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A model for coupled rotation-displacement modes of certain molecular crystals. Illustration for KNO3
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Kaynak :
Science Direct
Dergi:
Journal of Physics and Chemistry of Solids
Yayıncı:
Elsevier
Yazar(lar) :
A. Askar
Yıl :
1973
A. Askar
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A model is presented for the dynamics of crystal lattices whose elements have finite inertia and distinct equilibrium orientations. The model is based upon representing the non-central interactions by the bending of a flexible spring in analogy with the extensible spring of Born-Von Karman for central interactions in simple lattices. The model is stable for all configurations and the rotational and translational modes are coupled. The parameter expressing the bending rigidity can be determined from infrared or Raman spectroscopy and this is illustrated for a special mode of the KNO3 crystal. Dispersion relations for the lattice modes are given for a linear chain of identical molecules and KNO3 crystal.
DOI : 10.1016/s0022-3697(73)80112-x
ISSN: 0022-3697
Sayı: 11
Cilt: 34
Sayfa: 1901-1907
Sınıflandırma :
Fizik %27
2
0
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Kaynak :
Science Direct
Dergi:
Soil Dynamics and Earthquake Engineering
Yayıncı:
Elsevier
Yazar(lar) :
A. Askar
Yıl :
1988
A. Askar
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DOI : 10.1016/s0267-7261(88)80024-1
ISSN: 0267-7261
Sayı: 3
Cilt: 7
Sayfa: 177
Sınıflandırma :
3
Selenium content of food consumed by Egyptians
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Kaynak :
Science Direct
Dergi:
Food Chemistry
Yayıncı:
Elsevier
Yazar(lar) :
A Askar
Yıl :
1983
A Askar
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DOI : 10.1016/0308-8146(83)90059-6
ISSN: 0308-8146
Sayı: 3
Cilt: 10
Sayfa: 231-234
Sınıflandırma :
4
Dispersion Relation and Wave Solution for Anharmonic Lattices and Korteweg De Vries Continua
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Kaynak :
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Yazar(lar) :
A. Askar
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1973
A. Askar
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The set of coupled difference equations describing the dynamics of a monatomic chain is reduced to that of uncoupled anharmonic oscillators through the use of the translational invariance of the equations. Poincaré's perturbation scheme is then used to obtain a space- and time-wise periodic wave solution together with a nonlinear dispersion relation between frequency, wavenumber and the amplitude. For all wavelengths, the frequency of vibration is observed to increase beyond the corresponding value for the linear case by terms proportional to the square of the amplitude multiplied by the coefficients of the cubic as well as quartic interactions. This solution of the lattice equations suggests a class of solutions of the generalized Korteweg-de Vries (K. de V.) equation which is related to the long wave limit of the nonlinear lattice by means of a semicharacteristic variable stretching transformation. Numerical results for the dispersion relations are presented for the semi-empirical Morse, Born-Meyer and Lennard-Jones potentials. For these physical examples, the contributions of the cubic and quartic terms of the interaction potential are found to be of the same order.
Cilt: 334
Sayı: 1596
Sayfa: pp. 83-94
Yayın Tarihi: 1973-07-17
ISSN: 0080-4630
5
A micro method for the quantitative estimation of putrescine in tissues
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Kaynak :
Science Direct
Dergi:
Journal of Chromatography A
Yayıncı:
Elsevier
Yazar(lar) :
N. Seiler , A. Askar
Yıl :
1971
A. Askar
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Putrescine can be quantitatively estimated in tissue after its extraction by pre-separation of the amine mixture by ion-exchange chromatography on small columns, reaction of the putrescine fraction with i-dimethylaminonaphthalene-5-sulphonyl chloride, two-dimensional thin-layer chromatographic separation of the densylated amines, and fluorimetry of the bis-DANS-putrescine extracted from the carrier. Recovery of putrescine from tissue is 93–94%, independent of the amount of putrescine applied to the columns. Losses occur during ion-exchange chromatography. The sensitivity of the method is higher by a factor of 50–100 compared with existing methods. Reproducibility is ± 1–3% for reference samples. Concentrations of putrescine were determined in mouse brain and live.
