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Exact solution of D-dimensional Schrödinger equation generated from certain central power-law potentials 由某些中心幂律势生成的d维Schrödinger方程的精确解
Pub Date : 2014-04-23 DOI: 10.2478/s11534-014-0445-z
N. Bhagawati
AbstractBy applying Extended Transformation method we have generated exact solution of D-dimensional radial Schrödinger equation for a set of power-law multi-term potentials taking singular potentials $$V(r) = ar^{ - tfrac{1}{2}} + br^{ - tfrac{3}{2}}$$, $$V(r) = ar^{tfrac{2}{3}} + br^{ - tfrac{2}{3}} + cr^{ - tfrac{4}{3}}$$, V(r) = ar + br−1 + cr2 and V(r) = ar2+br−2+cr−4+dr−6 as input reference. The restriction on the parameters of the given potentials and angular momentum quantum number ℓ are obtained. The multiplet structure of the generated exactly solvable potentials are also shown.
摘要应用扩展变换方法,以奇异势$$V(r) = ar^{ - tfrac{1}{2}} + br^{ - tfrac{3}{2}}$$, $$V(r) = ar^{tfrac{2}{3}} + br^{ - tfrac{2}{3}} + cr^{ - tfrac{4}{3}}$$, V(r) = ar +br−1 + cr2和V(r) = ar2+br−2+cr−4+dr−6为输入参考,得到了幂律多项势集的d维径向方程Schrödinger的精确解。得到了给定势的参数和角动量量子数的限制。并给出了生成的精确可解电位的多重结构。
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引用次数: 2
Electro-osmotically actuated oscillatory flow of a physiological fluid on a porous microchannel subject to an external AC electric field having dissimilar frequencies 受具有不同频率的外部交流电场作用的生理流体在多孔微通道上的电渗透驱动振荡流动
Pub Date : 2014-04-23 DOI: 10.2478/s11534-014-0424-4
J. C. Misra, S. Chandra
Electro-osmotic flow of a physiological fluid with prominent micropolar characteristics, flowing over a microchannel has been analyzed for a situation, where the system is subject to the action of an external AC electric field. In order to account for the rotation of the micro-particles suspended in the physiological fluid, the fluid has been treated as a micropolar fluid. The microchannel is considered to be bounded by two porous plates executing oscillatory motion. Such motion of the plates will normally induce oscillatory flow of the fluid. The governing equations of the fluid include a second-order partial differential equation depicting Gauss’s law of electrical charge distributions and two other partial differential equations of second order that arise out of the laws of conservation of linear and angular momenta. These equations have been solved under the sole influence of electrokinetic forces, by using appropriate boundary conditions. This enabled us to determine explicit analytical expressions for the electro-osmotic velocity of the fluid and the microrotation of the suspended micro-particles. These expressions have been used to obtain numerical estimates of important physical variables associated with the oscillatory electro-osmotic flow of a blood sample inside a micro-bio-fluidic device. The numerical results presented in graphical form clearly indicate that the formation of an electrical double layer near the vicinity of the wall causes linear momentum to reduce. In contrast, the angular momentum increases with the enhancement of microrotation of the suspended microparticles. The study will find important applications in the validation of results of further experimental and numerical models pertaining to flow in micro-bio-fluidic devices. It will also be useful in the improvement of the design and construction of various micro-bio-fluidic devices.
