The Derivation of 1/N Energy-Solutions to the harper-Equation and Related Magnetizations

1998 ◽  
Vol 12 (18) ◽  
pp. 1847-1870 ◽  
Author(s):  
C. Micu ◽  
E. Papp
Keyword(s):  
Energy Spectrum ◽  
Fermi Level ◽  
Quantum Gas ◽  
One Dimensional ◽  
Implicit Form ◽  
Field Independent ◽  
The One ◽  
First Time ◽  
Harper Equation

Proofs are given for the first time that the energy-spectrum of the Harper-equation can be derived in a closed implicit form by using the one-dimensional limit of the 1/N-description. Explicitly solvable cases are discussed in some more detail for Δ=1. Here Δ expresses the Harper-parameter discriminating between metallic (Δ<1) and insulator (Δ>1) phases. Related magnetizations have been established by applying both Dingle- and quantum-gas approaches, now for a fixed value of the Fermi-level. The first description leads to large paramagnetic-like magnetizations oscillating with nearly field-independent amplitudes increasing with the temperature. In the second case one deals with magnetization-oscillations centered around the zero-value, such that the amplitudes decrease both with the field and the temperature.

scholarly journals Algebraic approach for the one-dimensional Dirac–Dunkl oscillator

2020 ◽  
Vol 35 (31) ◽  
pp. 2050255
Author(s):  
D. Ojeda-Guillén ◽  
R. D. Mota ◽  
M. Salazar-Ramírez ◽  
V. D. Granados
Keyword(s):  
Energy Spectrum ◽  
Irreducible Representation ◽  
Differential Equations ◽  
Representation Theory ◽  
Algebraic Approach ◽  
The Other ◽  
One Dimensional ◽  
The One

We extend the (1 + 1)-dimensional Dirac–Moshinsky oscillator by changing the standard derivative by the Dunkl derivative. We demonstrate in a general way that for the Dirac–Dunkl oscillator be parity invariant, one of the spinor component must be even, and the other spinor component must be odd, and vice versa. We decouple the differential equations for each of the spinor component and introduce an appropriate su(1, 1) algebraic realization for the cases when one of these functions is even and the other function is odd. The eigenfunctions and the energy spectrum are obtained by using the su(1, 1) irreducible representation theory. Finally, by setting the Dunkl parameter to vanish, we show that our results reduce to those of the standard Dirac-Moshinsky oscillator.

scholarly journals A note on inverse problem for strongly damped wave equation with Gaussian white noise

2018 ◽  
Vol 20 ◽  
pp. 02003
Author(s):  
Chu Duc Khanh ◽  
Nguyen Hoang Luc ◽  
Van Phan ◽  
Nguyen Huy Tuan
Keyword(s):  
White Noise ◽  
A Priori ◽  
Gaussian White Noise ◽  
True Solution ◽  
One Dimensional ◽  
Noise Data ◽  
Ill Posed ◽  
The One ◽  
First Time ◽  
Strongly Damped

In this paper, we study for the first time the inverse initial problem for the one-dimensional strongly damped wave with Gaussian white noise data. Under some a priori assumptions on the true solution, we propose the Fourier truncation method for stabilizing the ill-posed problem. Error estimates are given in both the L2– and Hp–norms.

scholarly journals Global Components of Positive Bounded Variation Solutions of a One-Dimensional Indefinite Quasilinear Neumann Problem

2019 ◽  
Vol 19 (3) ◽  
pp. 437-473 ◽  
Author(s):  
Julian López-Gómez ◽  
Pierpaolo Omari
Keyword(s):  
Neumann Problem ◽  
Positive Solutions ◽  
Bounded Variation ◽  
Connected Components ◽  
One Dimensional ◽  
Linearized Problem ◽  
Bounded Variation Functions ◽  
The One ◽  
First Time ◽  
Prime 2

Abstract This paper investigates the topological structure of the set of the positive solutions of the one-dimensional quasilinear indefinite Neumann problem \begin{dcases}-\Bigg{(}\frac{u^{\prime}}{\sqrt{1+{u^{\prime}}^{2}}}\Bigg{)}^{% \prime}=\lambda a(x)f(u)\quad\text{in }(0,1),\\ u^{\prime}(0)=0,\quad u^{\prime}(1)=0,\end{dcases} where {\lambda\in\mathbb{R}} is a parameter, {a\in L^{\infty}(0,1)} changes sign, and {f\in C^{1}(\mathbb{R})} is positive in {(0,+\infty)} . The attention is focused on the case {f(0)=0} and {f^{\prime}(0)=1} , where we can prove, likely for the first time in the literature, a bifurcation result for this problem in the space of bounded variation functions. Namely, the existence of global connected components of the set of the positive solutions, emanating from the line of the trivial solutions at the two principal eigenvalues of the linearized problem around 0, is established. The solutions in these components are regular, as long as they are small, while they may develop jump singularities at the nodes of the weight function a, as they become larger, thus showing the possible coexistence along the same component of regular and singular solutions.

