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helmholtz

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helmholtz Helmholtz , H.L.F.von 馮赫姆霍爾茲...

Helmholtz , H.L.F.von 馮赫姆霍爾茲〔1821-1894，德國生理學家及物理學家〕。 “helmholtz helmholtz free energy“ 中文翻譯：   赫爾姆霍茨自由能“coil helmholtz“ 中文翻譯：   亥姆霍線圈“helmholtz cell“ 中文翻譯：   亥姆霍茲電池；黑目合茲電池; 黑目合茲電池“helmholtz coil“ 中文翻譯：   亥姆霍茲線圈; 赫姆霍茲線圈; 探向線圈“helmholtz coils“ 中文翻譯：   氦氣測量; 亥姆霍茲線圈; 赫姆霍樂茲線圈“helmholtz contraction“ 中文翻譯：   亥姆霍茲收縮“helmholtz equation“ 中文翻譯：   亥姆霍茲方程式；黑目合茲方程式; 黑目合茲方程式“helmholtz flow“ 中文翻譯：   亥姆霍茲流“helmholtz formula“ 中文翻譯：   亥姆霍茲公式“helmholtz function“ 中文翻譯：   亥姆霍茲函數; 亥氏函數; 赫姆豪斯函數“helmholtz illusion“ 中文翻譯：   亥姆霍茨錯覺; 赫爾姆霍茨錯覺“helmholtz instability“ 中文翻譯：   亥姆霍茲不穩度“helmholtz ligament“ 中文翻譯：   黑爾姆霍爾茨韌帶“helmholtz resonance“ 中文翻譯：   黑爾姆霍爾茲共振“helmholtz resonator“ 中文翻譯：   helmholtz共振器; 亥姆霍蔣共鳴器; 亥姆霍茲共鳴器; 亥姆霍茲共振器; 亥姆霍茲共振體“helmholtz square“ 中文翻譯：   赫爾姆霍茨四方形“helmholtz telesterscope“ 中文翻譯：   亥姆霍茲望遠體視鏡“helmholtz theorem“ 中文翻譯：   亥姆霍茲定理“helmholtz theory“ 中文翻譯：   共振學說“helmholtz von“ 中文翻譯：   赫爾姆霍茲“helmholtz wave“ 中文翻譯：   亥姆霍茲波；黑目合茲波; 黑目合茲波“helmholtz-gemeinschaft“ 中文翻譯：   亥姆霍茲聯合會“fechner-helmholtz law“ 中文翻譯：   費-黑二氏定律:系數定律,用以解釋亮度覺; 用以解釋亮度覺“gibbs helmholtz equation“ 中文翻譯：   吉布斯 亥姆霍茲方程式“helmhohz free energy“ 中文翻譯：   亥姆霍茲自由能“helmhilfz trichromatic theory“ 中文翻譯：   楊赫爾姆霍茨三色說

helminth

In solving the helmholtz equation in the acoustical waveguides with a curved bottom , slow convergence may occurs when the linear local orthogonal transformation is adopted . in this paper , a class of nonlinear local orthogonal transformations ( nlot ) is proposed . it is an approach to improve the slow convergence mentioned above 本文嘗試通過在深度方向選取非線性局部正交變換，將曲底求解區域化為平坦求解區域，然后求解helmholtz方程的辦法，來改善用線性(深度方向)局部正交變換時，步進求解時會出現的局部收斂慢的問題。

Base on helmholtz integral equation , the incoherent scattering of plane wave from rough cone - shaped surface is derived with the far field theory and stationary phase method . and the incoherent scattering of plane wave from rough conical surface is also derived with shadowing function when the the radius of principal 最后計算并分析了入射光為= 0 . 48 m時,粗糙錐面的平面波散射特性,考察了入射波和散射波的幾何關系,偏振態以及粗糙面統計參量等對散射強度的影響。

This thesis consists three sections : in section one , first and for most , the author intends to illuminate that the development of german physics was at a standstill for the whole 18th century by giving a profile on it before the year of 1800 . then the author depicts the three - stages for german physical achievements from 1800 to 1930 , namely ohm time ( 1800 - 1840 ) , helmholtz time ( 1840 - 1880 ) and planck time ( 1880 - 1930 ) , in which the author focuses on the outline of the development of german physics to represent the dynamic feature of the development of german physics 本論文共分三部分：第一部分，首先通過對1800年以前德國物理學發展的概述，說明德國物理學的發展在整個18世紀幾乎處于停滯狀態；然后對1800 1930年的德國物理學的主要成就分三個時期：歐姆時期( 1800 1840 ) 、亥姆霍茲時期( 1840 1880 ) 、普朗克時期( 1880 - 1930 )進行描述，突出德國物理學發展過程的主體脈絡，體現德國物理學發展的動態特征。