DOI : 10.1016/s0021-9673(01)96817-7
ISSN: 0021-9673
Sayı: 1
Cilt: 62
Sayfa: 121-127
Sınıflandırma :
6
A structural model of a micropolar continuum
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Dergi Makalesi
Kaynak :
Science Direct
Dergi:
International Journal of Engineering Science
Yayıncı:
Elsevier
Yazar(lar) :
A. Askar , A.S. Cakmak
Yıl :
1968
A. Askar
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In their crystal lattice theory, Born-Von Karman have shown that the long wave approximation to their model yields the equations of the classical theory of elasticity. The Born-Von Karman model assumed that the interaction between the particles can be characterized by a simple spring which allows extensions only. Also, in their model, the dimensions of the particles are shrunk to zero thus resulting in non-orientable mathematical points. In this paper, a two dimensional model composed of orientable points, joined by extensible and flexible rods is presented in order to explain the foundations of the Cosserat [1] or the micropolar continuum [2]. As the long wave approximation from this model, one gets the coupled displacement and microration equations of the micropolar medium, similar to those given by Eringen and Suhubi[2, 3] and by Mindlin[4, 5]. Résumé Dans leur théorie du réseau cristallin, Born et von Karman ont démontré que l'approximation à ondes longues de leur modèle mène aux équations de la théorie classique de l'élasticité. Le modèle de Born-von Karman suppose que l'interaction des particules peut être représentée par un simple ressort travaillant en traction seulement. De plus, dans leur modèle, les dimensions des particules sont réduites à zéro, ce qui donne des points mathématiques non orientables. Le modèle bidimensionnel décrit dans le présent article est composé de points orientables réunis par des tiges extensibles et flexibles de façon à pouvoir expliquer les principes de base du continuum de Cosserat[1] ou du continuum micropolaire [2]. L'approximation à ondes longues de ce modèle fournit des équations du déplacement couplé et de la microrotation du milieu micropolaire semblables aux équations trouvées par Eringen et Suhubi[2, 3] et par Mindlin[4,5]. Zusammenfassung In ihrer Kristallgittertheorie haben Born und von Karman gezeigt, dass die Langwellennäherung ihres Modells die Gleichungen der klassischen Elastizitätstheorie ergibt. Das Born-von Karman-Modell nahm an, dass die Wechselwirkung zwischen den Partikeln durch eine einfache Feder charakterisiert werden kann, die nur Dehnungen erlaubt. In ihrem Modell sind die Dimensionen der Partikel auf null vermindert, so dass sich nichtorientierbare mathematische Punkte ergeben. In dieser Abhandlung wird ein zweidimensionales Modell aus orientierbaren Punkten, die duch dehnbare und flexible Stäbchen verbunden sind, verwendet, um die Grundlagen des Cosserat- oder[1] mikropolaren Kontinuums zu erklären[2]. Als Langwellennäherung dieses Modells erhält man die gekoppelten Verdrängungs- und Mikrorotations-gleichungen des mikropolaren Mediums, die denen von Eringen und Suhub[2,3] und denen von Mindlin gleich sind [4, 5]. Sumàrio Nella loro teoria del lattice dei cristalli, Born e Von Karman hanno dimostrato che l'appros-simazione dell'onda lunga al loro modello dà le equazioni della classica teoria d'elasticità. Il modello Born-Von Karman presume che l'azione reciproca fra le particelle possa essere caratterizzata con una semplice molla che permette solo l'estensione. Nel modello, inoltre, le dimensioni delie particelle sono ridotte a zero, risultando cosí in punti matematici non orientabili. In questa monografia, si presenta un modello bidimensionale di punti orientabili, uniti da tondini estensibili e flessibili, per spiegare le fondamenta del Cosserat [1]o del continuo micropolare [2]. Come approssimazione dell'onda lunga di questo modello si ha lo spostamento accoppiato e le equazioni di microrotazione del mezzo micropolare simili a quelle date da Eringen e Suhubi[2, 3] e da Mindlin[4, 5]. Реферат B cвoeй. тeoии кpиcтaлличecкoй peшeтки Бopнфoн Кapмaн дoкaзaли, чтo длиннoвoлнoвaя aппpoкcимaция иx мoдeли вeдeт к ypaвнeниям клaccичecкoи тeopии yпpгocти. B мoдeли щopнa-фoн Кapaнa пpинимaeтcя, чтo взaимoдeйcтвиe мeждy чacтицaми мoжeт xapaктepизoвaтьcя пpocтoй. пpyжинoй, кoтopaя пoддaeтcя тoлькo pacтяжeниям. B иx мoдeли тaкжe paзмepы чacтиц coкaщaютcя к нeлю, пpeвpaщaяcь в нeopeнтиpoвaнныe мaтeмaтичecиe тoчки. B этoй cтaтьe пpeдcтaвляeтcя двyxpaзмepнaя мoдeль cocтoящaя из opиeнтиpoвaнныx тoчeк, coeдинeнныx pacтяжимыми и гибкими пpyткaми, для тoгo чтoбы paзъяcнить ocнoвы cплoшнoй cpeды Кoccepaтa [1], или микpoпoляpнoй cплoшнoй cвeды [2]. B кaчecтвe длиннoвoй aппpoкcимaции вытeкaющeй из qeтoй мoдeли пoлyчaютcя coпpяжeнныe ypaвнeния пo пepeмeщeниям и микpoкoличecтвaм микпoпoляpнoй cpeды, пoдoбныe ypaвнeниям вывeдeнным Эpингeнoм и Cexeбoм [2,3] a тaкжe Mиндлинoм [4,5].
