77

10008892

Optimal Portfolio Selection in a DC Pension with Multiple Contributors and the Impact of Stochastic Additional Voluntary Contribution on the Optimal Investment Strategy

In this paper, we studied the optimal portfolio selection in a defined contribution (DC) pension scheme with multiple contributors under constant elasticity of variance (CEV) model and the impact of stochastic additional voluntary contribution on the investment strategies. We assume that the voluntary contributions are stochastic and also consider investments in a risk free asset and a risky asset to increase the expected returns of the contributing members. We derived a stochastic differential equation which consists of the members’ monthly contributions and the invested fund and obtained an optimized problem with the help of Hamilton Jacobi Bellman equation. Furthermore, we find an explicit solution for the optimal investment strategy with stochastic voluntary contribution using power transformation and change of variables method and the corresponding optimal fund size was obtained. We discussed the impact of the voluntary contribution on the optimal investment strategy with numerical simulations and observed that the voluntary contribution reduces the optimal investment strategy of the risky asset.

76

10007745

Geo-Spatial Methods to Better Understand Urban Food Deserts

Food deserts are a reality in some cities. These deserts can be described as a shortage of healthy food options within close proximity of consumers. The shortage in this case is typically facilitated by a lack of stores in an urban area that provide adequate fruit and vegetable choices. This study explores new avenues to better understand food deserts by examining modes of transportation that are available to shoppers or consumers, e.g. walking, automobile, or public transit. Further, this study is unique in that it not only explores the location of large grocery stores, but small grocery and convenience stores too. In this study, the relationship between some socio-economic indicators, such as personal income, are also explored to determine any possible association with food deserts. In addition, to help facilitate our understanding of food deserts, complex network spatial models that are built on adequate algorithms are used to investigate the possibility of food deserts in the city of Hamilton, Canada. It is found that Hamilton, Canada is adequate serviced by retailers who provide healthy food choices and that the food desert phenomena is almost absent.

75

10007394

The Spectral Power Amplification on the Regular Lattices

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.

74

10008144

A Study of Hamilton-Jacobi-Bellman Equation Systems Arising in Differential Game Models of Changing Society

This paper is concerned with a system of
Hamilton-Jacobi-Bellman equations coupled with an autonomous
dynamical system. The mathematical system arises in the differential
game formulation of political economy models as an infinite-horizon
continuous-time differential game with discounted instantaneous
payoff rates and continuously and discretely varying state variables.
The existence of a weak solution of the PDE system is proven and
a computational scheme of approximate solution is developed for a
class of such systems. A model of democratization is mathematically
analyzed as an illustration of application.

73

10006924

Topological Quantum Diffeomorphisms in Field Theory and the Spectrum of the Space-Time

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.

72

10006633

Super Harmonic Nonlinear Lateral Vibration of an Axially Moving Beam with Rotating Prismatic Joint

The motion of an axially moving beam with rotating prismatic joint with a tip mass on the end is analyzed to investigate the nonlinear vibration and dynamic stability of the beam. The beam is moving with a harmonic axially and rotating velocity about a constant mean velocity. A time-dependent partial differential equation and boundary conditions with the aid of the Hamilton principle are derived to describe the beam lateral deflection. After the partial differential equation is discretized by the Galerkin method, the method of multiple scales is applied to obtain analytical solutions. Frequency response curves are plotted for the super harmonic resonances of the first and the second modes. The effects of non-linear term and mean velocity are investigated on the steady state response of the axially moving beam. The results are validated with numerical simulations.

71

10006829

Process Optimisation for Internal Cylindrical Rough Turning of Nickel Alloy 625 Weld Overlay

Nickel-based superalloys are generally known to be difficult to cut due to their strength, low thermal conductivity, and high work hardening tendency. Superalloy such as alloy 625 is often used in the oil and gas industry as a surfacing material to provide wear and corrosion resistance to components. The material is typically applied onto a metallic substrate through weld overlay cladding, an arc welding technique. Cladded surfaces are always rugged and carry a tough skin; this creates further difficulties to the machining process. The present work utilised design of experiment to optimise the internal cylindrical rough turning for weld overlay surfaces. An L27 orthogonal array was used to assess effects of the four selected key process variables: cutting insert, depth of cut, feed rate, and cutting speed. The optimal cutting conditions were determined based on productivity and the level of tool wear.