First of all , the algorithm base on the boundary problem of helmholtz equation and finite - difference technique , calculate the field in “ cold ” cavity and disperse the helmholtz equation , as a result of the formula : ax = x . secondly , according to the eigenvalue of matrix theory and applied iterative methods , eigenmode adopt a numerical approach which allows the improved chebyshev polynomial iteration which based on the power method to extract the isolated eigenmode in the spectrum . finally , we resolve the problem of compatibility in software and insert the eigenmode module into the chipic which will have the function of eigenmode analysis 具體的說: ( 1 )首先以電磁理論中的亥姆霍茲方程的邊值問題理論和計算電磁學中的有限差分法為基礎,計算冷腔中的場分布并離散亥姆霍茲方程,得到標準的本征值問題: ax = x ; ( 2 )然后根據矩陣理論中的eigenvalue問題和數值計算中的迭代方法,采用改進后的chebyshev多項式,在power迭代法的基礎上對ax = x進行多項式迭代,實現對頻譜中孤立本征模的萃取; ( 3 )最后將用fortran語言編制的eigenmode模塊加入到chipic軟件中,解決了eigenmode模塊與chipic主代碼的兼容問題,從而實現了chipic軟件的模式分析功能。

The exhaust noise contains complex noise elements , including the exhaust noise with a base frequency measured in the number of exhausts in unit time , the resonance noise of the gas column in the pipe , the gas stream blowing noise at the exhaust manifold , the exhaust gas jetting and impact noise , the helmholtz resonance noise of the cylinder , the karman eddy noise and the turbulent noise inside the exhaust system 排氣噪聲包含了復雜的噪聲成分：以單位時間內排氣次數為基頻的排氣噪聲、管道內氣柱共振噪聲、排氣歧管處的氣流吹氣噪聲、廢氣噴注和沖擊噪聲、汽缸的亥姆霍茲共振噪聲、卡門渦流噪聲及排氣系統內部的湍流噪聲等。

In this dissertation , the numerical computation for the acoustic radiation problem ( arp ) is studied deeply and systematically in the theory , method and the application technique , based on analyzing the situation of the home and abroad on the numerical computation for the acoustic radiation problem . the calculation formulas of the boundary element method ( bem ) for the exterior acoustic radiation problem in the full - space and half - space are deduced , based on the wave propagation theorem ; the arising of the non - unique solutions , which is associated with the application of the boundary integral equation ( bie ) in acoustic radiation problem , is analyzed and proofed ; the improved combined helmholtz integral equation formulation ( ichief ) is presented to overcome the non - uniqueness problem more effectively and reliably ; the determination of the singular integral coefficients on various occasions is analyzed ; the properties and treatments of the singular integrals with different orders axe studied ; the computation program of the cubic spline ichief is developed and its ability to overcome the non - uniqueness problem and feasibility to discrete the surface coarsely with the sufficient calculation precision are examined through examples 第二章在聲波動理論基礎上，詳細地推導出對應于無限域和半無限域的外部振動聲輻射問題的邊界積分方程計算公式；根據fredholm積分理論，對利用邊界積分方程計算振動聲輻射問題過程中解的非唯一性的產生進行了分析和證明；改進了chief法以提高其克服解的非唯一性的有效性和可靠性；對不同條件下奇性系數的計算、強奇性積分的收斂性及其在變量替換時與普通積分的差異性、不同階奇性積分的計算、數值求積分等進行了研究；開發了三次樣條改進chief法計算軟件，并通過算例考核了該方法在特征波數處克服解的非唯一性的有效性和在保證計算精度的前提下實現剖分粗化以提高計算效率的可行性。

The fourth - order explicit upwind - biased compact difference schemes are used in the spatial discretization of the nonlinear convection terms . these difference schemes can be used in all computational region including the boundary neighborhood , and can overcome the difficulty not adapting simultaneously in the boundary neighborhood for general three - dimensional fourth - order central difference schemes , and improve computational stability a nd resolution . the compact difference equations with high accuracy and resolution for solving the incompressible n - s equations and perturbation equations are composed of these compact difference schemes , and provides an effective numerical method for the investigations of the turbulent spots and coherent structures 文中發展了四階時間分裂法用于navier - stokes方程及其擾動方程的時間離散；對分裂得出的關于壓力的poisson方程和關于速度的helmholtz方程，建立三維耦合四階緊致迎風差分格式；這些格式適用于包括鄰近邊界點在內的計算區域，克服了三維各自用四階中心差分格式離散不適用于邊界鄰域的困難，并提高了穩定性和分辨率，用這些格式分別組成了數值求解navier - stokes方程及其擾動方程的高精度、高分辨率的緊致差分方程組，為湍斑及湍流相干結構的研究提供了有效的數值方法。

