scholarly journals Shape equations for two-dimensional manifolds through a moving frame variational approach

2019 ◽  
Vol 16 (10) ◽  
pp. 1950155 ◽  
Author(s):  
Paul Bracken
Keyword(s):  
Variational Approach ◽  
Moving Frame ◽  
Two Dimensional ◽  
Second Variation ◽  
First Variation ◽  
Shape Equation ◽  
The Mean ◽  
The First Variation ◽  
The Second Variation ◽  
Area And Volume

A variational approach is given which can be applied to functionals of a general form to determine a corresponding Euler–Lagrange or shape equation. It is the intention to formulate the theory in detail based on a moving frame approach. It is then applied to a functional of a general form which depends on both the mean and Gaussian curvatures as well as the area and volume elements of the manifold. Only the case of a two-dimensional closed manifold is considered. The first variation of the functional is calculated in terms of the variations of the basic variables of the manifold. The results of the first variation allow for the second variation of the functional to be evaluated.

Dog Bites Postman

1998 ◽  
Vol 08 (03) ◽  
pp. 321-342 ◽  
Author(s):  
Olivier Devillers ◽  
Mordecai J. Golin
Keyword(s):  
Data Structure ◽  
Dynamic Structure ◽  
Query Point ◽  
Two Dimensional ◽  
Second Variation ◽  
Post Office ◽  
First Variation ◽  
Post Offices ◽  
The First Variation ◽  
The Second Variation

In this paper, we discuss two variations of the two-dimensional post-office problem that arise when the post-offices are n postmen moving with constant velocities. The first variation addresses the question: given a point q0and time t0who is the nearest postman to q0at time t0? We present a randomized incremental data structure that answers the query in expected O( log2n) time. The second variation views a query point as a dog searching for a postman to bite and finds the postman that a dog running with speed vdcould reach first. While it is quite straightforward to design a data structure for the first problem, designing one for the second appears more difficult. We show that if the dog is quicker than all of the postmen then there is a nice correspondence between the problems. This correspondence will permit us to use the data structure developed for the first problem to solve the second one in O( log2n) time as well.The proposed structure is semi-dynamic, that is the set of postmen can be modified by inserting new postmen. A fully dynamic structure that also supports deletions can be obtained, but in that case the query time becomes O( log3n).

scholarly journals Fabrication of dye Rhoeospathacea with concentration variation in dye-sensitized solar cells (DSSC)

2017 ◽  
Vol 1 (1) ◽  
pp. 83
Author(s):  
Sri Sumardiasih ◽  
Agus Supriyanto ◽  
C Cari
Keyword(s):  
Titanium Dioxide ◽  
Dye Sensitized Solar Cells ◽  
Electrical Energy ◽  
Second Variation ◽  
First Variation ◽  
Dye Sensitized ◽  
The First Variation ◽  
The Second Variation ◽  
Sensitized Solar Cells ◽  
Absorbance Spectra

<p class="Abstract">Dye-sensitized solar cell (DSSC) is a device that directly converts visible light into electrical energy. In this work we used dye was extracted from Rhoeo spathacea. A natural dye was directly mixed with TiO<sub>2 </sub>anatase to obtain <em>dyed titanium dioxide</em> which can be used as photoanode for DSSC by varying the volume of dye. The first variation is 2 ml dye mixed with 1 ml of TiO<sub>2</sub>, and the second variation is 3 ml dye mixed with 1 ml of TiO<sub>2</sub>. The absorbance spectra of the dye and dye titanium dioxide have been investigated by spectroscopy UV-<em>Visible Lambda </em>25 and the conversion efficiency of dye titanium dioxide used Keithley 2602A meter. The DSSC based on dye titanium dioxide with varying volume of dye showed that the efficiency of the the second variation is 0,033% which is higher than the first variation (0,023%) as obtained from I-V characterization.</p><p class="Abstract"> </p>

scholarly journals Symplectic connections and the linearisation of Hamiltonian systems

1991 ◽  
Vol 117 (3-4) ◽  
pp. 329-380 ◽  
Author(s):  
J. E. Marsden ◽  
T. Ratiu ◽  
G. Raugel
Keyword(s):  
Hamiltonian System ◽  
Symplectic Structure ◽  
Equilibrium Solution ◽  
Hamiltonian Structure ◽  
Second Variation ◽  
First Variation ◽  
Space Construction ◽  
Symplectic Connections ◽  
The First Variation ◽  
The Second Variation

SynopsisThis paper uses symplectic connections to give a Hamiltonian structure to the first variation equation for a Hamiltonian system along a given dynamic solution. This structure generalises that at an equilibrium solution obtained by restricting the symplectic structure to that point and using the quadratic form associated with the second variation of the Hamiltonian (plus Casimir) as energy. This structure is different from the well-known and elementary tangent space construction. Our results are applied to systems with symmetry and to Lie–Poisson systems in particular.

