Search results for: invariant ring

Authors: Zainab Al-Maamari, Yassir Dinar

Abstract:

The orbit space of an irreducible representation of a finite group is a variety with the ring of invariant polynomials as a coordinate ring. The invariant ring is a polynomial ring if and only if the representation is a reflection representation. Boris Dubrovin shows that the orbits spaces of irreducible real reflection representations acquire the structure of polynomial Frobenius manifolds. Dubrovin's method was also used to construct different examples of Frobenius manifolds on certain reflection representations. By successfully applying Dubrovin’s method on non-polynomial invariant rings of linear representations of dicyclic groups, it gives some results that magnify the relation between invariant theory and Frobenius manifolds.

Keywords: invariant ring, Frobenius manifold, inversion, representation theory

Procedia PDF Downloads 57

Authors: Reza Aghayan

Abstract:

Numerically invariant signatures were introduced as a new paradigm of the invariant recognition for visual objects modulo a certain group of transformations. This paper shows that the current formulation suffers from noise and indeterminacy in the resulting joint group-signatures and applies the n-difference technique and the m-mean signature method to minimize their effects. In our experimental results of applying the proposed numerical scheme to generate joint group-invariant signatures, the sensitivity of some parameters such as regularity and mesh resolution used in the algorithm will also be examined. Finally, several interesting observations are made.

Keywords: Euclidean and affine geometry, differential invariant G-signature curves, numerically invariant joint G-signatures, object recognition, noise, indeterminacy

Procedia PDF Downloads 364

Authors: Manoj Kumar Patel

Abstract:

In this paper, we introduce and give various properties of weak* Rad-plus-supplemented and cofinitely weak* Rad-plus-supplemented modules over some special kinds of rings, in particular, artinian serial ring and semiperfect ring. Also prove that ring R is artinian serial if and only if every right and left R-module is weak* Rad-plus-supplemented. We provide the counter example which proves that weak* Rad-plus-supplemented module is the generalization of plus-supplemented and Rad-plus-supplemented modules. Furthermore, as an application of above finding results of this research article, our main focus is to characterized the semisimple ring, artinian principal ideal ring, semilocal ring, semiperfect ring, perfect ring, commutative noetherian ring and Dedekind domain in terms of weak* Rad-plus-supplemented module.

Keywords: cofinitely weak* Rad-plus-supplemented module , Dedekind domain, Rad-plus-supplemented module, semiperfect ring

Procedia PDF Downloads 223

Authors: S. Pesina, T. Solonchak

Abstract:

Lexical invariants, being a sort of stereotypes within the frames of ordinary consciousness, are created by the members of a language community as a result of uniform division of reality. The invariant meaning is formed in person’s mind gradually in the course of different actualizations of secondary meanings in various contexts. We understand lexical the invariant as abstract language essence containing a set of semantic components. In one of its configurations it is the basis or all or a number of the meanings making up the semantic structure of the word.

Keywords: lexical invariant, invariant theories, polysemantic word, cognitive linguistics

Procedia PDF Downloads 283

Authors: Reza Aghayan

Abstract:

This paper illustrates that numerically invariant joint signatures suffer biases in the resulting signatures. Next, we classify the arising biases as Bias Type 1 and Bias Type 2 and show how they can be removed.

Keywords: Euclidean and affine geometries, differential invariant signature curves, numerically invariant joint signatures, numerical analysis, numerical bias, curve analysis

Procedia PDF Downloads 560

Authors: Surinder Singh, Meenakshi

Abstract:

In this paper MZI-FBG based optical add drop multiplexer is designed and its performance is analyzed in the ring network. In the ring network nodes are composed of optical add drop multiplexer, transmitter and receiver. OADM is used to add or drop any frequency at intermediate nodes without affecting other channels. In this paper the performance of the ring network is carried out by varying various kinds of fiber with or without amplifiers.

