained by FRAP experiments in cell plasma membranes are assumed to be described through means of two parameters, a diffusion coefficient D (as defined in a pure Brownian model) and a mobile fraction M. Nevertheless, it has also been shown that recoveries can be nicely fit using anomalous sub-diffusion. FRAP at variable radii has been developed using the Brownian diffusion model to access geometrical characteristics of the surrounding landscape of the molecule. Here we performed numerical simulations of continuous time random walk (CTRW) anomalous subdiffusion and interpreted them in the context of variable radii FRAP. These simulations were compared to experimental data obtained at variable radii on living cells using the PH domain of the membrane binding protein EFA6 (exchange factor for ARF6, a small G protein). This protein domain is an excellent candidate to explore the structure of the interface between cytosol and plasma membrane in cells. By direct comparison of our numerical simulations to the experiments, we show that this protein does not exhibit anomalous diffusion in BHK cells. The non Brownian PH-EFA6 dynamics observed here is more related to spatial heterogeneities such as cytoskeleton fences effects.

This paper studies the spatial joint evolution of cooperative behavior and a partially assortative matching institution that protects cooperators. We consider cooperation as characterized by a cultural trait transmitted via an endogenous socialization mechanism a la Bisin and Verdier (2001) and we assume that such trait can diffuse randomly in space due to some spatial noise in the socialization mechanism. Using mathematical techniques from reaction-diffusion equations theory, we show that, under some conditions, an initially localized domain of preferences for cooperation can invade the whole population and characterize the asymptotic speed of diffusion. We consider first thecase with exogenous assortativeness, and then endogeneize the degree of social segmentation in matching, assuming that it is collectively set at each point of time and space by the local community. We show how relatively low cost segmenting institutions can appear in new places thanks to the spatial random diffusion of cooperation, helping a localized cultural cluster of cooperation to invade the whole population. The endogenous assortative matching institution follows a life cycle process : appearing, growing and then disappearing once a culture of cooperation is suffciently established in the local population.

Alternative fuel vehicles, such as battery electric vehicles and hydrogen fuel cell vehicles, support the imperative to decarbonise the transport sector, but are not yet at a stage in their development where they can successfully compete with conventional fuel vehicles. This paper examines the influence of knowledge and persuasion on the decision to adopt or reject alternative fuel vehicles, underpinned by Rogers’ Diffusion of Innovations theory. A household questionnaire survey was undertaken with respondents in the Sutton Coldfield suburb of the United Kingdom city of Birmingham. This suburb was previously identified as having a strong spatial cluster of potential early adopters of alternative fuel vehicles. The results confirm that among respondents the knowledge of alternative fuel vehicles was limited and perceptions have led to the development of negative attitudes towards them. The reasons largely relate to three problems: purchase price, limited range, and poor infrastructure availability. The majority of respondents have passively rejected alternative fuel vehicles, such that they have never given consideration to adoption. This confirms that a concerted effort is required to inform the general public about alternative fuel vehicles.

Due to the complexity, high-risk, and conservative character of construction companies, advanced digital technologies do not become widely adopted in the short term, while vendors make determined efforts to overcome this and disseminate their technologies. This paper presents the methods of an investigation addressing the extremely complex issues related to the current practices of digital technology adoption in construction. It discusses how construction companies follow a specific logical process linked to need, project objectives, characteristics of the adopting organization, and the characteristics of the new technology to be adopted. The study aims to demonstrate a novel method of data collection and analysis including data and methodological triangulation techniques including the use of NVivo and AHP to explore how companies make the decision to uptake a new technology (e.g. advanced crane, tunnel boring machine or drones) by focusing on customer and vendor activities, their interactions, contributing factors, and people involved in the process. The major original contribution of this paper is to develop an innovative methodological Cube for investigating the Construction Technology Adoption Process (CTAP) covering technology adoption, acceptance, diffusion and implementation concepts. CTAP is a framework that delineates the phases of the process that customer organizations use when deciding to adopt a new digital technology and the parallel vendor activities. The significance of these contributions is that they enable vendors to understand how to match their strategies with customer expectations in each phase of the CTAP. It also provides a benchmark for new construction companies to use the current best practice of decision making. Future research is warranted to more clearly delineate any differences with developing nations or related industries such as mining and property management.