The decay of a plane shock wave

1970 ◽  
Vol 43 (4) ◽  
pp. 737-751 ◽  
Author(s):  
H. Ardavan-Rhad
Keyword(s):  
Analytic Solution ◽  
Weak Shock ◽  
Simple Wave ◽  
Plane Shock ◽  
One Dimensional ◽  
Conductive Medium ◽  
Expansion Theory ◽  
Particular Solution ◽  
The One ◽  
First Time

An analytic solution of the non-isentropic equations of gas-dynamics, for the one-dimensional motion of a non-viscous and non-conductive medium, is derived in this paper for the first time. This is a particular solution which contains only one arbitrary function. On the basis of this solution, the interaction of a centred simple wave with a shock of moderate strength is analyzed; and it is shown that, for a weak shock, this analysis is compatible with Friedrichs's theory. Furthermore, in the light of this analysis, it is explained why the empirical methods employed by the shock-expansion theory, including Whitham's rule for determining the shock path, work.

THE FUNDAMENTAL GROUP OF GALOIS COVER OF THE SURFACE 𝕋 × 𝕋

2008 ◽  
Vol 18 (08) ◽  
pp. 1259-1282 ◽  
Author(s):  
MEIRAV AMRAM ◽  
MINA TEICHER ◽  
UZI VISHNE
Keyword(s):  
Fundamental Group ◽  
Dimensional Torus ◽  
One Dimensional ◽  
Generic Projection ◽  
Galois Cover ◽  
The One ◽  
First Time

This is the final paper in a series of four, concerning the surface 𝕋 × 𝕋 embedded in ℂℙ8, where 𝕋 is the one-dimensional torus. In this paper we compute the fundamental group of the Galois cover of the surface with respect to a generic projection onto ℂℙ2, and show that it is nilpotent of class 3. This is the first time such a group is presented as the fundamental group of a Galois cover of a surface.

scholarly journals Small-Angle Ultra-Narrowband Tunable Mid-Infrared Absorber Composing from Graphene and Dielectric Metamaterials

Coatings ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 825
Author(s):  
Yan-Lin Liao ◽  
Huilin Wang ◽  
Yan Zhao ◽  
Xiang Chen ◽  
Jing Wu ◽  
...  
Keyword(s):  
Fermi Level ◽  
Small Angle ◽  
Resonance Absorption ◽  
Thermal Source ◽  
Mid Infrared ◽  
One Dimensional ◽  
Fabry Perot ◽  
Potential Applications ◽  
The One ◽  
Resonance Cavity

We report a small-angle ultra-narrowband mid-infrared tunable absorber that uses graphene and dielectric metamaterials. The absorption bandwidth of the absorber at the graphene Fermi level of 0.2 eV is 0.055 nm, and the absorption peaks can be tuned from 5.14803 to 5.1411 μm by changing the graphene Fermi level. Furthermore, the resonance absorption only occurs in the angle range of several degrees. The simulation field distributions show the magnetic resonance and Fabry–Pérot resonance at the resonance absorption peak. The one-dimensional photonic crystals (1DPCs) in this absorber act as a Bragg mirror to efficiently reflect the incidence light. The simulation results also show that the bandwidth can be further narrowed by increasing the resonance cavity length. As a tunable mid-infrared thermal source, this absorber can possess both high temporal coherence and near-collimated angle characteristics, thus providing it with potential applications.

scholarly journals Wappapello Dam Spillway Overtopping Event of 2011

2018 ◽  
Vol 46 (2018) ◽  
pp. 69-82
Author(s):  
Gregory H. Nail ◽  
Raymond J. Kopsky
Keyword(s):  
Discharge Coefficient ◽  
Open Channel ◽  
Lake Management ◽  
Hydraulic Modeling ◽  
Flow Modeling ◽  
Intense Rainfall ◽  
One Dimensional ◽  
Modeling Software ◽  
The One ◽  
First Time

Abstract The one-dimensional HEC-RAS multi-purpose open channel flow modeling software was successfully used, with ArcMap and HEC-GeoRAS, to simulate flow over the Wappapello Dam limited-use Ogee spillway (Wappapello, Missouri). Initial computational hydraulic modeling results predicted a lake elevation of 132.9 m (405.0 ft) [NAVD 1988] would be required for the resulting floodwaters overtopping the spillway to reach the nearby Wappapello Lake Management Office. An intense rainfall event during 2011 led to the spillway being overtopped for the first time since 1945. Spillway performance during the 2011 event was analyzed afterwards. Results indicated that the spillway crest was not submerged by backwater. A technique was employed which successfully estimated the design energy head of 7.160 m (23.49 ft) for the spillway. Hydraulic modeling developed after the 2011 event incorporated this estimated design energy head, allowing the spillway discharge coefficient to vary with discharge in the course of an unsteady modeling run. Results indicated that, while the spillway did perform as designed, the performance is limited by the shallow approach depth.

scholarly journals Three-step Predictor-Corrector Finite Element Schemes for Consolidation Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Mina Torabi ◽  
Manuel Pastor ◽  
Miguel Martín Stickle
Keyword(s):  
Integration Method ◽  
Time Integration ◽  
Spectral Element ◽  
Euler Method ◽  
One Dimensional ◽  
Time Integration Method ◽  
The One ◽  
Predictor Corrector ◽  
Finite Element Schemes ◽  
First Time

An accurate, stable, and efficient three-step predictor-corrector time integration method is considered, for the first time, to obtain numerical solution for the one-dimensional consolidation equation within a finite and spectral element framework. Theoretical order of accuracy and stability conditions are provided. The three-step predictor-corrector time integration method is third-order accurate and shows a larger stability region than the forward Euler method when applied to the one-dimensional consolidation equation. Furthermore, numerical results are in agreement with analytical solutions previously derived by the authors.

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