Keywords: OADM, ring network, MZI-FBG, transmitter

Procedia PDF Downloads 537

Authors: Masoud Karimi

Abstract:

‎Let R be a commutative ring‎. ‎The regular digraph of ideals of R, which is denoted by‎ Γ(R)‎, ‎is a digraph whose vertex-set is the set of all ‎non-‎trivial ideals of R and‎, ‎for every‎ two distinct vertices I and J‎, ‎there is an arc from I to J‎, ‎whenever I contains‎ a non-zero-divisor on J. In this article, ‎we ‎show ‎that an indecomposable ‎Noetherian ring ‎‎‎R ‎is ‎Artinian ‎local ‎if ‎and ‎only ‎if Z(I)=Z(R) ‎for ‎every ‎non-nilpotent ‎ideal ‎‎‎I‎. ‎Then ‎we ‎conclude ‎that ‎‎the ‎girth ‎of‎ Γ(R)‎ ‎is ‎not ‎equal ‎to ‎four.

Keywords: commutative ring‎, ‎girth‎, regular digraph‎, zero-divisor

Procedia PDF Downloads 246

Authors: Elvira Kusniyanti, Hanni Garminia, Pudji Astuti

Abstract:

This research studies an interconnection between finitely generated uniform modules and Dedekind prime rings. The characterization of modules over Dedekind prime rings that will be investigated is an adoption of Noetherian and hereditary concept. Dedekind prime rings are Noetherian and hereditary rings. This property of Dedekind prime rings is a background of the idea of adopting arises. In Noetherian area, it was known that a ring R is Noetherian ring if and only if every finitely generated R-module is a Noetherian module. Similar to that result, a characterization of the hereditary ring is related to its projective modules. That is, a ring R is hereditary ring if and only if every projective R-module is a hereditary module. Due to the above two results, we suppose that characterization of a Dedekind prime ring can be analyzed from finitely generated modules over it. We propose a conjecture: a ring R is a Dedekind prime ring if and only if every finitely generated uniform R-module is a Dedekind module. In this article, we will generalize a concept of the Dedekind module for non-commutative ring case and present a part of the above conjecture.

Keywords: dedekind domains, dedekind prime rings, dedekind modules, uniform modules

Procedia PDF Downloads 405

Authors: Surjit Angra, Pooja Rani, Vinod Kumar

Abstract:

In hydro power plant spiral casing and Stay ring is meant to guide the water flow to guide vane and runner. Spiral casing and Stay ring is subjected to static i.e. pressure load as well as fluctuating load acting on the structure due to water hammer effect in water conductor system. Finite element method has been used to calculate stresses on spiral casing and stay ring. These calculations were done for the maximum possible loading under operating condition "LC1 Quick Shut Down”. The design load is reached for the spiral casing and stay ring during the emergency closure of the guide apparatus "LC1 Quick Shut Down”. During this operation the forces from the head cover to the stay ring also reach their maximum.

Keywords: hydro-turbine, spiral casing, stay ring, structural analysis

Procedia PDF Downloads 478

Authors: Abdelhakim Chillali, Abdelhamid Tadmori, Muhammed Ziane

Abstract:

In this article we will study the elliptic curve defined over the ring An and we define the mathematical operations of ECC, which provides a high security and advantage for wireless applications compared to other asymmetric key cryptosystem.

Keywords: elliptic curves, finite ring, cryptography, study

Procedia PDF Downloads 345

Authors: Rafat M. Mohareb

Abstract:

Several D-ring alkylated estrone analogues display exceptionally high affinity for estrogen receptors. In particular, compounds in which an E-ring is formed are known to be involved in the inhibition of steroidogenic enzymes. Such compounds also have an effect on steroid dehydrogenase activity and the ability to inhibit the detrimental action of the steroid sulfatase enzyme. Generally, E-ring extended steroids have been accessed by modification of the C17-ketone in the D-ring by either arylimine or oximino formation, addition of a carbon nucleophile or hydrazone formation. Other approaches have included ketone reduction, silyl enol ether formation or ring-closing metathesis (giving five- or six-membered E-rings). Chemical modification of the steroid D-ring provides a way to alter the functional groups, sizes and stereochemistry of the D-ring, and numerous structure-activity relationships have been established by such synthetic alterations. Steroids bearing heterocycles fused to the D-ring of the steroid nucleus have been of pharmaceutical interest. In the present paper, we report on the efficient synthesis of estrone possessing pyran, pyrimidine and thiazole ring systems. This study focused on the synthesis and biochemical evaluation of newly synthesized heterocyclic compounds which were then subjected through inhibitory evaluations towards human cancer and normal cell lines.