We extended the usage of the expansion method based on Sine-Gordon equation to the two dimensional Fisher equation. The relation between the trigonometric and hyperbolic functions are derived from the Sine-Gordon equation dened in two space dimension. The complex-valued traveling wave solutions to the two dimensional Fisher and Nagumo equations are set in forms a nite series of multiplications of powers of sech(.) and tanh(.) functions.

Master equations define the dynamics that govern the time evolution of various physical processes on lattices. In the continuum limit, master equations lead to Fokker-Planck partial differential equations that represent the dynamics of physical systems in continuous spaces. Over the last few decades, nonlinear Fokker-Planck equations have become very popular in condensed matter physics and in statistical physics. Numerical solutions of these equations require the use of discretization schemes. However, the discrete evolution equation obtained by the discretization of a Fokker-Planck partial differential equation depends on the specific discretization scheme. In general, the discretized form is different from the master equation that has generated the respective Fokker-Planck equation in the continuum limit. Therefore, the knowledge of the master equation associated with a given Fokker-Planck equation is extremely important for the correct numerical integration of the latter, since it provides a unique, physically motivated discretization scheme. This paper shows that the Kinetic Interaction Principle (KIP) that governs the particle kinetics of many body systems, introduced in [G. Kaniadakis, Physica A 296, 405 (2001)], univocally defines a very simple master equation that in the continuum limit yields the nonlinear Fokker-Planck equation in its most general form.

Many empirical and theoretical studies indicate that Brownian motion and diffusion models as its mean field counterpart provide appropriate modelling techniques for individual insect movement. However, this traditional approach has been challenged and conflicting evidence suggests that an alternative movement pattern such as Lévy walks can provide a better description. Lévy walks differ from Brownian motion since they allow for a higher frequency of large steps, resulting in a faster movement. Identification of the ‘correct’ movement model that would consistently provide the best fit for movement data is challenging and has become a highly controversial issue. In this paper, we show that this controversy may be superficial rather than real if the issue is considered in the context of trapping or, more generally, survival probabilities. In particular, we show that almost identical trap counts are reproduced for inherently different movement models (such as the Brownian motion and the Lévy walk) under certain conditions of equivalence. This apparently suggests that the whole ‘Levy or diffusion’ debate is rather senseless unless it is placed into a specific ecological context, e.g. pest monitoring programmes.

Current education in biology is devoid of mathematics in many countries, probably because many relevant biological processes are explained from a qualitative point of view rather than addressing the quantitative aspects of these phenomena. Here, we employ a case study from the yeast physiology to illustrate the importance of numeracy skills for a deeper understanding of relevant biological problems. Yeast anaerobic growth on sugars is a widespread process as it is the basis for beer, bread, and winemaking and it is much akin to lactic acid fermentation in muscle cells in response to an increased energy demand. To study the physiology of yeasts under controlled conditions and being able to compare the results quantitatively, one ought to perform measurements and calculations involving concentrations of oxygen, biomass, and organic compounds. To set-up an “anaerobic” culture of Saccharomyces cerevisiae in a defined medium, one needs to calculate how much oxygen must enter the cultivation system, to meet the requirements for ergosterol and oleic acid biosyntheses, both of which require oxygen. Using basic physicochemical principles and simple mathematical skills, students will be able to compute the oxygen requirement for yeast growth under such “anaerobic” conditions.

In advanced world stroke is one of the disabling cause of death that can be managed with thrombolysis if presents early despite further risk of intracerebral haemorrhage. Secondary prevention is an important objective in ischaemic stroke where recurrence is very high with subsequent stroke. Carotid End Arterectomy impact a definitive and effective role for both symptomatic and asymptomatic carotid stenosis for secondary stroke prevention in selective cases. Thrombolysis is a potential primary management for certain group whereas carotid surgery employs secondary preventative measure in a specified ischaemic stroke group.