Fabrication of dye Rhoeospathacea with concentration variation in dye-sensitized solar cells (DSSC)

2017 ◽  
Vol 1 (1) ◽  
pp. 83
Author(s):  
Sri Sumardiasih ◽  
Agus Supriyanto ◽  
C Cari
Keyword(s):  
Titanium Dioxide ◽  
Dye Sensitized Solar Cells ◽  
Electrical Energy ◽  
Second Variation ◽  
First Variation ◽  
Dye Sensitized ◽  
The First Variation ◽  
The Second Variation ◽  
Sensitized Solar Cells ◽  
Absorbance Spectra

<p class="Abstract">Dye-sensitized solar cell (DSSC) is a device that directly converts visible light into electrical energy. In this work we used dye was extracted from Rhoeo spathacea. A natural dye was directly mixed with TiO<sub>2 </sub>anatase to obtain <em>dyed titanium dioxide</em> which can be used as photoanode for DSSC by varying the volume of dye. The first variation is 2 ml dye mixed with 1 ml of TiO<sub>2</sub>, and the second variation is 3 ml dye mixed with 1 ml of TiO<sub>2</sub>. The absorbance spectra of the dye and dye titanium dioxide have been investigated by spectroscopy UV-<em>Visible Lambda </em>25 and the conversion efficiency of dye titanium dioxide used Keithley 2602A meter. The DSSC based on dye titanium dioxide with varying volume of dye showed that the efficiency of the the second variation is 0,033% which is higher than the first variation (0,023%) as obtained from I-V characterization.</p><p class="Abstract"> </p>

Complete Riemannian Manifold with Curvature Bounded from Below

2012 ◽  
Vol 182-183 ◽  
pp. 1225-1229
Author(s):  
Qiong Xue ◽  
Xiao Feng Xiao
Keyword(s):  
Riemannian Manifold ◽  
Complete Riemannian Manifold ◽  
Second Variation ◽  
Variation Formula ◽  
Totally Geodesic Submanifold ◽  
Totally Geodesic ◽  
First Variation ◽  
Geodesic Submanifold ◽  
The First Variation ◽  
The Second Variation

In this paper, we study a complete -Riemannian manifold whose curvature bounded from below. Let be a compact totally geodesic submanifold of . Then, for any , we can make use of the first variation formula and the second variation formula of distance to prove that is bounded.

scholarly journals Analisis Drag dan Lift pada Variasi Bentuk After Body Kapal Selam Mini dengan Metode Computational Fluid Dynamics

2017 ◽  
Vol 2 (1) ◽  
pp. 25
Author(s):  
Putri Virliani ◽  
I Ketut Suastika ◽  
Wasis Dwi Aryawan
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Second Variation ◽  
First Variation ◽  
The Third ◽  
Ansys Cfx ◽  
The First Variation ◽  
Drag And Lift ◽  
The Second Variation ◽  
Submarine Maneuverability

One aspect that needs to be studied in submarine design is the hydrodynamic aspect relating to submarine maneuverability. This research begins by calculating the value of drag and lift  on the three variations of the after body’s mini submarine. The first variation as the initial design is rudder and stern plane arranged perpendicularly or named the+ Stern. Then for the second variation made changes to the arrangement of rudder and stern plane in the after body of the mini submarine with + Stern arrangement, the rudder arranged each other crossed so that it resembles the letter X and called the X-Stern arrangement. Further, for the third variation, the upper rudder of the X-Stern arrangement is replaced by the upper rudder of the + Sternarrangement so that it resembles the inverted Y letter and is called the Y-Stern arrangement. Drag and lift are calculated numerically by using ANSYS-CFX software. From the calculation of CFD found that the submarine with after-body Y-Stern arrangement has the smallest drag and lift value.