Keywords: estrone, heterocyclization, cytotoxicity, biomedicine

Procedia PDF Downloads 258

Authors: M. Berrehail, F. Benamira

Abstract:

We study the quantum motion of a particle in the presence of a time- dependent linear potential using an operator invariant that is quadratic in p and linear in q within the framework of the Lewis-Riesenfeld invariant, The special invariant operator proposed in this work is demonstrated to be an Hermitian operator which has an Airy wave packet as its Eigenfunction

Keywords: airy wave packet, ivariant, time-dependent linear potential, unitary transformation

Procedia PDF Downloads 462

Authors: Isao Tomita

Abstract:

Electrical conduction in a quasi-one-dimensional polycrystalline metallic ring with a long electron phase coherence length realized at low temperature is investigated. In this situation, the wave nature of electrons is important in the ring, where the electrical current I can be induced by a vector potential that arises from a static magnetic field applied perpendicularly to the ring’s area. It is shown that if the average grain size of the polycrystalline ring becomes large (or comparable to the Fermi wavelength), the electrical current I increases to ~I0, where I0 is a current in a disorder-free ring. The cause of this increasing effect is examined, and this takes place if the electron localization length in the polycrystalline potential increases with increasing grain size, which gives rise to coherent connection of tails of a localized electron wave function in the ring and thus provides highly coherent electrical conduction.

Keywords: electrical conduction, electron phase coherence, polycrystalline metal, magnetic field

Procedia PDF Downloads 353

Authors: D. H. Park, Y. H. Tak, H. H. Kwon, G. J. Kwon, H. G. Kim

Abstract:

This study focused on developing forging technology of a large-diameter cam ring gear from the small bar. The analyses of temperature variation and deformation behavior of the material are important to obtain the optimal forging products. The hot compression test was carried out to know formability at high temperature. In order to define the optimum forging conditions including material temperature, strain and forging load, the finite element method was used to simulate the forging process of cam ring gear parts. Test results were in good agreement with the simulations. An existing cam ring gear is presented the chips generated by cutting the rod material and the durability issues, but this would be to develop a large-diameter cam ring gear forging parts for truck in order to solve the durability problem and the material waste.

Keywords: forging technology, cam ring, gear, truck, small bar

Procedia PDF Downloads 258

Authors: Imam Muthohar, Budi Hartono, Sigit Priyanto, Hardiansyah Hardiansyah

Abstract:

The eruption of Merapi Volcano in Yogyakarta, Indonesia in 2010 caused many casualties due to minimum preparedness in facing disaster. Increasing population capacity and evacuating to safe places become very important to minimize casualties. Regional government through the Regional Disaster Management Agency has divided disaster-prone areas into three parts, namely ring 1 at a distance of 10 km, ring 2 at a distance of 15 km and ring 3 at a distance of 20 km from the center of Mount Merapi. The success of the evacuation is fully supported by road network infrastructure as a way to rescue in an emergency. This research attempts to model evacuation process based on the rise of refugees in ring 1, expanded to ring 2 and finally expanded to ring 3. The model was developed using SATURN (Simulation and Assignment of Traffic to Urban Road Networks) program version 11.3. 12W, involving 140 centroid, 449 buffer nodes, and 851 links across Yogyakarta Special Region, which was aimed at making a preliminary identification of road networks considered vulnerable to disaster. An assumption made to identify vulnerability was the improvement of road network performance in the form of flow and travel times on the coverage of ring 1, ring 2, ring 3, Sleman outside the ring, Yogyakarta City, Bantul, Kulon Progo, and Gunung Kidul. The research results indicated that the performance increase in the road networks existing in the area of ring 2, ring 3, and Sleman outside the ring. The road network in ring 1 started to increase when the evacuation was expanded to ring 2 and ring 3. Meanwhile, the performance of road networks in Yogyakarta City, Bantul, Kulon Progo, and Gunung Kidul during the evacuation period simultaneously decreased in when the evacuation areas were expanded. The results of preliminary identification of the vulnerability have determined that the road networks existing in ring 1, ring 2, ring 3 and Sleman outside the ring were considered vulnerable to the evacuation of Mount Merapi eruption. Therefore, it is necessary to pay a great deal of attention in order to face the disasters that potentially occur at anytime.