Magnetic nanoparticles are met across many biological species ranging from magnetosensitive bacteria, fishes, bees, bats, rats, birds, to humans. They can be both of biogenetic origin and due to environmental contamination, being either in paramagnetic or ferromagnetic state. The energy of such naturally occurring single-domain magnetic nanoparticles can reach up to 10-20 room k_BT in the magnetic field of the Earth, which naturally led to supposition that they can serve as sensory elements in various animals. This work explores within a stochastic modeling framework a fascinating hypothesis of magnetosensitive ion channels with magnetic nanoparticles serving as sensory elements, especially, how realistic it is given a highly dissipative viscoelastic interior of living cells and typical sizes of nanoparticles possibly involved.

Using a nonclassical symmetry of nonlinear reaction-diffusion equations, some exact multi-dimensional time-dependent solutions are constructed for a fourth-order Allen-Cahn-Hilliard equation. This models a phase field that gives a phenomenological description of a two-phase system near the critical temperature. Solutions are given for the changing phase of a cylindrical or spherical inclusion, allowing for a 'mushy zone' with mixed state that is controlled by imposing a pure state at the boundary. The diffusion coefficients for transport of one phase through the mixture, depend on the phase field value, since the physical structure of the mixture depends on the relative proportions of the two phases. A source term promotes stability of both of the pure phases but this tendency may be controlled or even reversed through the boundary conditions.

Aiming at the industrial scale development of a Scandium (Sc)-selective leaching process of Bauxite Residue (BR), a sufficiently numerous set of process design aspects has been investigated, by appropriate exploitation of available experimental data. The interpretation of experimental data for Sc leaching yield, with sulfuric acid as the leaching solvent, has shown significant impact from acid feed concentration, mixing residence time, liquid to solids ratio, and times of leachate re-usage onto fresh BR. The thin film diffusion model, as the fundamental theory for leaching, either with constant particle size for selective leaching, or with shrinking particle size for less-, or non-, selective leaching, interprets sufficiently well the relevant experimental data. In both cases, a concept for an unyielding core supplements the basic model. Especially for the selective leaching mild conditions, the simplest model version keeps step with the experiments, since both prove 1^st order kinetics, while especially for the extreme conditions including very low solvent excess, it is proposed a combined conversion rate model with diffusion and chemical reaction inside particles. The maximization of Sc recovery per unit of consumed solvent (i.e., specific recovery) emerged as highly critical for the process economics.

In this paper, the nanoscale dissipative mechanisms of a Cu pad in a Ball Grid Array (BGA) packaging structure during isothermal ageing and uniaxial tension were investigated by the molecular dynamics (MD) method and experiments. From the result of the isothermal ageing test, a nonuniform consumption of Cu and large amount of Kirkendall voids were observed at the interface of Cu and Cu₃Sn. To study the effect of pressure and orientation on this phenomenon, MD simulations were conducted on four types of Cu-Cu₃Sn interface structures with different orientations of Cu. By comparing the diffusion coefficients of atoms in those cases, it was found that the tensile stress would inhibit the diffusion of atoms, whereas compressive stress would accelerate it, and this would be more significant under a larger magnitude of stress and temperature. Note that, in the model with the (101) surface Cu at the interface, both Cu and Cu₃Sn have a higher diffusion coefficient compared with the model with (001) surface Cu. Thus, the orientation of Cu will also contribute to the uniform consumption of the pad. Uniaxial tension simulation combined with DXA and CSP analyses on those models also shows the model with (001) surface Cu has a greater mechanical reliability in our simulations and related experiments.

Complex and real valued exact solutions to some reaction-diffusion equations are suggested by using homogeneous balance and Sine-Gordon equation expansion method. The predicted solution of finite series of some hyperbolic functions are determined by using some relations between the hyperbolic functions and trigonometric functions based on Sine-Gordon equation and traveling wave transform. The Newel-Whitehead-Segel and Zeldovich equations are solved explicitly. Some real valued solutions are depicted for some particular choice of parameters.