This paper has presented the situation of intake silencer research and application and expounded the intake noise engendering cause and the basic theory on controlling the intake noise . then a research established in the accurate determination of resonance frequencies of different kind of helmholtz resonators is done . according to different assumptions , four kind of mathematical models are established , and the relations between them are discussed 本文介紹了進氣消聲器研究與應用的現狀與發展，闡述了進氣噪聲產生機理及控制的基本理論，研究了helmholtz共振型進氣消聲器的原理，立足于helmholtz共振型進氣消聲器的共振頻率的準確確定，建立了兩類四種共振腔模型，并討論了它們之間的相互推演關系。

Numerical results are consistent with that of sandia laboratory experiment and agree with that of cth code too . an adaptive mesh refinement under 2d euler structure grid for multi - fluid flow is developed for resolving richtmyer - meshkov , rayleigh - taylor and helmholtz multi - fluid instabilities , and the high resolution interface properties can be obtained 數值模擬多介質流體richtmyer - meshkov ， rayleigh - taylor ， helmholtz界面不穩定性，用levelset函數定義euler坐標系中界面附近網格自適應判據，使得網格剖分更加合理，既能提高計算精度又能節省計算時間。

( 4 ) on the efficient method for the dynamical core of the new generation multi - scale forecasting model i ) we present a new multi - level sparse approximate inverse preconditnioner for the complicated 3 - d helmholtz equations in the new generation weather forecasting model . as a result , the new sparse approximate inverse preconditioned gcr and gmres algorithms are given and successfully applied in the dynamical core . numerical tests show that the new algorithms perform very efficiently , and can greatly improve the efficiency of numerical model 對此，本文提出了一種基于逐層門限技術的近似逆矩陣稀疏模式預選方法，并構造了相應的稀疏近似逆預條件子，結合gcr算法和g州[ r衛s算法，首次將逐層門限稀疏近似逆預條件子應用于新一代多尺度預報模式動力內核的實際計算，數值實驗表明這里給出的方法可以大大提高數值模式的計算效率。

It also roundly researched the solution of the helmholtz equation in the circumrotating ellipsoidal coordinates , and discussed how to calculate the solution of the electro - magnetic field in the circumrotating ellipsoidal coordinates using special functions , and researched circumrotating ellipsoidal cavity ’ s latent value and quality parameter using arithmetic simulation , finally we compared the ellipsoidal cavity with the spheriform cavity . the main content of this thesis are as following : 1 . calculated the distribution of the electro - magnetic field inside the ellipsoidal cavity based on maxwell equations and boundary conditions , and confirmed the syntonic mode inside the ellipsoidal cavity using arithmetic methods 本文從maxwell方程及其邊界條件求解出橢球腔內的電磁場分布,較為全面的研究了旋轉橢球坐標系下赫姆霍茲方程的解的問題,討論了用特殊函數來求解旋轉橢球坐標系下電磁場的解,并通過數值仿真研究了旋轉橢球諧振腔的本征值和品質因數,并和球形諧振腔做了比較,主要內容為: 1 .用maxwell方程及其邊界條件求解出橢球腔內的電磁場分布,并且分析了橢球腔內的諧振模式。

On the base of mathematical domain decomposition method ( ddm ) , this paper investigates systematically the quasi - static problems based on laplace equation , the transmission problems in waveguide based helmholtz equation and the three - dimensional scattering and radiation problems based on maxwell equations . the theoretical system is built for the further exploration of ddm in electromagnetic problems 本文在區域分解法已有的數學基礎上，從基于laplace方程的準靜態問題，到基于helmholtz方程的波導傳輸問題以及基于maxwell方程的三維散射輻射問題，系統地探討了該方法在電磁領域中的應用，為進一步擴展應用研究建立了理論體系。

