A theoretical study of the effect of intraventricular pulsations on the pathogenesis of hydrocephalus

Hydrocephalus, a condition which affects thousands of people annually in the US alone, arises as a result of a build-up of cerebrospinal fluid (CSF) in the brain’s ventricular cavity due to an imbalance between the rates of CSF production and absorption. Although the earliest known instances of hydrocephalus date back to the time of Hippocrates, the pathophysiology of hydrocephalus is still poorly understood, and is the subject of active debate in the literature. Recently, the pulsations of the cerebrospinal fluid have been suggested as a possible mechanism for ventricular expansion. In this paper, we attempt to determine the significance of these pulsations in the development of hydrocephalus by simulating their mechanical effects on the brain. The brain parenchyma is modelled as a fractional Zener viscoelastic solid, which extends the work previously presented in Sivaloganathan et al. [S. Sivaloganathan, M. Stastna, G. Tenti, J. Drake, A viscoelastic model of the brain parenchyma with pulsatile ventricular pressure, Appl. Math. Comput. 165 (2005) 687-698]. Explicit solutions for the displacement and stresses are obtained by solving the boundary value problems corresponding to the cases of infant and adult hydrocephalus. As expected, when the cranial vault is a rigid container, as in adult hydrocephalus, very small displacements are predicted.     

Fluid Structure Interaction of Blood Vessels in Circle of Willis

This work involves studying the role of the Brain Blood Barriers (BBB) on damping the stress applied on brain tissue through blood pressure that is the main cause of brain aneurysm. The numerical simulations are focused on the geometry of the Anterior Communicating Artery (ACoA) because there is a 30 % higher probability for a brain aneurysm in this location. A linear elastic model is used to model the structure part including BBB and brain tissue. Regarding the fluid properties, blood is assumed to behave as a Newtonian fluid. The stress and deformation of the brain tissue is analyzed. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effective partitioning method for computing generalized inverses and their gradients

We extend the algorithm for computing {1}, {1, 3}, {1, 4} inverses and their gradients from [11] to the set of multiple-variable rational and polynomial matrices. An improvement of this extension, appropriate to sparse polynomial matrices with relatively small number of nonzero coefficient matrices as well as in the case when the nonzero coefficient matrices are sparse, is introduced. For that purpose, we exploit two effective structures form [6], which make use of only nonzero addends in polynomial matrices, and define their partial derivatives. Symbolic computational package MATHEMATICA is used in the implementation. Several randomly generated test matrices are tested and the CPU times required by two used effective structures are compared and discussed.     

Effect of aligned magnetic field on the steady viscous flow past a circular cylinder

The steady viscous incompressible and slightly conducting fluid flow around a circular cylinder with an aligned magnetic field is simulated for the range of Reynolds numbers 100 ? Re ? 500 using the Hartmann number, M. The multigrid method with defect correction technique is used to achieve the second order accurate solution of complete non-linear Navier–Stokes equations. The magnetic Reynolds number is assumed to be small. It is observed that volume of the separation bubble decreases and drag coefficient increases as M is increased. We noticed that the upstream base pressure increases slightly with increase of M whereas downstream base pressure decreases with increase of M. The effect of the magnetic field on the flow is discussed with contours of streamlines, vorticity, plots of surface pressure and surface vorticity.     

Investigation of secondary flow on an infinite yawed cylinder with 15 per cent. Thick Joukowski profile as section

This paper contains a theoretical investigation of the secondary flow in the laminar incompressible boundary layer on an infinite yawed cylinder with chordwise section as Joukowski profile of 15 per cent. thickness at zero incidence and with homogeneous suction, the suction mass flow coefficient being equal to 0·2085. The secondary flow profiles are obtained at different points of the wing section and for various angles of sweepback. It is found that in favourable pressure gradients and at pressure minimum, the secondary flow profiles have negative values. In regions of adverse pressure gradients after the pressure minimum the secondary flow changes sign from negative to positive values and have points of inflexion. The change of sign starts from the surface and extends to the edge of the boundary layer downstream. At some points in adverse pressure gradients the secondary flow profiles have double points of inflexion and values of both signs simultaneously. It is also found that an adverse pressure gradient produces more powerful secondary flow than a favourable pressure gradient of the same strength.     