We propose a wave-like design on the surface of cathode channels (wave form cathode channels) to improve oxidant delivery to gas diffusion layers (GDLs) [1-2]. We performed experiments using PEMFCs combined with wave form surface design on cathodes. We varied the factors of the distance between wave-bumps (the Adhesive distance, AD), and the size of the wave-bumps (the Expansion ratio, ER). The ADs are 3, 4, and 5 times the size of the half-circle bump’s radius, and the ERs are 1/1.5, 1/2, and 1/3 times the channel’s height. We evaluated the performances of the fuel cells, and compared the current-voltage (I-V) relations. For comparison, we prepared PEMFCs with conventional flat-surfaced oxygen channels. Our aim in this work is to identify fuel cell operation by modifying the surface design of channels, and ultimately to find the optimal design of cathode channels that will maximize fuel cell performance.

Pulsed-field gradient (PFG) diffusion experiments can be used to measure anomalous diffusion in many polymer or biological systems. However, it is still complicated to analyze PFG anomalous diffusion, particularly the finite gradient pulse width (FGPW) effect. In practical applications, the FGPW effect may not be neglected such as in clinical diffusion magnetic resonance imaging (MRI). Here, two significantly different methods are proposed to analyze PFG anomalous diffusion: the effective phase shift diffusion equation (EPSDE) method and an observing the signal intensity at the origin method. The EPSDE method describes the phase evolution in virtual phase space, while the method to observe the signal intensity at the origin describes the magnetization evolution in real space. However, these two approaches give the same general PFG signal attenuation including FGPW effect, which can be numerically evaluated by a direct integration method. The direct integration method is fast and without overflow. It is a convenient numerical evaluation method for Mittag-Leffler function type PFG signal attenuation. The methods here provide a clear view of spin evolution under field gradient, and their results will help the analysis of PFG anomalous diffusion.

In this paper we present the measurement of charged pion two-particle femtoscopic correlation functions in $\sqrt{S_{NN}}$= 200 GeV Au+Au collisions, in 31 average transverse mass bins, separately for positive and negative pion pairs. Lévy-shaped source distributions yield a statistically acceptable description of the measured correlation functions, with three physical parameters: correlation strength parameter λ , Lévy index α and Lévy scale parameter R. The transverse mass dependence of these Lévy parameters is then investigated. Their physical interpretation is also discussed, and the appearance of a new scaling variable is observed.

This work deals with the numerical investigation of the delivery of potential therapeutic agents through dentinal discs (i.e. a cylindrical segment of the dentinal tissue) towards the dentin-pulp junction. The aim is to assess the main key features (i.e. molecular size, initial concentration, consumption rate, disc porosity and thickness) that affect the delivery of therapeutic substances to the dental pulp and consequently to define the necessary quantitative and qualitative issues related to a specific agent before its potential application in clinical practice. The CFD code used for the computational study is validated with relevant experimental data obtained using micro Laser Induced Fluorescence (μ-LIF) a non-intrusive optical measuring technique. As the phenomenon is diffusion dominated and strongly dependent on the molecular size, the time needed for the concentration of released molecules to attain a required value can be controlled by their initial concentration. Finally, a model is proposed which, given the maximum acceptable time for the drug concentration to attain a required value at the pulpal side of the tissue along with the aforementioned key design parameters, is able to estimate the initial concentration to be imposed and vice versa.

In this paper, some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation are deduced. We start with the Mellin-Barnes representation of the fundamental solution that was derived in the previous publications of the author. The Mellin-Barnes integral is used to get two new representations of the fundamental solution in form of the Mellin convolution of the special functions of the Wright type. Moreover, some new closed form formulas for particular cases of the fundamental solution are derived. In particular, we solve an open problem of representation of the fundamental solution to the two-dimensional neutral-fractional diffusion-wave equation in terms of the known special functions.