70

10006928

Non-Linear Vibration and Stability Analysis of an Axially Moving Beam with Rotating-Prismatic Joint

In this paper, the dynamic modeling of a single-link flexible beam with a tip mass is given by using Hamilton's principle. The link has been rotational and translational motion and it was assumed that the beam is moving with a harmonic velocity about a constant mean velocity. Non-linearity has been introduced by including the non-linear strain to the analysis. Dynamic model is obtained by Euler-Bernoulli beam assumption and modal expansion method. Also, the effects of rotary inertia, axial force, and associated boundary conditions of the dynamic model were analyzed. Since the complex boundary value problem cannot be solved analytically, the multiple scale method is utilized to obtain an approximate solution. Finally, the effects of several conditions on the differences among the behavior of the non-linear term, mean velocity on natural frequencies and the system stability are discussed.

69

10006602

A Refined Nonlocal Strain Gradient Theory for Assessing Scaling-Dependent Vibration Behavior of Microbeams

A size-dependent Euler–Bernoulli beam model, which
accounts for nonlocal stress field, strain gradient field and higher
order inertia force field, is derived based on the nonlocal strain
gradient theory considering velocity gradient effect. The governing
equations and boundary conditions are derived both in dimensional
and dimensionless form by employed the Hamilton principle. The
analytical solutions based on different continuum theories are
compared. The effect of higher order inertia terms is extremely
significant in high frequency range. It is found that there exists
an asymptotic frequency for the proposed beam model, while for
the nonlocal strain gradient theory the solutions diverge. The effect
of strain gradient field in thickness direction is significant in low
frequencies domain and it cannot be neglected when the material
strain length scale parameter is considerable with beam thickness.
The influence of each of three size effect parameters on the natural
frequencies are investigated. The natural frequencies increase with
the increasing material strain gradient length scale parameter or
decreasing velocity gradient length scale parameter and nonlocal
parameter.

68

10005567

A Lagrangian Hamiltonian Computational Method for Hyper-Elastic Structural Dynamics

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.

67

10005445

Linear Dynamic Stability Analysis of a Continuous Rotor-Disk-Blades System

Nowadays, using rotating systems like shafts and disks in industrial machines have been increased constantly. Dynamic stability is one of the most important factors in designing rotating systems. In this study, linear frequencies and stability of a coupled continuous flexible rotor-disk-blades system are studied. The Euler-Bernoulli beam theory is utilized to model the blade and shaft. The equations of motion are extracted using the extended Hamilton principle. The equations of motion have been simplified using the Coleman and complex transformations method. The natural frequencies of the linear part of the system are extracted, and the effects of various system parameters on the natural frequencies and decay rates (stability condition) are clarified. It can be seen that the centrifugal stiffening effect applied to the blades is the most important parameter for stability of the considered rotating system. This result highlights the importance of considering this stiffing effect in blades equation.

66

10004653

Describing the Fine Electronic Structure and Predicting Properties of Materials with ATOMIC MATTERS Computation System

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.

65

10004599

Lyapunov Type Inequalities for Fractional Impulsive Hamiltonian Systems

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.

64

10004380

Hamiltonian Related Properties with and without Faults of the Dual-Cube Interconnection Network and Their Variations

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.

