Abstract: Recently, cavity-optomechanics becomes an extensive research field that has manipulated the mechanical effects of light for coupling of the optical field with other physical objects specifically with regards to dynamical localization. We investigate the dynamical localization (both in momentum and position space) for a vibrational mirror in a Fabry-Pérot cavity driven by a single mode optical field and a transverse probe field. The weak probe field phenomenon results in classical chaos in phase space and spatio temporal dynamics in position |ψ(x)²| and momentum space |ψ(p)²| versus time show quantum localization in both momentum and position space. Also, we discuss the parametric dependencies of dynamical localization for a designated set of parameters to be experimentally feasible. Our work opens an avenue to manipulate the other optical phenomena and applicability of proposed work can be prolonged to turn-able laser sources in the future.
Abstract: In this paper, we show that the conjecture of Chv tal, which states that any 1-tough graph is either a Hamiltonian graph or its complement contains a specific graph denoted by F, does not hold in general. More precisely, it is true only for graphs with six or seven vertices, and is false for graphs with eight or more vertices. A theorem is derived as a correction for the conjecture.
Abstract: We show that a simple transformation between the regular lattices (the square, the triangular, and the honeycomb) belonging to the same dimensionality can explain in a natural way the universality of the critical exponents found in phase transitions and critical phenomena. It suffices that the Hamiltonian and the lattice present similar writing forms. In addition, it appears that if a property can be calculated for a given lattice then it can be extrapolated simply to any other lattice belonging to the same dimensionality. In this study, we have restricted ourselves on the spectral power amplification (SPA), we note that the SPA does not have an effect on the critical exponents but does have an effect by the criticality temperature of the lattice; the generalisation to other lattice could be shown according to the containment principle.
Abstract: Through the Fukaya conjecture and the wrapped Floer cohomology, the correspondences between paths in a loop space and states of a wrapping space of states in a Hamiltonian space (the ramification of field in this case is the connection to the operator that goes from TM to T*M) are demonstrated where these last states are corresponding to bosonic extensions of a spectrum of the space-time or direct image of the functor Spec, on space-time. This establishes a distinguished diffeomorphism defined by the mapping from the corresponding loops space to wrapping category of the Floer cohomology complex which furthermore relates in certain proportion D-branes (certain D-modules) with strings. This also gives to place to certain conjecture that establishes equivalences between moduli spaces that can be consigned in a moduli identity taking as space-time the Hitchin moduli space on G, whose dual can be expressed by a factor of a bosonic moduli spaces.
Abstract: Performance of a Hamiltonian based particle method in simulation of nonlinear structural dynamics is subjected to investigation in terms of stability and accuracy. The governing equation of motion is derived based on Hamilton's principle of least action, while the deformation gradient is obtained according to Weighted Least Square method. The hyper-elasticity models of Saint Venant-Kirchhoff and a compressible version similar to Mooney- Rivlin are engaged for the calculation of second Piola-Kirchhoff stress tensor, respectively. Stability along with accuracy of numerical model is verified by reproducing critical stress fields in static and dynamic responses. As the results, although performance of Hamiltonian based model is evaluated as being acceptable in dealing with intense extensional stress fields, however kinds of instabilities reveal in the case of violent collision which can be most likely attributed to zero energy singular modes.
Abstract: We present the concept and scientific methods and algorithms of our computation system called ATOMIC MATTERS. This is the first presentation of the new computer package, that allows its user to describe physical properties of atomic localized electron systems subject to electromagnetic interactions. Our solution applies to situations where an unclosed electron 2p/3p/3d/4d/5d/4f/5f subshell interacts with an electrostatic potential of definable symmetry and external magnetic field. Our methods are based on Crystal Electric Field (CEF) approach, which takes into consideration the electrostatic ligands field as well as the magnetic Zeeman effect. The application allowed us to predict macroscopic properties of materials such as: Magnetic, spectral and calorimetric as a result of physical properties of their fine electronic structure. We emphasize the importance of symmetry of charge surroundings of atom/ion, spin-orbit interactions (spin-orbit coupling) and the use of complex number matrices in the definition of the Hamiltonian. Calculation methods, algorithms and convention recalculation tools collected in ATOMIC MATTERS were chosen to permit the prediction of magnetic and spectral properties of materials in isostructural series.