DOI : 10.1016/0020-7225(68)90060-8
ISSN: 0020-7225
Sayı: 10
Cilt: 6
Sayfa: 583-589
Sınıflandırma :
7
Seismic waves in random media
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Kaynak :
Science Direct
Dergi:
Probabilistic Engineering Mechanics
Yayıncı:
Elsevier
Yazar(lar) :
A. Askar , A.S. Cakmak
Yıl :
1988
A. Askar
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Earthquake waves travel in a medium that is naturally stochastic. Stochasticity is manifested by introducing uncertainties into the model as well as reductions in the mean field and mean amplitudes through random mode coupling and physical scattering from the random irregularities. This survey shows the effect of the stochasticity in wave amplitudes, in standard deviations for defining reliability limits, summarizes various perturbation schemes, and draws attention to the differences between media with random values and stochastic media.
DOI : 10.1016/0266-8920(88)90024-0
ISSN: 0266-8920
Sayı: 3
Cilt: 3
Sayfa: 124-129
Sınıflandırma :
8
Remarks on the discussions1,2 of the paper ‘subsoil geology and soil amplification in Mexico City’3
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Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Soil Dynamics and Earthquake Engineering
Yayıncı:
Elsevier
Yazar(lar) :
A.S. Cakmak , A. Askar
Yıl :
1992
A. Askar
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DOI : 10.1016/0267-7261(92)90040-k
ISSN: 0267-7261
Sayı: 4
Cilt: 11
Sayfa: 246-248
Sınıflandırma :
9
Studies on finite amplitude waves in bounded water bodies
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Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Advances in Water Resources
Yayıncı:
Elsevier
Yazar(lar) :
A. Askar , A.S. Cakmak
Yıl :
1978
A. Askar
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The problem treated here is the dynamics of a bay where water is driven through its opening periodically in time. The basic equations are expressed in the two horizontal coordinates and time and they are obtained by an integration of the Navier-Stokes equations in the vertical coordinate. The equations are nonlinear because of the convective terms in the acceleration. The problem of harbor dynamics provides a natural parameter as the ratio of mass of water entering the bay through the waves to the total mass of water in the bay. This small parameter multiplies the nonlinear terms and thus the problem is ideally suited for a perturbation analysis. The nonlinear terms are responsible for the generation of secondary flows and are particularly important near resonant frequences. The analysis further indicates the existence of a time independent flow analogous to acoustic streaming, known from solutions of the Navier-Stokes equations. The question of vorticity is studied and is seen that: a constant dissipation coefficient precludes the generation of vorticity even for the nonlinear case: and that only a weak (second order) vorticity can exist in the case of a variable dissipation term expressed through the Chezy coefficient. The study suggests also a semi analytic-numerical scheme with savings of 0(102) for irregular geometries through the separation of the various order harmonics as opposed to the usual integration in time.
DOI : 10.1016/0309-1708(78)90007-6
ISSN: 0309-1708
Sayı: 4
Cilt: 1
Sayfa: 229-246
Sınıflandırma :
10
Solving the continuum problem of collision-induced dissociation and recombination
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Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Chemical Physics Letters
Yayıncı:
Elsevier
Yazar(lar) :
G.-D. Barg , A. Askar
Yıl :
1980
A. Askar
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The stationary Schrödinger equation with continuum boundary conditions is solved numerically. Quantum probabilities of collision-induced dissociation/recombination for models with two degrees of freedom are calculated using an integral-equation matching procedure together with analytical wavefunctions or finite element solutions alternatively. Model results for He+Ne2 → He+2Ne are reported.