Numerical computation of end plate effect on Taylor vortices between rotating conical cylinders

End plate effect on Taylor vortices between rotating conical cylinders is studied by numerical method in this paper. We suppose that the inner cone rotates together with the end plate at the top and the outer one as well as the end plate at the bottom remains at rest. It is found that the instability sets in at a critical Reynolds number about Re = 80. Increase Re to about Re = 200 the first single clockwise vortex is formed near the top of the flow system. Further increase Re to about Re = 440 another clockwise vortex is formed under the first one. At about Re = 448 the third vortex is formed which rotates in counterclockwise direction between the first two vortices. With increasing of Re the process continues. Finally, a configuration is obtained with an odd number of vortices in the annulus at about Re = 700, which confirms the experimental observation. Moreover, the local extreme values of pressure and velocity are achieved at the adjacent lines between neighboring vortices or at the medium lines of vortices. The effect of gap size on vortices is also considered. It is shown that the number of vortices increases with decreasing of the gap size and the end plates play an important role in the parity of the number of the vortices.     

A Liouville-type theorem for the p-Laplacian with potential term

In this paper we prove a sufficient condition, in terms of the behavior of a ground state of a singular p  -Laplacian problem with a potential term, such that a nonzero subsolution of another such problem is also a ground state. Unlike in the linear case (p=2$p=2$), this condition involves comparison of both the functions and of their gradients.     

Multiphasic modelling of human brain tissue for intracranial drug-infusion studies

A direct intracranial infusion of a therapeutic solution into the extra-vascular space of human brain tissue is a promising medical application for the effective treatment of malignant brain tumours [1]. The advantage of this method, compared to an intra-vascular medication, is the targeted delivery with the circumvention of the blood-brain barrier (BBB), which prohibits the passing of therapeutic macro-molecules across the vascular walls into the brain parenchyma. The prediction of the resulting therapeutical distribution by a numerical simulation is challenging, since the spreading is affected by the complex nature of living brain tissue. For this purpose, a macroscopic continuum-mechanical model is established within the Theory of Porous Media (TPM), proceeding from a homogenisation of the underlying micro-structure [5]. The ternary four-component model consists of an elastically deformable solid skeleton (composed of tissue cells and vascular walls), which is perfused by two mobile but separated liquid phases, the blood and the overall interstitial fluid (treated as a real two-component mixture of the liquid solvent and the dissolved therapeutic solute). The strongly coupled solid-liquid-transport problem is simultaneously approximated in all primary unknowns using mixed finite elements (uppc-formulation) and consequently solved in a monolithic manner with an implicit time-integration scheme. This numerical investigation allows the computational study of several circumstances influencing the irregular distribution of infused drugs, as observed in clinical studies. Therefore, the microstructural perfusion characteristics in the extra-cellular space of the white-matter tracts are considered by a spatial diversification of the anisotropic permeability tensors, provided by Diffusion Tensor Imaging (DTI). Furthermore, Magnetic Resonance Angiography (MRA) enables the in vivo location of blood vessels within the brain tissue. Finally, the selection of appropriate material parameters has a crucial influence on the drug distribution profile and further occurring effects beyond. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Pressure and flow in two dimensional numerical bifurcation models

The finite element method has been used to solve the Navier-Strokes equations for steady flow conditions in bifurcations. The results are presented as pressure, velocity and streamline plots at different Reynolds number. The three bifurcations considered have rigid walls and bifurcation angles of 0°, 20° and 180°. For the bifurcation with branch angles 0° and 20° there is flow separation along the inner wall of the outlet branches and large spatial pressure variations, these phenomena being more pronounced at the higher Reynolds numbers. For the bifurcation with a branch angle of 180° the high pressure gradients occured at the outer corner and for the high Reynolds number a vortex formation developed downstream of this corner.     

Analyses on 3-D gas flow and heat transfer in ladle furnace lid

In order to verify the reasonableness of off-gas pressure and wall temperature, a mathematical model for gas flow and heat transfer in ladle furnace (LF) lid is developed based on 3-D Navier–Stokes equations and k–ε two equation turbulent models as well as energy conservation equation. The gas velocity vector distribution of skirt clearance between the top edge of ladle and furnace lid and electrode gaps between three graphite electrodes and furnace lid, the gas flow line distribution, pressure and temperature distribution on the furnace lid wall are simulated. Simulation results show that appropriate off-gas pressures are 200 Pa, 200 Pa and 150 Pa when electric arc emerges from molten steel surface and alloy hole is unsealed, electric arc emerges from molten steel surface and alloy hole is closure, electric arc immerges into molten steel surface and alloy hole is closure, respectively. The maximum temperature presents in the middle of LF lid in all of heating conditions, and the temperature value are 563, 603 and 343 K. Finally, the relations between gas volume and off-gas pressure are analyzed in different width of skirt clearance, and some relevant mathematical expressions are obtained. By comparing both simulation results and practical data, the advice on reducing off-gas pressure is proposed, and the maximum temperatures of furnace lid wall have good agreement with actual data.     