Keywords: model, evacuation, SATURN, vulnerability

Procedia PDF Downloads 137

Authors: Atef Ahmad Bleibel

Abstract:

Most codes of practice, like ACI 318-14, require the use of strut-and-tie modeling to analyze and design reinforced concrete deep beams. Though, investigations that conducted on deep beams do not include ring deep beams of influential parameters. This work presents an analytical parametric study using strut-and-tie modeling stated by ACI 318-14 to predict load capacity of 20 reinforced concrete ring deep beam specimens with different parameters. The parameters that were under consideration in the current work are ring diameter (Dc), number of supports (NS), width of ring beam (bw), concrete compressive strength (f'c) and width of bearing plate (Bp). It is found that the load capacity decreases by about 14-36% when ring diameter increases by about 25-75%. It is also found that load capacity increases by about 62-189% when number of supports increases by about 33-100%, while the load capacity increases by about 25-75% when the beam ring width increases by about 25-75%. Finally, it is found that load capacity increases by about 24-76% when compressive strength increases by about 24-76%, while the load capacity increases by about 5-16% when Bp increases by about 25-75%.

Keywords: load parameters, reinforced concrete, ring deep beam, strut and tie

Procedia PDF Downloads 76

Authors: Saroj Bijarnia, Preety Singh

Abstract:

We propose a simple and effective biometrics system based on face verification across aging using a new variant of texture feature, Pyramid Binary Pattern. This employs Local Binary Pattern along with its hierarchical information. Dimension reduction of generated texture feature vector is done using Principal Component Analysis. Support Vector Machine is used for classification. Our proposed method achieves an accuracy of 92:24% and can be used in an automated age-invariant face verification system.

Keywords: biometrics, age invariant, verification, support vector machine

Procedia PDF Downloads 313

Authors: A. Suparmi, C. Cari, M. Yunianto, B. N. Pratiwi

Abstract:

D-dimensional Dirac equations of q-deformed shape invariant potentials were solved using supersymmetric quantum mechanics (SUSY QM) in the case of exact spin symmetry. The D dimensional radial Dirac equation for shape invariant potential reduces to one-dimensional Schrodinger type equation by an appropriate variable and parameter change. The relativistic energy spectra were analyzed by using SUSY QM and shape invariant properties from radial D dimensional Dirac equation that have reduced to one dimensional Schrodinger type equation. The SUSY operator was used to generate the D dimensional relativistic radial wave functions, the relativistic energy equation reduced to the non-relativistic energy in the non-relativistic limit.

Keywords: D-dimensional dirac equation, non-central potential, SUSY QM, radial wave function

Procedia PDF Downloads 314

Authors: Siti Noor Farwina Anwar, Hailiza Kamarulhaili

Abstract:

In this paper, we present the idea of implementing the Integer Sub-Decomposition (ISD) method on elliptic curves with j-invariant 1728. The ISD method was proposed in 2013 to compute scalar multiplication in elliptic curves, which remains to be the most expensive operation in Elliptic Curve Cryptography (ECC). However, the original ISD method only works on integer number field and solve integer scalar multiplication. By extending the method into the complex quadratic field, we are able to solve complex multiplication and implement the ISD method on elliptic curves with j-invariant 1728. The curve with j-invariant 1728 has a unique discriminant of the imaginary quadratic field. This unique discriminant of quadratic field yields a unique efficiently computable endomorphism, which later able to speed up the computations on this curve. However, the ISD method needs three endomorphisms to be accomplished. Hence, we choose all three endomorphisms to be from the same imaginary quadratic field as the curve itself, where the first endomorphism is the unique endomorphism yield from the discriminant of the imaginary quadratic field.