DOI : 10.1016/0009-2614(80)80679-8
ISSN: 0009-2614
Sayı: 3
Cilt: 76
Sayfa: 609-614
Sınıflandırma :
11
Proton Migration in Hydrogen-bonded Chains
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Kaynak :
Springer Nature
Dergi:
Nature
Yayıncı:
Springer Science and Business Media LLC
Yazar(lar) :
J. H. WEINER , A. ASKARJ. H. WEINER , A. ASKAR
Yıl :
1970
A. ASKAR
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DOI : 10.1038/226842a0
ISSN: 0028-0836
Sayı: 5248
Cilt: 226
Sayfa: 842-844
12
Combined bony closure of oroantral fistula and sinus lift with mandibular bone grafts for subsequent dental implant placement
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Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology, and Endodontology
Yayıncı:
Elsevier
Yazar(lar) :
Mamdouh S. Ahmed , Niveen A. Askar
Yıl :
2011
Niveen A. Askar
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Sinus lifting and reconstruction of localized alveolar defects are often required after closure of a large oroantral fistula (OAF) to allow for subsequent implant installation. This study describes a combined surgical technique that involves sinus lifting, bony closure, and reconstruction of the alveolar defect at the site of an OAF. The sinus membrane was reconstructed as a continuous layer by combining the residual sinus membrane with a rotated part of oral mucosa around the OAF. Autogenous bone from the chin and/or ramus was grafted into the prepared sinus space and alveolar defect, and the graft was covered by a buccal advancement flap. This technique was used to treat 8 patients who had large OAFs in the posterior maxillary region. The treatment was successful in all cases, and the technique appears to be suitable for large OAFs where implants are subsequently desired.
DOI : 10.1016/j.tripleo.2011.01.003
ISSN: 1079-2104
Sayı: 4
Cilt: 111
Sayfa: e8-e14
Sınıflandırma :
13
Soil-structure interaction in coupled rocking and sliding vibration - the plane problem
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Dergi Makalesi
Kaynak :
Science Direct
Dergi:
International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts
Yayıncı:
Elsevier
Yazar(lar) :
X. Zeng , A. Askar , A.S. Cakmak
Yıl :
1985
A. Askar
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DOI : 10.1016/0148-9062(85)90204-9
ISSN: 0148-9062
Sayı: 6
Cilt: 22
Sayfa: 191
14
Particle method for the numerical solution of the time-dependent schrödinger equation
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Dergi Makalesi
Kaynak :
Wiley Online Library
Dergi:
International Journal of Quantum Chemistry
Yazar(lar) :
J. H. Weiner , A. Askar
Konu :
Physical and Theoretical Chemistry, Atomic and Molecular Physics, and Optics, Condensed Matter Physics
Yıl :
2009
A. Askar
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DOI : 10.1002/qua.560050830
ISSN: 0020-7608
Sayı: S5
Cilt: 5
Sayfa: 259-259
15
Earthquake wave propagation in layered media by boundary integral methods
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Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Soil Dynamics and Earthquake Engineering
Yayıncı:
Elsevier
Yazar(lar) :
P.K. Hadley , A. Askar , A.S. Cakmak
Yıl :
1991
A. Askar
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The authors have previously presented work on the use of boundary methods to solve steady-state wave scattering problems in two-dimensional homogenous systems and on the use of these solutions with Fourier transforms to solve problems of transient input waves. This paper extends that work to nonhomogeneous systems. The methodology is now applicable to profiles with various material parameters in media bounded by irregularly shaped interfaces subjected to transient or periodic incident waves of any form. The profiles which can be solved are layers of finite extent, layers of infinite extent, cavities, inclusions of different materials, lenses, cases of three media and three interfaces meeting at a single point, and any combination thereof. The paper presents the basic equations of wave propagation in a single medium, the extension of these equations to multiple media, and the methodology of correcting for the truncation of the numerical portions of a problem. Using these techniques, several simple geometries are solved and the solutions are computed to closed-form solutions when available. Th comparisons are good and the value of correcting for the truncation is verified. The methodology is then applied to a test case of real data taken from real earthquake records, to wit: the response of the Santa Felicia earth dam to the San Fernando (1971) earthquake. The comparison is good in the time domain but in the frequency domain shows some inaccuracy at the higher frequencies. This loss of quality is attributed to the fact that a linear elastic system is not a good model for soil response. The final section an initial attempt to examine the effects of some simple damping schemes. Great improvement is shown in the attempt to reproduce numerically the response of the Santa Felicia earth dam.