63

10001136

Solar Radiation Time Series Prediction

A model was constructed to predict the amount of solar radiation that will make contact with the surface of the earth in a given location an hour into the future. This project was supported by the Southern Company to determine at what specific times during a given day of the year solar panels could be relied upon to produce energy in sufficient quantities. Due to their ability as universal function approximators, an artificial neural network was used to estimate the nonlinear pattern of solar radiation, which utilized measurements of weather conditions collected at the Griffin, Georgia weather station as inputs. A number of network configurations and training strategies were utilized, though a multilayer perceptron with a variety of hidden nodes trained with the resilient propagation algorithm consistently yielded the most accurate predictions. In addition, a modeled direct normal irradiance field and adjacent weather station data were used to bolster prediction accuracy. In later trials, the solar radiation field was preprocessed with a discrete wavelet transform with the aim of removing noise from the measurements. The current model provides predictions of solar radiation with a mean square error of 0.0042, though ongoing efforts are being made to further improve the model’s accuracy.

62

10000360

A Further Study on the 4-Ordered Property of Some Chordal Ring Networks

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.

61

9999602

Vibration Analysis of Functionally Graded Engesser- Timoshenko Beams Subjected to Axial Load Located on a Continuous Elastic Foundation

This paper studies free vibration of functionally graded beams Subjected to Axial Load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton's principle, the governing equation is established. Resulting equation is solved using the Euler's Equation. The effects of the constituent volume fractions and foundation coefficient on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

60

9997757

Isospectral Hulthén Potential

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.

59

9997118

Antioxidant Properties and Nutritive Values of Raw and Cooked Pool Barb (Puntius sophore) of Eastern Himalayas

Antioxidant properties and nutritive values of raw and cooked Pool barb, Puntius sophore (Hamilton-Buchanan) of Eastern Himalayas, India were determined. Antioxidant activity of the methanol extract of the raw, steamed, fried and curried Pool barb was evaluated by using 1,1-diphenyl-2-picrylhydrazyl (DPPH) scavenging assay. In DPPH scavenging assay the IC50 value of the raw, steamed, fried and curried Pool barb was 1.66 micro-gram/ml, 16.09 micro-gram/ml, 8.99 micro-gram/ml, 0.59 micro-gram/ml whereas the IC50 of the reference ascorbic acid was 46.66miro-gram/ml. These results showed that the fish have high antioxidant activity. Protein content was found highest in raw (20.50±0.08%) and lowest in curried (18.66±0.13%). Moisture content in raw, fried and curried was 76.35±0.09, 46.27±0.14 and 57.46±0.24 respectively. Lipid content was recorded 2.46±0.14% in raw and 21.76±0.10% in curried. Ash content varied from 12.57±0.11 to 22.53±0.07%. The total amino acids varied from 36.79±0.02 and 288.43±0.12 mg/100g. Eleven essential mineral elements were found abundant in all the samples. The samples had considerable amount of Fe ranging from 152.17 to 320.39 milli-gram/100gram, Ca 902.06 to 1356.02 milli-gram/100gram, Zn 91.07 to 138.14 milli-gram/100gram, K 193.25 to 261.56 milli-gram/100gram, Mg 225.06 to 229.10 milli-gram/100gram. Ni was not detected in the curried fish. The Mg and K contents were significantly decreased in frying method; however the Fe, Cu, Ca, Co and Mn contents were increased significantly in all the cooked samples. The Mg and Na contents were significantly increased in curried sample and the Cr content was decreased significantly (p<0.05) in all the cooked samples.

58

17344

A Homogenisation Procedure for the Free Vibration Analysis of Functionally Graded Beams at Large Vibration Amplitudes

The purpose of the present paper is to show that the problem of geometrically nonlinear free vibrations of functionally graded beams (FGB) with immovable ends can be reduced to that of isotropic homogeneous beams with effective bending stiffness and axial stiffness parameters by using an homogenization procedure. The material properties of the functionally graded composites examined are assumed to be graded in the thickness direction and estimated through the rule of mixture. The theoretical model is based on the Euler-Bernouilli beam theory and the Von Kármán geometrical nonlinearity assumptions. Hamilton’s principle is applied and a multimode approach is derived to calculate the fundamental nonlinear frequency parameters, which are found to be in a good agreement with the published results. The non-dimensional curvatures associated to the nonlinear fundamental mode are also given for various vibration amplitudes in the case of clamped-clamped FGB.