Almost all modern inorganic light-emitting diode (LED) designs are based on double heterojunctions (DHJs) whose structure and current injection principle have remained essentially unchanged for decades. Although highly efficient devices based on the DHJ design have been developed and commercialized for energy-efficient general lighting, the conventional DHJ design requires burying the active region (AR) inside a pn-junction. This has hindered the development of emitters utilizing nanostructured ARs located close to device surfaces such as nanowires or surface quantum wells. Modern DHJ III-N LEDs also exhibit resistive losses which arise from the DHJ device geometry. The recently introduced diffusion-driven charge transport (DDCT) emitter design offers a novel way to transport charge carriers to unconventionally placed ARs. In a DDCT device, the AR is located apart from the pn-junction and the charge carriers are injected into the AR by bipolar diffusion. This device design allows the integration of surface ARs to semiconductor LEDs and offers a promising method to reduce resistive losses in high power devices. In this work, we present a review of the recent progress in gallium nitride (GaN) based DDCT devices, and an outlook of potential DDCT has for opto- and microelectronics.

The biophysical consequences of nanoscale curvature have been challenging to resolve due to size-dependent membrane behavior and the experimental resolution limits imposed by optical diffraction. Recent advances in nanoengineering and super-resolution techniques have enabled new capabilities for creating and observing curvature. In particular, draping supported lipid bilayers over lithographically patterned substrates provides a model system for endocytic pits. The experiments and simulations presented below describe the possible detection of membrane curvature through fluorescence recovery after photobleaching (FRAP), fluorescence correlation spectroscopy (FCS), single particle tracking (SPT), and polarized localization microscopy (PLM). FRAP and FCS depend on diffraction-limited illumination and detection. In particular, a simulation of FRAP shows no effects on lipids diffusion due to a 50 nm diameter membrane bud at any stage in the budding process. Simulated FCS demonstrated small effects due to a 50 nm radius membrane bud that was amplified with curvature-dependent lipid mobility changes. However, PLM and SPT achieve sub-diffraction-limited resolution of membrane budding and lipid mobility through the identification of the single-lipid positions with ≤15 nm spatial and ≤20 ms temporal resolution. By mapping the single-lipid step lengths to locations on the membrane, the effects of curvature on lipid behavior have been resolved.

Background: Early identification and prevention of hypoxic ischemic encephalopathy (HIE) may reduce neonatal mortality and morbidity. Objective: We aimed to correlate between urinary Activin-A and MRI (conventional and Diffusion-weighted) and the severity of HIE in full-term neonates. Methods: Forty-five full-term neonates with HIE admitted to NICU and 15 normal neonates were enrolled into the study. The concentration of urinary Activin-A was determined using enzyme immunoassay kits and MRI were done. Correlations between urinary Activin-A and MRI with the degree of HIE were done. Results: Urinary Activin-A levels were significantly higher in neonates with HIE than controls (P<0.001). It was positively correlated with the clinical grading of HIE and a cutoff value of 0.08µg/l on day-1 after birth had a sensitivity of 98.6% and specificity of 97.1% for prediction of HIE. DW-MRI detected HIE with a high sensitivity (85%) compared to the low sensitivity of conventional MRI (35%). An ADC value of ≤ 0.8 was the best sensitivity-specificity cutoff point for detecting severe ischemic injury. DW-MRI imaging was positively correlated with Urinary Activin-A and both of them were positively correlated with the clinical grades of HIE (P < 0.001). Conclusions: DW-MRI imaging is correlated well with urinary Activin-A in full-term neonates with HIE and both of them are correlated with the degree of HIE. Early determination of urinary Activin-A combined with DW-MRI imaging can early detect HIE and its severity in full-term neonates with HIE.

In wireless sensor networks (WSNs), each sensor node can estimate the global parameter from the local data in distributed manner. This paper proposed a robust diffusion estimation algorithm based on minimum error entropy criterion with self-adjusting step-size, which are referred to as diffusion MEE-SAS (DMEE-SAS) algorithm. The DMEE-SAS algorithm has fast speed of convergence and is robust against non-Gaussian noise in the measurements. The detailed performance analysis of the DMEE-SAS algorithm is performed. By combining the DMEE-SAS with diffusion minimum error entropy (DMEE) algorithms, an Improving DMEE-SAS algorithm is proposed, in non-stationary environment where tracking is very important. The Improving DMEE-SAS algorithm can avoid insensitivity of the DMEE-SAS algorithm due to the small effective step-size near the optimal estimator, and obtain a fast convergence speed. Numerical simulations are given to verify the effectiveness and advantages of these proposed algorithms.

