The problem of fluid-dynamics in semicircular canal

An analytical solution with high accuracy which holds for any values of ɛfor fluid-dynamics model equation in a single semicircular canal presented by Buskirk and his co-workers has been obtained It not only includes all of the results of Buskirk et al. but also covers three possible kinds of dynamical response modes in practice. The theoretical results are in better agreement with those of experimental observations. This investigation has laid a reliable theoretical foundation for quantitatively understanding fluid-dynamics in semicircular canal, especially fluid dynamical response. The distribution of the velocity of the endolymph in semicircular canal is given. A nonstandard method of the inverse Laplace transform is presented.     

Fluidmechanics of semicircular canals – revisited

In this work we find the exact solution for the flow field in a semicircular canal which is the main sensor for angular motion in the human body. When the head is rotated the inertia of the fluid in the semicircular canal leads to a deflection of sensory hair cells which are part of a gelatinous structure called cupula. A modal expansion of the governing equation shows that the semicircular organ can be understood as a dynamic system governed by duct modes and a single cupular mode. We use this result to derive an explicit expression for the displacement of the cupula as a function of the angular motion of the head. This result shows in a mathematically and physically clean way that the semicircular canal is a transducer for angular velocity. Received: March 16, 2006; revised: November 11, 2006 and May 26, 2007     

Fluidmechanics of semicircular canals – revisited

In this work we find the exact solution for the flow field in a semicircular canal which is the main sensor for angular motion in the human body. When the head is rotated the inertia of the fluid in the semicircular canal leads to a deflection of sensory hair cells which are part of a gelatinous structure called cupula. A modal expansion of the governing equation shows that the semicircular organ can be understood as a dynamic system governed by duct modes and a single cupular mode. We use this result to derive an explicit expression for the displacement of the cupula as a function of the angular motion of the head. This result shows in a mathematically and physically clean way that the semicircular canal is a transducer for angular velocity.     

The equilibrium of a flexible membrane under hydrostatic pressure

In the construction industry it is often necessary to drain a section of a canal. This may be done after the insertion of flexible membranes made of PVC‐coated polyester. This paper discusses a simple mathematical model to examine the equilibrium of such a membrane under hydrostatic pressure. The model predicts that the maximum displacement of a membrane from the vertical occurs at a depth which varies between l/‐√3 and l/‐√2 , where l is the depth of the canal.     

Noncrossing Partitions, Catalan Words, and the Semicircle Law

As is well known, the joint limit distribution of independent Wigner matrices is free with the marginals being semicircular. This freeness is intimately tied to noncrossing pair partitions or, equivalently what are known as Catalan words, each of which contributes one to the limit moments. We investigate the following questions. Consider a sequence of patterned matrices: (i) When do only Catalan words contribute (one), so that we get the semicircle limit? (ii) When does each Catalan word contribute one (with possible nonzero contribution from non-Catalan words)? (iii) For what matrix models do Catalan words not necessarily contribute one each and non-semicircle limits arise, even when non-Catalan words have zero contribution? In particular we show that in a general sense, the semicircle law serves as a lower bound for possible limits. Further, there is a large class of non-Wigner matrices whose limit is the semicircle. This may be viewed as robustness of the semicircle law. Similarly, there is a large class of block matrices whose limit is not semicircular.     

Vibrations of a semicircular membrane containing thin rigid inclusions

This article examines problems concerning steady-state vibrations of a semicircular membrane containing thin rigid inclusions of different configurations. The generalized method of integral transforms is used to formulate the problem in the form of a system of singular integral equations in each specific case. With the use of the asymptote of the sought functions as a basis, these equations are solved approximately by the method of orthogonal polynomials. A study is made of the validity of using the reduction method to approximately solve the infinite linear algebraic matrix system which is obtained. The results of calculations are analyzed.Translated from Dinamicheskie Sistemy, No. 5, pp. 49–55, 1986.     