本文分析了一种具有显著微极性特征的生理流体在微通道上的电渗透流动,该微通道在系统受到外部交流电场作用的情况下。为了解释悬浮在生理流体中的微颗粒的旋转,该流体被视为微极性流体。微通道被认为是由两个执行振荡运动的多孔板所包围。板的这种运动通常会引起流体的振荡流动。流体的控制方程包括描述高斯电荷分布定律的二阶偏微分方程和由线动量和角动量守恒定律产生的另外两个二阶偏微分方程。这些方程在电动势的单独影响下,通过使用适当的边界条件得到了解。这使我们能够确定流体的电渗透速度和悬浮微粒的微旋转的显式解析表达式。这些表达式已用于获得与微生物流体装置内血液样本的振荡电渗透流动相关的重要物理变量的数值估计。以图形形式给出的数值结果清楚地表明,在壁面附近形成的双电层使线性动量减小。相反,角动量随着悬浮微粒微旋度的增强而增大。该研究将在进一步验证有关微流体装置流动的实验和数值模型的结果中找到重要的应用。对改进各种微流体装置的设计和结构也有一定的参考价值。
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引用次数: 8
The vortex flow caused by sound in a bubbly liquid 气泡液体中由声音引起的涡流
Pub Date : 2014-04-11 DOI: 10.2478/s11534-014-0454-y
A. Perelomova, P. Wojda
Generation of vorticity in the field of intense sound in a bubbly liquid in the free half-space is considered. The reasons for generation of vorticity are nonlinearity, diffraction, and dispersion. Acoustic streaming differs from that in a Newtonian fluid. Under some conditions, the vortex flow changes its direction. Conclusions concern streaming induced by a harmonic or an impulse Gaussian beam.
研究了自由半空间气泡液体中强声场涡量的产生。涡度产生的原因有非线性、衍射和色散。声波流不同于牛顿流体中的声波流。在某些条件下,涡流会改变方向。结论涉及谐波或脉冲高斯光束引起的流。
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引用次数: 3
Thermal self-action effects for acoustic beams containing fronts in a Maxwell relaxing fluid 麦克斯韦弛豫流体中包含锋面的声束的热自作用效应
Pub Date : 2014-04-03 DOI: 10.2478/s11534-014-0449-8
A. Perelomova
This paper examines the thermal self-action of acoustic beams in a Maxwell relaxing fluid. This type of thermal self-action differs from that in a Newtonian fluid and behaves differently depending on a ratio of sound period and time of thermodynamic relaxation. The self-action which relates to sound beams containing shock fronts is also discussed. In addition, stationary and non-stationary types of self-action are considered.
本文研究了声波束在麦克斯韦弛豫流体中的热自作用。这种类型的热自作用与牛顿流体中的热自作用不同,其表现取决于声周期和热力学松弛时间的比值。讨论了含激波前沿的声束的自作用。此外,还考虑了平稳型和非平稳型的自作用。
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引用次数: 0
Numerical study of the three-state Ashkin-Teller model with competing dynamics 具有竞争动力学的三态Ashkin-Teller模型的数值研究
Pub Date : 2014-04-03 DOI: 10.2478/s11534-014-0446-y
Prosper Ndizeye, F. Hontinfinde, B. Kounouhewa, S. Bekhechi
An open ferromagnetic Ashkin-Teller model with spin variables 0, ±1 is studied by standard Monte Carlo simulations on a square lattice in the presence of competing Glauber and Kawasaki dynamics. The Kawasaki dynamics simulates spin-exchange processes that continuously flow energy into the system from an external source. Our calculations reveal the presence, in the model, of tricritical points where first order and second order transition lines meet. Beyond that, several self-organized phases are detected when Kawasaki dynamics become dominant. Phase diagrams that comprise phase boundaries and stationary states have been determined in the model parameters’ space. In the case where spin-phonon interactions are incorporated in the model Hamiltonian, numerical results indicate that the paramagnetic phase is stabilized and almost all of the self-organized phases are destroyed.