DOI : 10.1016/0267-7261(91)90027-w
ISSN: 0267-7261
Sayı: 3
Cilt: 10
Sayfa: 130-140
Sınıflandırma :
16
Subsoil geology and soil amplification in Mexico valley
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Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Soil Dynamics and Earthquake Engineering
Yayıncı:
Elsevier
Yazar(lar) :
P.K. Hadley , A. Askar , A.S. Cakmak
Yıl :
1991
A. Askar
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DOI : 10.1016/0267-7261(91)90040-7
ISSN: 0267-7261
Sayı: 2
Cilt: 10
Sayfa: 101-109
Sınıflandırma :
17
The effect of surface curvature and discontinuity on the surface energy density and other induced fields in elastic dielectrics with polarization gradient
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Dergi Makalesi
Kaynak :
Science Direct
Dergi:
International Journal of Solids and Structures
Yayıncı:
Elsevier
Yazar(lar) :
A. Askar , P.C.Y. Lee , A.S. Cakmak
Yıl :
1971
A. Askar
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Mindlin's theory of elastic dielectrics with polarization gradient is used along with the values of material coefficients obtained by Askar et al. to solve two types of problems involving cylindrical and spherical cavities and a free linear crack in “plane-strain”. In the case of the two cavities the surface energy density of deformation and polarization is found to be changed by an amount directly proportional to a length parameter l1, of order of magnitude of the interatomic distance, and inversely proportional to the radius of curvature of the cavity. As for the crack a stress singularity of the order ε−½ as ε → 0 is obtained in the absence of any external forces. This singularity is of the same order as those given by classical elasticity and couple stress theories. However, the surface energy density of the crack surface is bounded. Реферат Для pacчeтa двyч типoв зaдaч кacaющичcя цилиндpичecкич и cфepичecкич тpeшин и cвoбoднoй линeйнoй щeли в плocкoм дeфopмиpoвaннoм cocтoянии, иcпoльзyeтcя тeopия Mиндлинa yпpyгич диэлeктpикoв и знaчeния кoэффициeнтoв мaтepиaлa, пoлyчeны Acкapoм, Ли и Kaкмaкoм, Для cлyчaя двyч тpeщин, плoтнocть пoвepчнocтнoй энepгии дeфopмaции и пoляpизaции oпpeдeляeтcя тaк, чтo oнa измeняeтcя пpocтo пpoпopциoнaльнo к пapaмeтpy длины l1 пppядкa вeличины мeждyaтoмнoгo paccмoяния и oбpaтнo пpoпopциoнaльнo к paдиycy кpивизны тpeщины, Taк, кaк для щeли пoлyчaeтcя cингyляpнocть пopядкa (ε−½ пpи (ϵ → 0 и пpи oтcyтcтвии вceч внeшнич cил. Этa cингyляpнocть oкaзывaeтcя тaкoгo жe caмoгo poдa, кaк cингyляpнocть, вытeкaющaя из тeopии yпpyгocти и тeopии мoмeнтныч нaпpяжeний. Ho oднaкo плoтнocть пoвepчнocтнoй энepгии oгpaничeнa нa пoвepчнocти щeли.