Abstract: This paper deals with study about fractional
order impulsive Hamiltonian systems and fractional impulsive
Sturm-Liouville type problems derived from these systems. The
main purpose of this paper devotes to obtain so called Lyapunov
type inequalities for mentioned problems. Also, in view point on
applicability of obtained inequalities, some qualitative properties such
as stability, disconjugacy, nonexistence and oscillatory behaviour of
fractional Hamiltonian systems and fractional Sturm-Liouville type
problems under impulsive conditions will be derived. At the end,
we want to point out that for studying fractional order Hamiltonian
systems, we will apply recently introduced fractional Conformable
operators.
Abstract: In this paper, a thorough review about dual-cubes, DCn,
the related studies and their variations are given. DCn was introduced
to be a network which retains the pleasing properties of hypercube Qn
but has a much smaller diameter. In fact, it is so constructed that the
number of vertices of DCn is equal to the number of vertices of Q2n
+1. However, each vertex in DCn is adjacent to n + 1 neighbors and
so DCn has (n + 1) × 2^2n edges in total, which is roughly half the
number of edges of Q2n+1. In addition, the diameter of any DCn is 2n
+2, which is of the same order of that of Q2n+1. For selfcompleteness,
basic definitions, construction rules and symbols are
provided. We chronicle the results, where eleven significant theorems
are presented, and include some open problems at the end.
Abstract: Given a graph G. A cycle of G is a sequence of
vertices of G such that the first and the last vertices are the same.
A hamiltonian cycle of G is a cycle containing all vertices of G.
The graph G is k-ordered (resp. k-ordered hamiltonian) if for any
sequence of k distinct vertices of G, there exists a cycle (resp.
hamiltonian cycle) in G containing these k vertices in the specified
order. Obviously, any cycle in a graph is 1-ordered, 2-ordered and 3-
ordered. Thus the study of any graph being k-ordered (resp. k-ordered
hamiltonian) always starts with k = 4. Most studies about this topic
work on graphs with no real applications. To our knowledge, the
chordal ring families were the first one utilized as the underlying
topology in interconnection networks and shown to be 4-ordered.
Furthermore, based on our computer experimental results, it was
conjectured that some of them are 4-ordered hamiltonian. In this
paper, we intend to give some possible directions in proving the
conjecture.
Abstract: Supersymmetric Quantum Mechanics is an interesting
framework to analyze nonrelativistic quantal problems. Using these
techniques, we construct a family of strictly isospectral Hulth´en
potentials. Isospectral wave functions are generated and plotted for
different values of the deformation parameter.
Abstract: The ionization energy in semiconductor
systems in nano scale was investigated by using effective mass
approximation. By introducing the Hamiltonian of the system, the
variational technique was employed to calculate the ground state and
the ionization energy of a donor at the center and in the case that the
impurities are randomly distributed inside a cubic quantum well. The
numerical results for GaAs/GaAlAs show that the ionization energy
strongly depends on the well width for both cases and it decreases as
the well width increases. The ionization energy of a quantum wire
was also calculated and compared with the results for the well.
Abstract: In this paper we consider a nonlinear feedback control called augmented automatic choosing control (AACC) for nonlinear systems with constrained input. Constant terms which arise from section wise linearization of a given nonlinear system are treated as coefficients of a stable zero dynamics.Parameters included in the control are suboptimally selectedby extremizing a combination of Hamiltonian and Lyapunov functions with the aid of the genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.
Abstract: In this paper, we use Generalized Hamiltonian systems approach to synchronize a modified sixth-order Chua's circuit, which generates hyperchaotic dynamics. Synchronization is obtained between the master and slave dynamics with the slave being given by an observer. We apply this approach to transmit private information (analog and binary), while the encoding remains potentially secure.
Abstract: In this paper we consider a nonlinear feedback
control called augmented automatic choosing control (AACC)
using the automatic choosing functions of gradient optimization
type for nonlinear systems. Constant terms which arise from sectionwise
linearization of a given nonlinear system are treated as
coefficients of a stable zero dynamics. Parameters included in the
control are suboptimally selected by minimizing the Hamiltonian
with the aid of the genetic algorithm. This approach is applied to
a field excitation control problem of power system to demonstrate
the splendidness of the AACC. Simulation results show that the
new controller can improve performance remarkably well.