采用标准蒙特卡罗模拟方法,研究了一个自旋变量为0,±1的开放铁磁Ashkin-Teller模型。川崎动力学模拟了自旋交换过程,该过程连续地从外部源向系统输送能量。我们的计算显示,在模型中,一阶和二阶过渡线相交的三临界点的存在。除此之外,当川崎动力学成为主导时,检测到几个自组织相。在模型参数空间中确定了相边界和定态相图。在模型哈密顿量中加入自旋声子相互作用的情况下,数值结果表明顺磁相稳定,几乎所有的自组织相都被破坏。
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引用次数: 4
Investigation of complex impedance and modulus properties of Nd doped 0.5BiFeO3-0.5PbTiO3 multiferroic Composites Nd掺杂0.5BiFeO3-0.5PbTiO3多铁复合材料复阻抗和模量特性研究
Pub Date : 2014-03-31 DOI: 10.2478/s11534-014-0523-2
A. Behera, N. K. Mohanty, S. K. Satpathy, B. Behera, P. Nayak
Abstract0.5BiNdxFe1−xO3 − 0.5PbTiO3 (BNxF1−x − PT)(x = 0.05, 0.10, 0.15, 0.20) composites were successfully synthesized by a solid state reaction technique. At room temperature, X-ray diffraction shows tetragonal structure for all concentrations of Nd doped 0.5BiFeO3 − 0.5PbTiO3 composites. The nature of Nyquist plot confirms the presence of bulk effects only for BNxF1−x − PT (x = 0.05, 0.10, 0.15, 0.20) composites. The bulk resistance is found to decreases with the increasing temperature as well as Nd concentration and exhibits a typical negative temperature coefficient of resistance (NTCR) behavior. Both the complex impedance and modulus studies have suggested the presence of non-Debye type of relaxation in the composites. Conductivity spectra reveal the presence of hopping mechanism in the electrical transport process of the composites. The activation energy calculated from impedance plot of the composite decreases with increasing Ndx concentration and found to be 0.89, 0.76, 0.71 and 0.70 eV for x=0.05, 0.10, 0.15 and 0.20 respectively.
摘要采用固相反应技术成功合成了0.5 bindxfe1−xO3−0.5PbTiO3 (BNxF1−x−PT)(x = 0.05, 0.10, 0.15, 0.20)复合材料。在室温下,x射线衍射表明,掺钕浓度均为0.5BiFeO3−0.5PbTiO3的复合材料呈四方结构。Nyquist图的性质证实了只有BNxF1−x−PT (x = 0.05, 0.10, 0.15, 0.20)复合材料存在体效应。体电阻随温度和Nd浓度的升高而减小,呈现典型的负温度电阻系数(NTCR)行为。复合阻抗和模量的研究都表明复合材料中存在非德拜型弛豫。电导率谱揭示了复合材料在电传递过程中存在跳变机制。复合材料阻抗图计算的活化能随Ndx浓度的增加而减小,当x=0.05、0.10、0.15和0.20时,活化能分别为0.89、0.76、0.71和0.70 eV。
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引用次数: 42
Classical analogue of the statistical operator 统计算子的经典类比
Pub Date : 2014-03-13 DOI: 10.2478/s11534-014-0438-y
A. Plastino, A. Plastino, C. Zander
We advance the notion of a classical density matrix, as a classical analogue of the quantum mechanical statistical operator, and investigate its main properties. In the case of composite systems a partial trace-like operation performed upon the global classical density matrix leads to a marginal density matrix describing a subsystem. In the case of dynamically independent subsystems (that is, non-interacting subsystems) this marginal density matrix evolves locally, its behavior being completely determined by the local phase-space flow associated with the subsystem under consideration. However, and in contrast with the case of ordinary marginal probability densities, the marginal classical density matrix contains information concerning the statistical correlations between a subsystem and the rest of the system.
我们提出了经典密度矩阵的概念,作为量子力学统计算符的经典类比,并研究了它的主要性质。在复合系统的情况下,对全局经典密度矩阵进行部分轨迹式运算,得到描述子系统的边际密度矩阵。在动态独立子系统(即非相互作用子系统)的情况下,该边际密度矩阵在局部演化,其行为完全由与所考虑的子系统相关的局部相空间流决定。然而,与普通边际概率密度的情况相反,边际经典密度矩阵包含有关子系统与系统其余部分之间统计相关性的信息。
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引用次数: 0
Four-body treatment of the K-shell positronium formation from multi-electron atoms 多电子原子形成k壳层正电子的四体处理
Pub Date : 2014-03-13 DOI: 10.2478/s11534-014-0436-0
E. Ghanbari-Adivi, A. Velayati
The four-body Coulomb-Born distorted-wave approximation with correct boundary conditions (CBDW-4B) is applied to the K-shell positronium formation from multi-electron atoms at intermediate and high impact energies. In the present approach, both K-shell electrons are treated as active electrons. For collisions of positrons with helium, carbon, and neon atoms, both the post and prior forms of the transition amplitude are calculated and the corresponding differential and integral cross sections are compared with the results of the three-body version of the formalism (CBDW-3B). In order to investigate the effects of the static electronic correlations on the process, initial bound states of the active electrons in helium atoms are described by Hylleraas and Silverman wave functions. Also for positronium formation from helium atoms the obtained cross sections are compared with the available experimental data and also with the results of the other theories.