DOI : 10.1016/0020-7683(71)90103-x
ISSN: 0020-7683
Sayı: 5
Cilt: 7
Sayfa: 523-537
Sınıflandırma :
18
An analytic method for strong motion studies in layered media†
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Dergi Makalesi
Kaynak :
Science Direct
Dergi:
International Journal of Non-Linear Mechanics
Yayıncı:
Elsevier
Yazar(lar) :
H. Engin , A. Askar , A.S. Cakmak
Yıl :
1981
A. Askar
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An analytic method is presented for calculating strong motion spectra and response to arbitrary input in layered media. The method is based on the removal of secular terms at resonance of the equations with polynomial non-linearity. The non-linear effects are introduced by the frequency shifts calculated from the secular term according to the method by Millman and Keller. The procedure, through a convenient parametrizarion of the frequency, allows one to deal with linear equations. This possibility permits the extension of the method to multilayer systems by the use of transfer matrices. The response to an arbitrary input motion is obtained from the response spectrum in the frequency domain by the use of (Fast) Fourier Transform. Zusammenfassung Eine analytische Methode zur Berechnung der Spektra starker Bewegungen und des Verhaltens unter willkürlicher Erregung von geschichteten Materialen wird dargestellt. Die Methode basiert auf der Entfernung sekulärer Glieder im Resonanzgebiet der Gleichungen mit polynomialer Nichtlinearität. Die nichtlinearen Einwirkungen werden durch Frequenzverschiebungen hervorgerufen, die mit Hilfe der Methode nach Millman und Keller von den sekulären Gliedern berechnet werden. Durch die Verwendung einer geeigneten Parameterdarstellung der Frequenz ermöglicht das Verfahren eine Behandlung mit linearen Gleichungen. Dadurch kann die Methode unter Verwendung von Überführungsmatrizen auf mehrfach geschichtete Systeme erweitert werden. Das Verhalten bezüglich einer willkürlichen Erregungsbewegung wird aus dem Antwortspektrum im Frequenzbereich mit Hilfe (schneller) Fouriertransformationen ermittelt.
DOI : 10.1016/0020-7462(81)90007-x
ISSN: 0020-7462
Sayı: 2
Cilt: 16
Sayfa: 165-186
Sınıflandırma :
19
Linear theory of hereditary micropolar materials
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Dergi Makalesi
Kaynak :
Science Direct
Dergi:
International Journal of Engineering Science
Yayıncı:
Elsevier
Yazar(lar) :
A. Askar , A.S. Cakmak , T. Ariman
Yıl :
1968
A. Askar
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A theory of hereditary micropolar materials is presented for polar materials. The relaxation and creep behaviour of three simple micropolar viscoelastic models are presented and compared to the nonpolar case. The micropolar-elastic and viscoelastic analogy is formulated and applied to the problem of stress concentration in a plate. Résumé On présente, pour les matériaux polaires, une théorie de l'hérédité des matériaux micropolaires. On étudie le comportement, en relaxation et en écoulement, de trois modèles visco-élastiques, micropolaires, simples et on le compare au cas de la non-polarité. L'analogie micro-polaire élastique et visco-Platte angewendet. Zusammenfassung Eine Theorie der in der Nachwirkung mikropolaren Materialien wird für polare Materialien vorgelegt. Das Relaxations- und Kriechverhalten von drei einfachen mikropolaren visko-elastischen Modellen wird dargestellt und mit dem nichtpolaren Fall verglichen. Die mikropolar-elastischen und -viskoelastische Analogie wird formuliert und auf das Problem der Spannungskonzentration in einer Platte angewendet. Sumàrio Si présenta una teoria de matériau micropolari ereditari per i materiau polar i. Il comportamento del rilassamento e dello scorrimento di tre modelli viscoelastici micropolari semplici viene presentato e confrontato con il caso non polare. Si formula l'analogia micropolare-elastica e micropolare-viscoelastica, che viene quindi applicata al problema delia concentrazione delia sollecitazione in un piano. Реферат Пo вoпpocu пoляpныx мaтepиaлoв излaгaeтcя тeopия иa cлeдcтвeнныx микpoпoляpныx мaтepиaлoв. Пpeдcтaвлeны cвoйcтвa peлaкcaции и пoлзuч ecти для тpex пpocтыx мнкpoпoляpныx вязкouпpuгиx мoдeлeй, кoтopыe cpaвнивaютcя co cвoйcтв aми иeпoляpиыx мaтepиaлoв. Фopмuлиpueтcя микpoпoляpнo-uпpuгaя и микpoпoляpнo-вязкouпpuгaя aиa лoгия, кoтopaя пpимeняeтcя к зaдaчe пo кoнцeнтpaции нaпpяжeний в плитe.