57

9996643

Geometrically Non-Linear Axisymmetric Free Vibration Analysis of Functionally Graded Annular Plates

In this paper, the non-linear free axisymmetric vibration of a thin annular plate made of functionally graded material (FGM) has been studied by using the energy method and a multimode approach. FGM properties vary continuously as well as non-homogeneity through the thickness direction of the plate. The theoretical model is based on the classical plate theory and the Von Kármán geometrical non-linearity assumptions. An approximation has been adopted in the present work consisting of neglecting the in-plane deformation in the formulation. Hamilton’s principle is used to derive the governing equation of motion. The problem is solved by a numerical iterative procedure in order to obtain more accurate results for vibration amplitudes up to 1.5 times the plate thickness. The numerical results are given for the first axisymmetric non-linear mode shape for a wide range of vibration amplitudes and they are presented either in tabular form or in graphical form to show the effect that the vibration amplitude and the variation in material properties have significant effects on the frequencies and the bending stresses in large amplitude vibration of the functionally graded annular plate.

56

9996658

Geometrically Non-Linear Free Vibration Analysis of Functionally Graded Rectangular Plates

In the present study, the problem of geometrically non-linear free vibrations of functionally graded rectangular plates (FGRP) is studied. The theoretical model, previously developed and based on Hamilton’s principle, is adapted here to determine the fundamental non-linear mode shape of these plates. Frequency parameters, displacements and stress are given for various power-law distributions of the volume fractions of the constituents and various aspect ratios. Good agreement with previous published results is obtained in the case of linear and non-linear analyses.

55

16714

Large Vibration Amplitude of Circular Functionally Graded Plates Resting on Pasternak Foundations

In the present study, the problem of geometrically nonlinear free vibrations of functionally graded circular plates (FGCP) resting on Pasternak elastic foundation with immovable ends was studied. The material properties of the functionally graded composites examined were assumed to be graded in the thickness direction and estimated through the rule of mixture. The theoretical model is based on the classical Plate theory and the Von Kármán geometrical nonlinearity assumptions. Hamilton’s principle is applied and a multimode approach is derived to calculate the fundamental nonlinear frequency parameters, which are found to be in a good agreement with the published results dealing with the problem of functionally graded plates. On the other hand, the influence of the foundation parameters on the nonlinear frequency to the linear frequency ratio of the FGCP has been studied. The effect of the linear and shearing foundations is to decrease the frequency ratio, where it increases with the effect of the nonlinear foundation stiffness.

54

17346

Geometrically Non-Linear Axisymmetric Free Vibrations of Thin Isotropic Annular Plates

The effects of large vibration amplitudes on the first axisymetric mode shape of thin isotropic annular plates having both edges clamped are examined in this paper. The theoretical model based on Hamilton’s principle and spectral analysis by using a basis of Bessel’s functions is adapted اhere to the case of annular plates. The model effectively reduces the large amplitude free vibration problem to the solution of a set of non-linear algebraic equations.

The governing non-linear eigenvalue problem has been linearised in the neighborhood of each resonance and a new one-step iterative technique has been proposed as a simple alternative method of solution to determine the basic function contributions to the non-linear mode shape considered.

Numerical results are given for the first non-linear mode shape for a wide range of vibration amplitudes. For each value of the vibration amplitude considered, the corresponding contributions of the basic functions defining the non-linear transverse displacement function and the associated non-linear frequency, the membrane and bending stress distributions are given. By comparison with the iterative method of solution, it was found that the present procedure is efficient for a wide range of vibration amplitudes, up to at least 1.8 times the plate thickness,

53

16363

Motion Control of a Ball Throwing Robot with a Flexible Robotic Arm

Motion control of flexible arms is more difficult than that of rigid arms, however utilizing its dynamics enables improved performance such as a fast motion in short operation time. This paper investigates a ball throwing robot with one rigid link and one flexible link. This robot throws a ball at a set speed with a proper control torque. A mathematical model of this ball throwing robot is derived through Hamilton’s principle. Several patterns of torque input are designed and tested through the proposed simulation models. The parameters of each torque input pattern is optimized and determined by chaos embedded vector evaluated particle swarm optimization (CEVEPSO). Then, the residual vibration of the manipulator after throwing is suppressed with input shaping technique. Finally, a real experiment is set up for the model checking.