Abstract: Qk
n has been shown as an alternative to the hypercube
family. For any even integer k ≥ 4 and any integer n ≥ 2, Qk
n is
a bipartite graph. In this paper, we will prove that given any pair of
vertices, w and b, from different partite sets of Qk
n, there exist 2n
internally disjoint paths between w and b, denoted by {Pi | 0 ≤ i ≤ 2n-1}, such that 2n-1
i=0 Pi covers all vertices of Qk
n. The result is
optimal since each vertex of Qk
n has exactly 2n neighbors.
Abstract: In a graph G, a cycle is Hamiltonian cycle if it contain all vertices of G. Two Hamiltonian cycles C_1 = 〈u_0, u_1, u_2, ..., u_{n−1}, u_0〉 and C_2 = 〈v_0, v_1, v_2, ..., v_{n−1}, v_0〉 in G are independent if u_0 = v_0, u_i = ̸ v_i for all 1 ≤ i ≤ n−1. In G, a set of Hamiltonian cycles C = {C_1, C_2, ..., C_k} is mutually independent if any two Hamiltonian cycles of C are independent. The mutually independent Hamiltonicity IHC(G), = k means there exist a maximum integer k such that there exists k-mutually independent Hamiltonian cycles start from any vertex of G. In this paper, we prove that IHC(C_n × C_n) = 4, for n ≥ 3.
Abstract: In this paper smooth trajectories are computed in the Lie group SO(2, 1) as a motion planning problem by assigning a Frenet frame to the rigid body system to optimize the cost function of the elastic energy which is spent to track a timelike curve in Minkowski space. A method is proposed to solve a motion planning problem that minimizes the integral of the Lorentz inner product of Darboux vector of a timelike curve. This method uses the coordinate free Maximum Principle of Optimal control and results in the theory of integrable Hamiltonian systems. The presence of several conversed quantities inherent in these Hamiltonian systems aids in the explicit computation of the rigid body motions.
Abstract: In the last decade, energy based control theory has undergone a significant breakthrough in dealing with underactated mechanical systems with two successful and similar tools, controlled Lagrangians and controlled Hamiltanians (IDA-PBC). However, because of the complexity of these tools, successful case studies are lacking, in particular, MIMO cases. The seminal theoretical paper of controlled Lagrangians proposed by Bloch and his colleagues presented a benchmark example–a 4 d.o.f underactuated pendulum on a cart but a detailed and completed design is neglected. To compensate this ignorance, the note revisit their design idea by addressing explicit control functions for a similar device motivated by a vector thrust body hovering in the air. To the best of our knowledge, this system is the first MIMO, underactuated example that is stabilized by using energy based tools at the courtesy of the original design idea. Some observations are given based on computer simulation.
Abstract: Let a and b be nonnegative integers with 2 ≤ a < b, and
let G be a Hamiltonian graph of order n with n ≥ (a+b−4)(a+b−2)
b−2 .
An [a, b]-factor F of G is called a Hamiltonian [a, b]-factor if F
contains a Hamiltonian cycle. In this paper, it is proved that G has a
Hamiltonian [a, b]-factor if |NG(X)| > (a−1)n+|X|−1
a+b−3 for every nonempty
independent subset X of V (G) and δ(G) > (a−1)n+a+b−4
a+b−3 .
Abstract: Fractional Fourier Transform, which is a
generalization of the classical Fourier Transform, is a powerful tool
for the analysis of transient signals. The discrete Fractional Fourier
Transform Hamiltonians have been proposed in the past with varying
degrees of correlation between their eigenvectors and Hermite
Gaussian functions. In this paper, we propose a new Hamiltonian for
the discrete Fractional Fourier Transform and show that the
eigenvectors of the proposed matrix has a higher degree of
correlation with the Hermite Gaussian functions. Also, the proposed
matrix is shown to give better Fractional Fourier responses with
various transform orders for different signals.