First , in virtual of identification of flaws is a typical of in - verse problems , proceeding from time - harmonic electromagnetic maxwell ' s equa - tion and helmholtz equation , the uniqueness and existence of direct scattering problems including the numerical algorithms of diverse of boundary conditions is given . second , the uniqueness and existence of inverse scattering problems and the theory of ill - posed integral equation are briefly looked back upon . finally , indicator function method for boundary identification is set up under all kinds of boundary conditions for inverse scattering of homogenous and inhomogenous objects , meanwhile , the proof of possibility for near - field measurements and nu - merical simulation are given 由于缺陷的識別是一類典型的反問題，因而首先從時諧電磁maxwell方程和helmholz方程出發，具體地闡述了求解正散射問題的有關方法，包括各種(夾雜)邊界條件下的數值解法，就解的存在性唯一性給予了肯定的回答；隨后對逆散射問題的理論作了簡短的回顧，包括解的唯一性以及非線性不適定積分方程的處理等；然后對均勻介質和非均勻介質的逆散射問題建立了在各種邊界條件下的邊界識別的指示函數方法，鑒于近場數據獲得的重要性，對近場測試時邊界識別的方法給予了相應的證明，并且實現了數值模擬。

The solving steps are as follows : the field is divided into three regions by the cylindrical surface of the finite - length cylinder and the location of the delta - coils . because “ the surface current source is placed at the interface , the non - homogenous restricted equation on the magnetic vector potential is transformed into the homogenous helmholtz equation . by using the method of separation of variables to solve equation and according to the interface conditions and the condition at infinity to determine the unknown constants , the expressions for the magnetic vector potential of the three regions are solved out 在求解過程中，假定放置式圓柱線圈是由無窮多個對稱圓環線圈密饒而成，首先求解含有有限長磁芯的通電對稱圓環線圈的電磁場：以有限長圓柱磁芯的側面和圓環線圈所在圓柱面為分界面將場域劃分為三個小區域，由于場源放置在內邊界面上，使得關于矢量磁位的非齊次約束方程轉化成齊次亥姆霍茲方程，利用分離變量法求解，根據分界面鄭州大學碩十研究生畢業論文摘要條件以及無限遠條件確定待定常數，從而得到各場區矢量磁位的表達式。

A new approach , the multipole theory ( mt ) method , is briefly described for analysis of waveguide eigenvalue problems . the essential concept is to represent the solution of the waveguide partial differential equation by the generalized mt formula of 2 - d helmholtz equation . the applied rules and the procedure of the mt method are also introduced . by calculating and analyzing some engineering problems , it is shown that the mt method is an effective approach for analysis of waveguide eigenvalue problems 本文利用多極理論分析波導本征值問題.給出用多極理論分析波導本征值問題的使用規則和實施方法.實例計算結果表明，用多極理論分析波導本征值問題，不僅具有較高的計算精度，而且可以很方便地應用于波導工程問題的設計與計算，多極理論是一種有效的波導本征值分析方法

The fft of helmholtz equation on the regular domain is studied . and the multifrontal algorithm is used to solve the matrix equations in computational electromagnetics . finally , the finite - difference approximate forms of maxwell equations and the despres transmission condition are discussed 為了充分提高算法的計算效率，研究了規則區域上helmholtz方程的fft快速算法，以及有效地將多波前算法引入計算電磁學領域用于求解差分稀疏矩陣方程。

Secondly , the physical nature of divergence of iterative ddm based on the schwarz alternating method in treating waveguide problems is given in this paper . also an absorbing fictitious boundary condition ( fbc ) is presented to generate an iterative ddm for waveguide problems 其次，針對helmholtz方程微分算子的系數矩陣非正定，基于schwarz交替法的迭代區域分解法，在分析波導問題時迭代不收斂的困難，探討了產生這一問題的物理本質。

A dynamic interaction schematic of an end bearing or elastic bearing pile with arbitrary force at pile top is founded . by using helmholtz resolution and the operator decomposition method , biot ' s equations governing motions of a porous solid saturated with interstitial fluid are decoupled 建立飽和土中端承樁和摩擦樁在任意激振力作用下的理論模型，利用位移勢函數及微分算子分解方法，得到飽和土層biot動力固結方程的分離變量解。

2 ) in order to solve the scattering and diffraction of sound radiation , in this dissertation , based on helmholtz equation and its boundary equations , modeling of three - dimensional fem is given for computing low frequency sound transfer function in small enclosures 2 )為解決聲音在傳播過程中所發生的散射和衍射現象，本文基于有源helmholtz方程及其邊界條件，建立了求解小尺度封閉空間內低頻聲傳遞函數的三維有限元模型。