Exact and approximation algorithms for the min–max k-traveling salesmen problem on a tree

Given k identical salesmen, where k ? 2 is a constant independent of the input size, the min–max k-traveling salesmen problem on a tree is to determine a set of k tours for the salesmen to serve all customers that are located on a tree-shaped network, so that each tour starts from and returns to the root of the tree with the maximum total edge weight of the tours minimized. The problem is known to be NP-hard even when k = 2. In this paper, we have developed a pseudo-polynomial time exact algorithm for this problem with any constant k ? 2, closing a question that has remained open for a decade. Along with this, we have further developed a (1 + ?)-approximation algorithm for any ? > 0.     

A Porous Media Model to Describe the Behaviour of Brain Tissue

The human brain is a very sensitive organ. Even small changes in the cranium cavity can cause life–threatening effects. In case of medical intervention, biomechanics can assist the therapy decisions by simulating the physical behaviour of brain tissue, e.g., the coupled interaction of the fluid motion and the deformation of the brain tissue. In the context of the Theory of Porous Media (TPM), a convenient model of the brain is introduced, which is able to simulate essential mechanical effects in the porous structure of the brain material. The fluid–saturated brain can be treated as an immiscible binary mixture of constituents. In this macroscopic biphasic model, the mixture consists of a solid phase (brain tissue) and a fluid phase (interstitial fluid or blood plasma). Both constituents are assumed to be materially incompressible. The resulting set of coupled partial differential equations is then spatially discretised using mixed finite elements with a backward Euler time integration. Numerical examples are presented illustrating the fundamental effects on the brain tissue under heart–rate dependent pulsative pressure variations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Time-dependent magnetothermoelastic creep modeling of FGM spheres using method of successive elastic solution

Magnetothermoelastic creep behavior of thick-walled spheres made of functionally graded materials (FGM) placed in uniform magnetic and distributed temperature fields and subjected to an internal pressure is investigated using method of successive elastic solution. The material creep, magnetic and mechanical properties through the radial graded direction are assumed to obey the simple power law variation. Using equations of equilibrium, stress-strain and strain-displacement a differential equation, containing creep strains, for displacement is obtained. A semi-analytical method in conjunction with the Mendelson’s method of successive elastic solution has been developed to obtain history of stresses and strains. History of stresses, strains and effective creep strain rate from their initial elastic distribution at zero time up to 55 years are presented in this paper. Stresses, strains and effective creep strain rate are changing in time with a decreasing rate so that after almost 50 years the time-dependent solution approaches the steady state condition when there is no distinction between stresses and strains at 50 and 55 years.     

Modeling of mixed liquor inorganic suspended solids and membrane flux at different ratio of SRT to HRT in a submerged membrane bioreactor

In order to investigate the influence of mixed liquor inorganic suspended solids (MLISS) on membrane flux at different ratio of sludge retention time (SRT) to hydraulic retention time (HRT) in a submerged membrane bioreactor (SMBR), a pilot scale test was conducted for 452 days using traditional Chinese medicine (TCM) wastewater as influent. SRT/HRT was controlled at 150, 480 and 750, respectively. The experimental results showed that the average values of MLISS were 1271.9, 1664.5 and 6898.8 mg/L at different SRT/HRT, respectively; MLISS were accumulated from 265.5 g/h to 4912.93 g/h, which indicated that SMBR could not steadily operate for a long period without sludge withdrawal. Sludge oxygen utilized rate (SOUR) decreased from 5.115 to 1.292 mgO₂/(gVSS h) and volume oxygen utilized rate (VOUR) increased from 10.84 to 18.13 mgO₂/(L h). Model of membrane flux and MLISS were developed under different temperature and operational pressure by regressions, which were then satisfactorily employed to predict the trend of membrane flux during the experiment.     