DOI : 10.1016/0020-7225(68)90027-x
ISSN: 0020-7225
Sayı: 5
Cilt: 6
Sayfa: 283-293
Sınıflandırma :
20
An assessment of the poincare scheme for non-linear oscillators and an improvement of its range of validity
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
International Journal of Non-Linear Mechanics
Yayıncı:
Elsevier
Yazar(lar) :
H. Engin , A. Askar , A.S. Cakmak
Yıl :
1979
A. Askar
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The range of validity of the Poincare method is studied by comparison with the exact solution for the anharmonic and Morse oscillators. The exact solutions for these cases are expressible respectively in terms of elliptic and inverse trigonometric functions. The oscillation frequency is taken as the basis for the comparison. It is seen that the Poincare perturbation gives fairly accurate results up to amplitudes that are 20–30 per cent of the maximum value allowed for periodic solutions depending on the form of the potential energy. A new method is presented as a slight variation over the standard Poincare method. This method differs from the former only by a rearrangement of the differential equation through a collocation approximation for the potential. In spite of its simplicity, the method proves to be a better approximation than the standard Poincare method and gives remarkably accurate results for amplitudes up to 60–70 per cent of the maximum value allowed for periodic solutions. Résumé On etudie la domaine de validite de la methode de Poincare en la comparant avec la solution exacte pour les oscillateurs anharmonique et de Morse. Dans ces cas, on peut exprimer les solutions exactes respectivement en termes de fonctions elliptiques et trigonometriques inverses. On prend la frequence d'oscillation comme base de comparaison. On montre que la perturbation de Poincare donne des resultats assez precis jusqu'a des amplitudes de 20 a 30% de la valeur maximum autorisee pour les solutions periodiques selon la forme de l'energie potentielle. On presente une nouvelle methode en tant que legere variante de la methode de Poincare standard. Cette methode differe de la precedente seulement par un rearrangement de l'equation differentielle a l'aide d'une approximation par une reorganisation du potentiel. Malgre sa simplicite, cette methode prouve etre une meilleure approximation que la methode de Poincare standard et donne des resultats remarquablement precis pour des amplitudes jusqu'a 60–70% de la valeur maximum autorisee pour les solutions periodiques. Zusammenfassung Der Gultigkeitsbereich der Poincareschen Methode wird durch Vergleich mit der exakten Losung fur den Anharmonischen und den Morseschen Scwinger untersucht. Die exakten Losungen fur diese Falle konnen durch elliptische Funktionen und triginometrisehe Umkehrfunktionen bestimmt werden. Der Vergleich wird mit Hilfe der Schwingungsfrequenz durchgefuhrt. Es zeigt sich, dass in Abhangigkeit von der Form der potentiellen Energie und fur Amplituden, die 20–30% oder weniger des fur periodische Losungen zulassigen Wertes betragen, die Poincaresche Perturbation ziemlich genaue Resultate liefert. Eine neue Methode, die eine geringfuge Variation der gangigen Methode nach Poincare darstellt, wird vorgestellt. Dabei wird nur, mit Hilfe einer Kollokationsnaherung fur das Potential, die Differentialgleichung umgeordnet. Trotz ihrer Einfachheit ist die neue Methode eine bessere Annaherung als die gangige Poincaresche Methode. Sie liefert bemerkenswert genaue Resultate fur Amplituden bis zu 60–70% des fur periodische Losungen zulassigen Hochstwertes
DOI : 10.1016/0020-7462(79)90004-0
ISSN: 0020-7462
Sayı: 5-6
Cilt: 14
Sayfa: 305-314
Sınıflandırma :
Fizik %20
21
Aroma changes in mango juice during processing and storage
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Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Food Chemistry
Yayıncı:
Elsevier
Yazar(lar) :
S.E. El-Nemr , I.A. Ismail , A. Askar
Yıl :
1988
A. Askar
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Mango juice was analysed after bottling and during storage for 2 and 4 months, in order to follow the changes in aroma constitutents which have an adverse influence on the juice quality. Heat processing at 85°C/10 min caused the reduction of all volatile fractions due to evaporation and, in addition, the formation of acetyl furan, 5-methyl furfural, β-terpineol, terpinen-4-ol and butyl-3-hydroxy butanoate, which were not found in fresh juice. These compounds were attributable to degradation reactions and especially to ascorbic acid. Storage of bottled mango juice at room temperature resulted in the appearance of ethyl fatty acids and seline-11-ene-4-ol, in addition to a decrease in hydrocarbons and oxygenated components; these very important factors affected the flavour of mango juice. According to these findings, the furan derivatives, α- and β-terpineol, terpinen-4-ol and ethyl fatty acids, are detrimental factors resulting from heat-processing and storage of bottled mango juice.