Numerical simulation of the flow in semicircular canals with the method of fundamental solutions

We present a numerical model for the simulation of the flow in semicircular canals (SCCs). The governing equations for the flow are solved with the method of fundamental solutions (MFS), a mesh free method for boundary value problems. We describe the flow field in a SCC with utricle, and we find a vortex that had not yet been reported in literature. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling the dynamics of block-and-fault systems and seismicity

A model of block-and-fault system dynamics (a block model) has been developed to analyze how the basic features of seismicity depend on the lithosphere structure in a region under consideration and on the peculiarities of the lithosphere dynamics. The lithosphere in the region is modeled by a system of perfectly rigid blocks divided by infinitely thin fault planes. The viscoelastic interaction between the blocks and with the underlying medium is specified. Displacements and rotations of the blocks at each time are determined so that the whole block system is in a quasi-static equilibrium state. When the ratio of the stress to the pressure exceeds the critical level in some part of a fault zone, a stress drop occurs that is considered in the model as an earthquake. The paper contains a review of results obtained by numerical simulation of the dynamics of different block structures including the structures approximating the lithosphere structure in specific seismic regions. These results suggest that the block model is a useful tool for studying the influence of geometry of faults and motions of blocks on seismicity features.     

A hydrodynamic model of human cochlea

A two-compartment model of the human cochlea is proposed. When stretched out, the bony spiral tube looks like two chambers separated by a membrane. Both chambers are filled with viscous fluid called perilymph; they communicate with one another via a canal. Sound vibrations enter the cochlea through the oval window and cause periodic change of pressure in the perilymph, which, in turn, causes the membrane to vibrate. The motion of the fluid is described by hydrodynamic equations, which are supplemented with the membrane vibration equation. The equations are linearized in the amplitude of the vibrations, and their solution is sought in the form of Fourier harmonics with a given frequency. To determine the harmonics, a system of linear boundary value problems for ordinary differential equations with variable coefficients is obtained. The numerical solution of this system using finite difference method fails because it involves a large parameter and the problem is close to a singular one. We propose a novel numerical method without saturation that enables us to obtain solutions in a wide range of frequencies up to an arbitrary and controllable accuracy. The computations confirm the Bekesy theory stating that high-frequency sounds cause the membrane to bend near the apex of the cochlea, and low-frequency sounds cause it to bend near the base of the cochlea.     

Numerical simulation of the endolymph flow in a semicircular canal

We present a concept for the simulation of the fluid flow in the semicircular canals of the inner ear. Based on the temporal dynamics of an idealized model configuration we formulate the governing equations and devise a strategy for their numerical solution. We analyze the proposed method and find a numerical instability. This instability is characterized by an error bound which can serve as a guideline for tuning the numerical method to the specific boundary conditions. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stochastic vs deterministic programming in water management: the value of flexibility

In the paper we develop a two stage scenario-based stochastic programming model for water management in the Indus Basin Irrigation System (IBIS). We present a comparison between the deterministic and scenario-based stochastic programming model. Our model takes stochastic inputs on hydrologic data i.e. inflow and rainfall. We divide the basin into three rainfall zones which overlap on 44 canal commands. Data on crop characteristics are taken on canal command levels. We then use ten-daily and monthly time intervals to analyze the policies. This system has two major reservoirs and a complex network of rivers, canal head works, canals, sub canals and distributaries. All the decisions on hydrologic aspects are governed by irrigation and agricultural development policies. Storage levels are maintained within the minimum and maximum bounds for every time interval according to a power generation policy. The objective function is to maximize the expected revenue from crops production. We discuss the flexibility of two stochastic optimization models with varying time horizon.     

Influence of the pile shape on wind erosion CFD emission simulation

When designing an open storage system for bulk material like coal or iron ore, operational and investment parameters are to be considered. Those inputs are always managed by engineers and prolific literature can be found. But entering into environmental parameters like wind erosion, few methodologies are available, US EPA being one of the most extensive. This source is focused on certain conditions of wind direction, pile shape, etc. what sometimes are not matching the most interesting way of storing the material: area restrictions, stacking means, etc. Based on state of the art computational fluid dynamics (CFD) software, in this case we have used ANSYS CFX 5.7., modelling system was developed and compared to EPA results for conical and oval with flattop piles. After adjusting the calculation process and selecting the most effective variables, the semicircular shape was studied finding that for the same amount of material stored, lower emissions and wind erosions are to be expected; however depending on wind direction higher values of friction per surface unit are found but due to its higher volume of storage per square metre, the balance is positive to the semicircular pile.     