Keywords: efficiently computable endomorphism, elliptic scalar multiplication, j-invariant 1728, quadratic field

Procedia PDF Downloads 165

Authors: Rana Muhammad Armaghan Ayaz, Yigit Uysallı, Nima Bavili, Berna Morova, Alper Kiraz

Abstract:

Traditional optical methods for example resonance wavelength shift and cavity ring-down spectroscopy used for material detection and sensing have disadvantages, for example, less resistance to laser noise, temperature fluctuations and extraction of the required information can be a difficult task like ring downtime in case of cavity ring-down spectroscopy. Phase shift cavity ring down spectroscopy is not only easy to use but is also capable of overcoming the said problems. This technique compares the phase difference between the signal coming out of the cavity with the reference signal. Detection of any material is made by the phase difference between them. By using this technique, air, water, and isopropyl alcohol can be recognized easily. This Methodology has far-reaching applications and can be used in air pollution detection, human breath analysis and many more.

Keywords: materials, noise, phase shift, resonance wavelength, sensitivity, time domain approach

Procedia PDF Downloads 114

Authors: Ning Xue, Srinivas Merugu, Ignacio Delgado Martinez, Tao Sun, John Tsang, Shih-Cheng Yen

Abstract:

We have developed a polyimide based neural interface electrode to record nerve signals from the sciatic nerve of a rat. The neural interface electrode has a split-ring shape, with four protruding gold electrodes for recording, and two reference gold electrodes around the split-ring. The split-ring electrode can be opened up to encircle the sciatic nerve. The four electrodes can be bent to sit on top of the nerve and hold the device in position, while the split-ring frame remains flat. In comparison, while traditional cuff electrodes can only fit certain sizes of the nerve, the developed device can fit a variety of rat sciatic nerve dimensions from 0.6 mm to 1.0 mm, and adapt to the chronic changes in the nerve as the electrode tips are bendable. The electrochemical impedance spectroscopy measurement was conducted. The gold electrode impedance is on the order of 10 kΩ, showing excellent charge injection capacity to record neural signals.

Keywords: impedance, neural interface, split-ring electrode, neural signal recording

Procedia PDF Downloads 339

Authors: Krish Jhurani

Abstract:

The research paper presents an in-depth analysis of symmetry properties in linear algebraic systems under the operation of non-canonical scalar multiplication structures, specifically semirings, and near-rings. The objective is to unveil the profound alterations that occur in traditional linear algebraic structures when we replace conventional field multiplication with these non-canonical operations. In the methodology, we first establish the theoretical foundations of non-canonical scalar multiplication, followed by a meticulous investigation into the resulting symmetry properties, focusing on eigenvectors, eigenspaces, and invariant subspaces. The methodology involves a combination of rigorous mathematical proofs and derivations, supplemented by illustrative examples that exhibit these discovered symmetry properties in tangible mathematical scenarios. The core findings uncover unique symmetry attributes. For linear algebraic systems with semiring scalar multiplication, we reveal eigenvectors and eigenvalues. Systems operating under near-ring scalar multiplication disclose unique invariant subspaces. These discoveries drastically broaden the traditional landscape of symmetry properties in linear algebraic systems. With the application of these findings, potential practical implications span across various fields such as physics, coding theory, and cryptography. They could enhance error detection and correction codes, devise more secure cryptographic algorithms, and even influence theoretical physics. This expansion of applicability accentuates the significance of the presented research. The research paper thus contributes to the mathematical community by bringing forth perspectives on linear algebraic systems and their symmetry properties through the lens of non-canonical scalar multiplication, coupled with an exploration of practical applications.