A novel group ranking model for revealing sequence and quantity knowledge

The aggregation of individuals’ preferences into a consensus ranking is a group ranking problem which has been widely utilized in various applications, such as decision support systems, recommendation systems, and voting systems. Gathering the comparison of preferences and aggregate them to gain consensuses is a conventional issue. For example, b > c ? d ? a indicates that b is favorable to c, and c (d) is somewhat favorable but not fully favorable to d (a), where > and ? are comparators, and a, b, c, and d are items. Recently, a new type of ranking model was proposed to provide temporal orders of items. The order, b&c → a, means that b and c can occur simultaneously and are also before a. Although this model can derive the order ranking of items, the knowledge about quantity-related items is also of importance to approach more real-life circumstances. For example, when enterprises or individuals handle their portfolios in financial management, two considerations, the sequences and the amount of money for investment objects, should be raised initially. In this study, we propose a model for discovering consensus sequential patterns with quantitative linguistic terms. Experiments using synthetic and real datasets showed the model’s computational efficiency, scalability, and effectiveness.     

Precise Spectral Asymptotics for the Dirichlet Problem − u″(t) + g(u(t)) = λsinu(t)

We consider the nonlinear eigenvalue problem on an interval−u″(t)+g(u(t))=λsinu(t),u(t)>0,t∈I:=(−T,T),u(±T)=0,where λ > 0 is a parameter and T > 0 is a constant. It is known that if λ ? 1, then the corresponding solution has boundary layers. In this paper, we characterize λ by the boundary layers of the solution when λ ? 1 from a variational point of view. To this end, we parameterize a solution pair (λ, u) by a new parameter 0 < ?< T, which characterizes the boundary layers of the solution, and establish precise asymptotic formulas for λ(?) with exact second term as ? → 0. It turns out that the second term is a constant which is explicitly determined by the nonlinearity g.     

Equivalent definitions of BV space and of total variation on metric measure spaces

In this paper we introduce a new definition of BV   based on measure upper gradients and prove the equivalence of this definition, and the coincidence of the corresponding notions of total variation, with the definitions based on relaxation of L¹$L^1$ norm of the slope of Lipschitz functions or upper gradients. As in the previous work by the first author with Gigli and Savaré in the Sobolev case, the proof requires neither local compactness nor doubling and Poincaré.     

Eigenvalues and the One-Dimensional p-Laplacian

We consider the boundary value problem (?_p(u′))′ + λF(t, u) = 0, with p > 1, t ∈ (0, 1), u(0) = u(1) = 0, and with λ > 0. The value of λ is chosen so that the boundary value problem has a positive solution. In addition, we derive an explicit interval for λ such that, for any λ in this interval, the existence of a positive solution to the boundary value problem is guaranteed. In addition, the existence of two positive solutions for λ in an appropriate interval is also discussed.     

Generalized GM (1, 1) model and its application in forecasting of fuel production

Grey theory is one approach that can be used to construct a model with limited samples to provide better forecasting advantage for short-term problems. Generally, the GM (1, 1) and Discrete GM (1, 1) models are two typical grey forecasting models in grey theory. However, there are two shortcomings in the above grey models respectively, i.e., the homogeneous-exponent simulative deviation in GM (1, 1) model, and the unequal conversion between the original and white equations in DGM (1, 1) model. In this paper, we firstly propose a novel Generalized GM (1, 1) model termed GGM (1, 1) model, based on GM (1, 1) and DGM (1, 1) models, to overcome the above shortcomings. Then, we detailedly study four important properties in this new grey model. Four estimative approaches of stepwise ratio in GGM (1, 1) model context is also covered. In the end, we simulate and forecast the fuel production in China during the period 2003–2010 using three GM (1, 1) models. The empirical results show that GGM (1, 1) model has higher simulative and predictive accuracy than GM (1, 1) and DGM (1, 1) models. This work contributes significantly to improve grey forecasting theory and proposes a optimized GM (1, 1) model.     

Approximating a two-machine flow shop scheduling under discrete scenario uncertainty

This paper deals with the two machine permutation flow shop problem with uncertain data, whose deterministic counterpart is known to be polynomially solvable. In this paper, it is assumed that job processing times are uncertain and they are specified as a discrete scenario set. For this uncertainty representation, the min-max and min-max regret criteria are adopted. The min-max regret version of the problem is known to be weakly NP-hard even for two processing time scenarios. In this paper, it is shown that the min-max and min-max regret versions of the problem are strongly NP-hard even for two scenarios. Furthermore, the min-max version admits a polynomial time approximation scheme if the number of scenarios is constant and it is approximable with performance ratio of 2 and not (4/3 − ?)-approximable for any ? > 0 unless P = NP if the number of scenarios is a part of the input. On the other hand, the min-max regret version is not at all approximable even for two scenarios.