Enhancement of membrane computing model implementation on GPU by introducing matrix representation for balancing occupancy and reducing inter-block communications

In previous studies, objects of each membrane were assigned to threads of one thread block of the graphic processing unit (GPU). The number of active threads was low if the number of objects inside a membrane was low. This study represents objects of membranes as entities of a matrix. Then a sub-matrix represents the appropriate number of objects assigned to threads of each thread block to balance the load and keep the occupancy high even when the number of objects per membrane is low. The size of the sub-matrix or the appropriate number of active threads is determined automatically. Furthermore, by this approach it is possible to assign more than one membrane to each thread block and to execute communication between membranes in the same thread block without the need for time-consuming inter-block communication. For example, using the previous algorithm, for two objects per membrane the speed up is 0.6×, while for the proposed algorithm the speed up is 32.4×.     

A Meshless Boundary Method for Computation of Stokes Flow with Particles in the Semicircular Canals of the Inner Ear

Benign paroxismal positional vertigo (BPPV) is modeled by introducing free-floating particles (canaliths) which settle inside the semicircular canals (SCC). The Stokes flow induced by a canalith is evaluated by coupling the force coupling method (FCM) to the method of fundamental solutions (MFS). The proposed methodology results in a straightforward meshless boundary method for the simulation of bounded Stokes flow with finite-size particles. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parallel constrained molecular dynamics

A block version of the Shake method for heavy atom simulation in biological systems is presented in this paper. The method solves successively, independent blocks of constraints of small size by a Newton method. This algorithm is implemented in TAKAKAW, an efficient parallel molecular dynamics code. This method has been tested on a small system and on an ionic canal of 67671 atoms. This revised version was published online in June 2006 with corrections to the Cover Date.     

电网安全调度中输电阻塞管理的演化策略

输电阻塞是电力系统运行中的常见问题 .本文建立了用于电网安全调度中输电阻塞管理的数学模型——带线性约束的多目标模糊优化问题模型 ,给出了求解该模型的演化策略 .实际的计算结果表明 ,演化策略解决输电阻塞问题是有效的 .     

A DLM/FD/IB Method for Simulating Compound Cell Interacting with Red Blood Cells in a Microchannel

In this article, a computational model and related methodologies have been tested for simulating the motion of a malaria infected red blood cell (iRBC for short) in Poiseuille flow at low Reynolds numbers. Besides the deformability of the red blood cell membrane, the migration of a neutrally buoyant particle (used to model the malaria parasite inside the membrane) is another factor to determine the iRBC motion. Typically an iRBC oscillates in a Poiseuille flow due to the competition between these two factors. The interaction of an iRBC and several RBCs in a narrow channel shows that, at lower flow speed, the iRBC can be easily pushed toward the wall and stay there to block the channel. But, at higher flow speed, RBCs and iRBC stay in the central region of the channel since their migrations are dominated by the motion of the RBC membrane.     

A class of asynchronous multisplitting two-stage iterations for large sparse block systems of weakly nonlinear equations

For the block system of weakly nonlinear equations Ax=G(x), where is a large sparse block matrix and is a block nonlinear mapping having certain smoothness properties, we present a class of asynchronous parallel multisplitting block two-stage iteration methods in this paper. These methods are actually the block variants and generalizations of the asynchronous multisplitting two-stage iteration methods studied by Bai and Huang (Journal of Computational and Applied Mathematics 93(1) (1998) 13–33), and they can achieve high parallel efficiency of the multiprocessor system, especially, when there is load imbalance. Under quite general conditions that is a block H-matrix of different types and is a block P-bounded mapping, we establish convergence theories of these asynchronous multisplitting block two-stage iteration methods. Numerical computations show that these new methods are very efficient for solving the block system of weakly nonlinear equations in the asynchronous parallel computing environment.