Keywords: eigenspaces, eigenvectors, invariant subspaces, near-rings, non-canonical scalar multiplication, semirings, symmetry properties

Procedia PDF Downloads 77

Authors: Isik Cetintav, Cenk Misirli, Yilmaz Can

Abstract:

This work investigates upsetting of the tri-metallic cylindrical billets both experimentally and analytically with a reduction ratio 30%. Steel, brass, and copper are used for the outer and outmost rings and aluminum for the inner core. Two different models have been designed to show material flow and the cavity took place over the two interfaces during forming after this reduction ratio. Each model has an outmost ring material as steel. Model 1 has an outer ring between the outmost ring and the solid core material as copper and Model 2 has a material as brass. Solid core is aluminum for each model. Billets were upset in press machine by using parallel flat dies. Upsetting load was recorded and compared for models and single billets. To extend the tests and compare with experimental procedure to a wider range of inner core and outer ring geometries, finite element model was performed. ABAQUS software was used for the simulations. The aim is to show how contact between outmost ring, outer ring and the inner core are carried on throughout the upsetting process. Results have shown that, with changing in height, between outmost ring, outer ring and inner core, the Model 1 and Model 2 had very good interaction, and the contact surfaces of models had various interface behaviour. It is also observed that tri-metallic materials have lower weight but better mechanical properties than single materials. This can give an idea for using and producing these new materials for different purposes.

Keywords: tri-metallic, upsetting, copper, brass, steel, aluminum

Procedia PDF Downloads 315

Authors: D. Sersab, M. Aberkane

Abstract:

Residual stresses, in high-density polyethylene (HDPE) pipes, result from a nonhomogeneous cooling rate that occurs between the inner and outer surfaces during the extrusion process in manufacture. Most known methods of measurements to determine the magnitude and profile of the residual stresses in the pipe wall thickness are layer removal and ring slitting method. The combined layer removal and ring slitting methods described in this paper involves measurement of the circumferential residual stresses with minimal local disturbance. The existing methods used for pipe geometry (ring slitting method) gives a single residual stress value at the bore. The layer removal method which is used more in flat plate specimen is implemented with ring slitting method. The method permits stress measurements to be made directly at different depth in the pipe wall and a well-defined residual stress profile was consequently obtained.

Keywords: residual stress, layer removal, ring splitting, HDPE, wall thickness

Procedia PDF Downloads 307

Authors: Wei Feilong

Abstract:

In this study, an local invariant generalized Houghtransform (LI-GHT) method is proposed for integrated circuit (IC) visual positioning. The original generalized Hough transform (GHT) is robust to external noise; however, it is not suitable for visual positioning of IC chips due to the four-dimensionality (4D) of parameter space which leads to the substantial storage requirement and high computational complexity. The proposed LI-GHT method can reduce the dimensionality of parameter space to 2D thanks to the rotational invariance of local invariant geometric feature and it can estimate the accuracy position and rotation angle of IC chips in real-time under noise and blur influence. The experiment results show that the proposed LI-GHT can estimate position and rotation angle of IC chips with high accuracy and fast speed. The proposed LI-GHT algorithm was implemented in IC visual positioning system of radio frequency identification (RFID) packaging equipment.

Keywords: Integrated Circuit Visual Positioning, Generalized Hough Transform, Local invariant Generalized Hough Transform, ICpacking equipment

Procedia PDF Downloads 236

Authors: Teoman Ozer, Ozlem Orhan

Abstract:

This study deals with symmetry group properties and conservation laws of partial differential equations. We give a geometrical interpretation of notion of μ-prolongations of vector fields and of the related concept of μ-symmetry for partial differential equations. We show that these are in providing symmetry reduction of partial differential equations and systems and invariant solutions.

Keywords: λ-symmetry, μ-symmetry, classification, invariant solution

Procedia PDF Downloads 276

Authors: Maba Boniface Matadi

Abstract:

This paper analyses the model of Malaria endemic from the point of view of the group theoretic approach. The study identified new independent variables that lead to the transformation of the nonlinear model. Furthermore, corresponding determining equations were constructed, and new symmetries were found. As a result, the findings of the study demonstrate of the integrability of the model to present an invariant solution for the Malaria model.