将具有正确边界条件的四体库仑-玻生畸变波近似(CBDW-4B)应用于多电子原子在中高冲击能下形成k壳层正电子。在目前的方法中,两个k壳层电子都被视为活性电子。对于正电子与氦、碳和氖原子的碰撞,计算了跃迁振幅的前后形式,并将相应的微分截面和积分截面与三体形式(CBDW-3B)的结果进行了比较。为了研究静态电子相关对这一过程的影响,用Hylleraas和Silverman波函数描述了氦原子中活性电子的初始束缚态。对氦原子形成正电子的横截面也与现有的实验数据和其他理论的结果进行了比较。
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引用次数: 3
Planck-scale corrections to Friedmann equation 弗里德曼方程的普朗克尺度修正
Pub Date : 2014-03-12 DOI: 10.2478/s11534-014-0441-3
A. Awad, A. Ali
Recently, Verlinde proposed that gravity is an emergent phenomenon which originates from an entropic force. In this work, we extend Verlinde’s proposal to accommodate generalized uncertainty principles (GUP), which are suggested by some approaches to quantum gravity such as string theory, black hole physics and doubly special relativity (DSR). Using Verlinde’s proposal and two known models of GUPs, we obtain modifications to Newton’s law of gravitation as well as the Friedmann equation. Our modification to the Friedmann equation includes higher powers of the Hubble parameter which is used to obtain a corresponding Raychaudhuri equation. Solving this equation, we obtain a leading Planck-scale correction to Friedmann-Robertson-Walker (FRW) solutions for the p = ωp equation of state.
最近,Verlinde提出重力是一种源于熵力的涌现现象。在这项工作中,我们扩展了Verlinde的提议,以适应广义不确定性原理(GUP),这是由一些量子引力方法提出的,如弦理论、黑洞物理和双重狭义相对论(DSR)。利用Verlinde的建议和两个已知的gps模型,我们得到了牛顿万有引力定律和弗里德曼方程的修正。我们对弗里德曼方程的修正包括哈勃参数的更高次幂,用来得到相应的雷乔杜里方程。通过求解该方程,我们得到了p = ωp状态方程弗里德曼-罗伯逊-沃克(FRW)解的领先的普朗克尺度修正。
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引用次数: 18
Electrical characterization of polymer matrix — TiO2 filler composites through isothermal polarization / depolarization currents and I–V tests 通过等温极化/退极化电流和I-V测试表征聚合物基质- TiO2填料复合材料的电学特性
Pub Date : 2014-03-12 DOI: 10.2478/s11534-014-0442-2
I. Stavrakas, D. Triantis, G. Hloupis, K. Moutzouris
Specimens of polymer matrix — ceramic TiO2 filler composites were prepared. The contribution of the filler content on the electrical conductivity and energy storage properties of the samples was examined. I–V and Isothermal Polarization/Depolarization Current (IPC/IDC) measurements were conducted. Dc conductivity values directly calculated from the I–V curves exhibited excellent agreement with corresponding values derived from the IPC/IDC recordings. Standard models were employed for fitting the IPC/IDC data. In specific, the short and the very long depolarization times were fitted by use of power laws of different slopes, while the intermediate depolarization times were fitted as a sum of three exponential decays. The present study reveals a strong dependence of the depolarization and polarization processes, as well as of the dc conductivity, on the filler concentration.
制备了聚合物基-陶瓷TiO2填料复合材料。考察了填料含量对样品电导率和储能性能的影响。进行了I-V和等温极化/去极化电流(IPC/IDC)测量。由I-V曲线直接计算的直流电导率值与IPC/IDC记录的相应值具有良好的一致性。采用标准模型拟合IPC/IDC数据。其中,短退极化时间和超长退极化时间采用不同斜率的幂律进行拟合,中间退极化时间采用三个指数衰减之和进行拟合。本研究揭示了去极化和极化过程以及直流电导率对填料浓度的强烈依赖。
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引用次数: 0
期刊
Central European Journal of Physics
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