ON TWO VARIATIONS OF THE REVERSAL MEDIAN PROBLEM

2012 ◽  
Vol 09 ◽  
pp. 285-292
Author(s):  
ZHONG ZHOU ◽  
MELVIN ZHANG ◽  
FANCHANG HAO ◽  
HON WAI LEONG
Keyword(s):  
Exact Algorithm ◽  
Compact Representation ◽  
Ancestral Genome ◽  
Second Variation ◽  
Median Problem ◽  
First Variation ◽  
Additional Input ◽  
The First Variation ◽  
The Second Variation ◽  
Do So

We have developed an exact algorithm that solves certain instances of the Reversal Median Problem (RMP) when provided with additional input – the optimal sorting sequences between every pair of genomes. Our algorithm is able to provide an exact solution (the median genome) or determine that it is not able to do so for every instance of the problem. We have also proven the correctness of the algorithm in a theorem. RMP is the problem of finding an ancestral genome (the median) given the gene orders of three genomes. It is commonly encountered when constructing phylogeny, and is NP-hard. Two variations of the RMP were considered. In the first variation, we are given one sorting sequence for each pair of genomes. And in the second variation, we make use of a compact representation of all possible optimal sorting sequences for each pair of genomes that was developed by Braga et al.

scholarly journals THE FIRST AND SECOND VARIATION OF THE TOTAL ENERGY OF CLOSED DUPLEX DNA IN PLANAR CASE

2010 ◽  
Vol 24 (05) ◽  
pp. 587-597 ◽  
Author(s):  
XIAO-HUA ZHOU
Keyword(s):  
Total Energy ◽  
Equilibrium Shape ◽  
Variation Method ◽  
Second Variation ◽  
General Shape ◽  
Planar Case ◽  
The First Variation ◽  
The Second Variation ◽  
First And Second Variation ◽  
Classical Variation

DNA's shape mostly lies on its total energy F. Its corresponding equilibrium shape equations can be obtained by classical variation method: letting the first energy variation δ(1)F = 0. Here, we not only provide the first variation δ(1)F but also give the second variation δ(2)F in planar case. Moreover, the general shape equations of DNA are abstained and a mistake in Zhang et al., [Phys. Rev. E70, 051902 (2004)] is pointed out.

On general transformations and variational principles for the magnetohydrodynamics of ideal fluids. Part 2. Stability criteria for two-dimensional flows

1996 ◽  
Vol 329 ◽  
pp. 187-205 ◽  
Author(s):  
V. A. Vladimirov ◽  
H. K. Moffatt ◽  
K. I. Ilin
Keyword(s):  
Magnetic Field ◽  
Vector Potential ◽  
Variational Principles ◽  
Two Dimensional ◽  
Ideal Fluids ◽  
The Mean ◽  
And Variational Principles ◽  
The Second Variation ◽  
The Magnetic Field ◽  
Standard Techniques

The techniques developed in Part 1 of the present series are here applied to two-dimensional solutions of the equations governing the magnetohydrodynamics of ideal incompressible fluids. We first demonstrate an isomorphism between such flows and the flow of a stratified fluid subjected to a field of force that we describe as ‘pseudo-gravitational’. We then construct a general Casimir as an integral of an arbitrary function of two conserved fields, namely the vector potential of the magnetic field, and the analogous potential of the ‘modified vorticity field’, the additional frozen field introduced in Part 1. Using this Casimir, a linear stability criterion is obtained by standard techniques. In §4, the (Arnold) techniques of nonlinear stability are developed, and bounds are placed on the second variation of the sum of the energy and the Casimir of the problem. This leads to criteria for nonlinear (Lyapunov) stability of the MHD flows considered. The appropriate norm is a sum of the magnetic and kinetic energies and the mean-square vector potential of the magnetic field.

scholarly journals An Iterative Technique for the Synthesis of Active Antenna Oscillator Arrays

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Theodoros N. Kaifas ◽  
John N. Sahalos
Keyword(s):  
Design Procedure ◽  
Active Antenna ◽  
Stopping Criteria ◽  
First Variation ◽  
Tuning Parameters ◽  
The Mean ◽  
The First Variation ◽  
Oscillator Arrays ◽  
The Cost ◽  
Final Array

A design procedure for the synthesis of a coupled active antenna oscillator array is presented. Such an array is synthesized by deriving two sets of parameters: the radiators' positions and the oscillators' outputs. The outputs are used to excite the radiators. Minimization of the mean square error between the desired pattern and the resulting one is made. Synthesis starts from an initial array, which is perturbed iteratively by varying simultaneously the element excitations and positions. In the iteration, the first variation of the cost function is set equal to zero. The final array results from the last iteration, where the stopping criteria are met. The procedure designs simultaneously both the antenna and the attached coupled oscillator array providing viable solutions. The second by properly configuring the tuning parameters through the use of closed-form formulas. The resulting arrays are shown to comply with the desired pattern and the nonlinear dynamics thus proving the validity of our method.

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