Keywords: group theory, lie symmetry, invariant solutions, malaria

Procedia PDF Downloads 76

Authors: Tayebeh Sahraeibelverdi, Ahmad Shirazi Hadi Veladi, Mazdak Radmalekshah

Abstract:

Optical sensors became attractive due to preciseness, low power consumption, and intrinsic electromagnetic interference-free characteristic. Among the waveguide optical sensors, cavity-based ones attended for the high Q-factor. Micro ring resonators as a potential platform have been investigated for various applications as biosensors to pressure sensors thanks to their sensitive ring structure responding to any small change in the refractive index. Furthermore, these small micron size structures can come in an array, bringing the opportunity to have any of the resonance in a specific wavelength and be addressed in this way. Another exciting application is applying a strain to the ring and making them an optical strain gauge where the traditional ones are based on the piezoelectric material. Making them in arrays needs electrical wiring and about fifty times bigger in size. Any physical element that impacts the waveguide cross-section, Waveguide elastic-optic property change, or ring circumference can play a role. In comparison, ring size change has a larger effect than others. Here an engineered ring structure is investigated to study the strain effect on the ring resonance wavelength shift and its potential for more sensitive strain devices. At the same time, these devices can measure any strain by mounting on the surface of interest. The idea is to change the" O" shape ring to a "C" shape ring with a small opening starting from 2π/360 or one degree. We used the Mode solution of Lumbrical software to investigate the effect of changing the ring's opening and the shift induced by applied strain. The designed ring radius is a three Micron silicon on isolator ring which can be fabricated by standard complementary metal-oxide-semiconductor (CMOS) micromachining. The measured wavelength shifts from1-degree opening of the ring to a 6-degree opening have been investigated. Opening the ring for 1-degree affects the ring's quality factor from 3000 to 300, showing an order of magnitude Q-factor reduction. Assuming a strain making the ring-opening from 1 degree to 6 degrees, our simulation results showing negligible Q-factor reduction from 300 to 280. A ring resonator quality factor can reach up to 108 where an order of magnitude reduction is negligible. The resonance wavelength shift showed a blue shift and was obtained to be 1581, 1579,1578,1575nm for 1-, 2-, 4- and 6-degree ring-opening, respectively. This design can find the direction of the strain-induced by applying the opening on different parts of the ring. Moreover, by addressing the specified wavelength, we can precisely find the direction. We can open a significant opportunity to find cracks and any surface mechanical property very specifically and precisely. This idea can be implemented on polymer ring resonators while they can come with a flexible substrate and can be very sensitive to any strain making the two ends of the ring in the slit part come closer or further.

Keywords: optical ring resonator, strain gauge, strain sensor, surface mechanical property analysis

Procedia PDF Downloads 91

Authors: Matthaios Katsanikas

Abstract:

We study the structure of the invariant manifolds of complex unstable periodic orbits of a family of periodic orbits, in a 3D autonomous Hamiltonian system of galactic type, after a transition of this family from stability to complex instability (Hamiltonian Hopf bifurcation). We consider the case of a supercritical Hamiltonian Hopf bifurcation. The invariant manifolds of complex unstable periodic orbits have two kinds of structures. The first kind is represented by a disk confined structure on the 4D space of section. The second kind is represented by a complicated central tube structure that is associated with an extended network of tube structures, strips and flat structures of sheet type on the 4D space of section.

Keywords: dynamical systems, galactic dynamics, chaos, phase space

Procedia PDF Downloads 111

Authors: Michele Aleandri, Matteo Colangeli, Davide Gabrielli

Abstract:

We study a generalization to a continuous setting of the classical Markov chain tree theorem. In particular, we consider an irreducible diffusion process on a metric graph. The unique invariant measure has an atomic component on the vertices and an absolutely continuous part on the edges. We show that the corresponding density at x can be represented by a normalized superposition of the weights associated to metric arborescences oriented toward the point x. A metric arborescence is a metric tree oriented towards its root. The weight of each oriented metric arborescence is obtained by the product of the exponential of integrals of the form ∫a/b², where b is the drift and σ² is the diffusion coefficient, along the oriented edges, for a weight for each node determined by the local orientation of the arborescence around the node and for the inverse of the diffusion coefficient at x. The metric arborescences are obtained by cutting the original metric graph along some edges.

Keywords: diffusion processes, metric graphs, invariant measure, reversibility

Procedia PDF Downloads 133