52

16412

Implicit Lyapunov Control of Multi-Control Hamiltonians Systems Based On the State Error

In the closed quantum system, if the control system is strongly regular and all other eigenstates are directly coupled to the target state, the control system can be asymptotically stabilized at the target eigenstate by the Lyapunov control based on the state error. However, if the control system is not strongly regular or as long as there is one eigenstate not directly coupled to the target state, the situations will become complicated. In this paper, we propose an implicit Lyapunov control method based on the state error to solve the convergence problems for these two degenerate cases. And at the same time, we expand the target state from the eigenstate to the arbitrary pure state. Especially, the proposed method is also applicable in the control system with multi-control Hamiltonians. On this basis, the convergence of the control systems is analyzed using the LaSalle invariance principle. Furthermore, the relation between the implicit Lyapunov functions of the state distance and the state error is investigated. Finally, numerical simulations are carried out to verify the effectiveness of the proposed implicit Lyapunov control method. The comparisons of the control effect using the implicit Lyapunov control method based on the state distance with that of the state error are given.

51

2231

Large Vibration Amplitudes of Circular Functionally Graded Thin Plates Resting on Winkler Elastic Foundations

This paper describes a study of geometrically
nonlinear free vibration of thin circular functionally graded (CFGP)
plates resting on Winkler elastic foundations. The material properties
of the functionally graded composites examined here are assumed to
be graded smoothly and continuously through the direction of the
plate thickness according to a power law and are estimated using the
rule of mixture. The theoretical model is based on the classical Plate
theory and the Von-Kármán geometrical nonlinearity assumptions.
An homogenization procedure (HP) is developed to reduce the
problem considered here to that of isotropic homogeneous circular
plates resting on Winkler foundation. Hamilton-s principle is applied
and a multimode approach is derived to calculate the fundamental
nonlinear frequency parameters which are found to be in a good
agreement with the published results. On the other hand, the
influence of the foundation parameters on the nonlinear fundamental
frequency has also been analysed.

50

2862

The Frequency Graph for the Traveling Salesman Problem

Traveling salesman problem (TSP) is hard to resolve
when the number of cities and routes become large. The frequency
graph is constructed to tackle the problem. A frequency graph
maintains the topological relationships of the original weighted graph.
The numbers on the edges are the frequencies of the edges emulated
from the local optimal Hamiltonian paths. The simplest kind of local
optimal Hamiltonian paths are computed based on the four vertices
and three lines inequality. The search algorithm is given to find the
optimal Hamiltonian circuit based on the frequency graph. The
experiments show that the method can find the optimal Hamiltonian
circuit within several trials.

49

11706

Evolved Disease Avoidance Mechanisms, Generalized Prejudice, Modern Attitudes towards Individuals with Intellectual Disability

Previous research has demonstrated that negative
attitudes towards people with physical disabilities and obesity are
predicted by a component of perceived vulnerability to disease; germ
aversion. These findings have been suggested as illustrations of an
evolved but over-active mechanism which promotes the avoidance of
pathogen-carrying individuals. To date, this interpretation of attitude
formation has not been explored with regard to people with
intellectual disability, and no attempts have been made to examine
possible mediating factors. This study examined attitudes in 333
adults and demonstrated that the moderate positive relationship
between germ aversion and negative attitudes toward people with
intellectual disability is fully mediated by social dominance
orientation, a general preference for hierarchies and inequalities
among social groups. These findings have implications for the
design of programs which attempt to promote community acceptance
and inclusion of people with disabilities.

48

14050

Mutually Independent Hamiltonian Cycles of Cn x Cn

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.