The separation of sister chromatids during anaphase is the culmination of mitosis and one of the most strikingly beautiful examples of cellular movement. It consists of two distinct processes: Anaphase A, the movement of chromosomes toward spindle poles via shortening of the connecting fibers, and anaphase B, separation of the two poles from one another via spindle elongation. I focus here on anaphase A chromosome-to-pole movement. The chapter begins by summarizing classical observations of chromosome movements, which support the current understanding of anaphase mechanisms. Live cell fluorescence microscopy studies showed that poleward chromosome movement is associated with disassembly, or ‘melting’ of the kinetochore-attached microtubule fibers that link chromosomes to poles. Microtubule-marking techniques established that kinetochore-fiber disassembly often occurs through a ‘pac-man’ mechanism, where tubulin subunits are lost from kinetochore-attached plus ends and the kinetochore appears to consume its microtubule track as it moves poleward. In addition, kinetochore-fiber disassembly in many cells occurs partly through ‘flux’, where the microtubules flow continuously toward the poles and tubulin subunits are lost from minus ends. Molecular mechanistic models for how load-bearing attachments are maintained to disassembling microtubule ends, and how the forces are generated to drive pac-man and flux-based movements, are discussed.

The aim of this work is to present a design approach of a Shock-Induced Combustion Ramjet (Shcramjet) inlet, and present its optimization in terms of the flow and geometrical parameters. The flow properties of mixed compression type inlet of a Shcramjet are examined using analytical and numerical techniques. The geometries obtained with variations in the wedge angles, length, height and cowl lip positions are used to study the flow characteristics of inlet, identifying bow shock temperature ratio as the optimization parameter. The two-dimensional geometries of two-shock and three-shock inlet models designed analytically for shock-on-lip condition at Mach 12.5 and an altitude of 32.5 km are numerically simulated in OpenFOAM CFD Toolbox. A density based compressible CFD solver based on central upwind schemes of Kurganov and Tadmore is used to solve 2D inviscid Euler equations. The inlet total pressure recovery is expressed as a function of temperature ratios of compression shocks, and is found to have a maxima at a bow shock temperature ratio at the design condition when the bow and external shocks have equal strengths. The effect of considering the flow to be calorically imperfect is studied numerically, and the deviation from the analytical design is presented.

Tissue-like phantoms are widely used as a model for mimicking the optical properties of live tissue. This paper presents the results of a diffusion reflection method as well as fluorescence lifetime imaging microscopy measurements of fluorescein-conjugated gold nanorods in solution as well as inserted in solid tissue-imitating phantoms. A lack of consistency between the fluorescence lifetime results of the solutions and the phantoms raises a question about the ability of tissue-like phantoms to maintain the optical properties of inserted contrast agents.

In this paper we report a new development on the numerical model for aluminum-steam combustion. This model is based on diffusion flame of continuum regime and the thermal equilibrium between the particle and the flow field, which can be used to calculate the aluminum particle combustion model for two phase calculation conditions. The model prediction is in good agreement with the experimental data. A new type of vortex combustor was proposed for the combustion of aluminum and steam, and the mathematical model of the two phase reacting flow with in this combustor was established. The turbulence effects are modeled using the Reynolds Stress Model (RSM) with Linear Pressure-Strain approach, and the Eddy-Dissipation model is used to simulate the gas phase combustion. Aluminum particles are injected into the vortex combustor and form a swirling flow around the chamber and their trajectories are traced using the Discrete Phase Model (DPM). The simulation results show that the vortex combustor can achieve high efficient combustion of aluminum and steam. The influencing factors, such as the eccentric distance of the inlet of aluminum particles, particle size and steam inlet diameter, etc., are studied. The work described in this paper represents an attempt to the design of a vortex combustor in order to increase aluminum combustion efficiency.