DOI : 10.1016/0308-8146(88)90113-6
ISSN: 0308-8146
Sayı: 4
Cilt: 30
Sayfa: 269-275
Sınıflandırma :
Kimya %100
Yemek Bilimi %98
22
The multigrid method for accelerated solution of the discretized Schrödinger equation
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Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Computational Physics
Yayıncı:
Elsevier
Yazar(lar) :
F.F Grinstein , H Rabitz , A Askar
Yıl :
1983
A Askar
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The use of the new multigrid method for the numerical solution of the discretized Schrödinger equation is discussed. A simple approach is chosen to circumvent the difficulties associated with the fact that the Schrödinger differential operator is not positive definite. The scheme is applied to a two-dimensional model problem which includes the essential features present in actual scattering problems. The results show that significant savings can be achieved both in computational work and core memory requirements. The multigrid method should greatly increase the utility of meshing procedures for solving the partial differential equations of quantum mechanics.
DOI : 10.1016/0021-9991(83)90162-6
ISSN: 0021-9991
Sayı: 3
Cilt: 51
Sayfa: 423-443
Sınıflandırma :
23
DISPERSION-RELATION AND WAVE SOLUTION FOR ANHARMONIC LATTICES AND KORTEWEG DELAUNAYS VRIES CONTINUA
Araştırma Makalesi

Araştırma Makalesi
Open Access
Kaynak :
Aperta - TÜBİTAK Açık Arşivi
Dergi:
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES
Yazar(lar) :
A ASKAR
Yıl :
1973
A ASKAR
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Öz bulunamadı.
DOI : 10.81043/aperta.102157
Sayi :334
issue :1596
Sayfa :83-94
Sınıflandırma :
24
STABILITY OF NEMATIC LIQUID-CRYSTALS UNDER A TEMPERATURE-GRADIENT - CALCULATIONS FOR PAA
Araştırma Makalesi

Araştırma Makalesi
Open Access
Kaynak :
Aperta - TÜBİTAK Açık Arşivi
Dergi:
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
Yazar(lar) :
A ASKAR
Yıl :
1976
A ASKAR
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Öz bulunamadı.
DOI : 10.81043/aperta.102015
Sayi :14
issue :3
Sayfa :259-271
Sınıflandırma :
25
Electromagnetic wave propagation in non-linear dielectric media
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Dergi Makalesi
Kaynak :
Springer Link
Dergi:
Acta Mechanica
Yazar(lar) :
C. Rogers , H. M. Cekirge , A. Askar
Konu :
Mechanical Engineering, Computational Mechanics
Yıl :
1977
A. Askar
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A modification of Bergman's integral operator method is applied to a hodograph system descriptive of linearly polarised plane electromagnetic pulse propagation in non-linear dielectrics. Series solutions of the system are thereby generated corresponding to general D-E and B-H relations. For certain non-linear ‘constitutive laws’ the governing wave propagation equations are reduced to a hyperbolic canonical form associated with the classical wave equation and closed form integration is thereby achieved. The availability of arbitrary parameters in these laws allows approximation to non-linear dielectric laws derived empirically. Moreover, it is noted how a generalised version of Weinstein's Correspondence Principle may be utilised to generate iteratively more general non-linear constitutive laws for which reduction to canonical form may be obtained.
DOI : 10.1007/bf01177136
Anahtar Kelimeler : Canonical Form, Weinstein, Dielectric Medium, Electromagnetic Pulse, Arbitrary Parameter
ISSN: 0001-5970 1619-6937
Sayı: 1-4
Cilt: 26
Sayfa: 59-73
26
Evaluation of the pH and thermal stabilities of rosella anthocyanin extracts under solar light
Dergi Makalesi

Dergi Makalesi
Open Access
Kaynak :
Directory of Open Access Journals (DOAJ)
Dergi:
Beni-Suef University Journal of Basic and Applied Sciences
Yazar(lar) :
Kahtan A. Askar , Zabarjad H. Alsawad , Moayad N. Khalaf
Yıl :
2015
Kahtan A. Askar
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Anthocyanin is considered as an unstable pigment, undergoes gradual degradation processes throughout the storage or use. The degradation of Rosella anthocyanin extract (RAE) in different pH solutions was studied under solar light and compared with solutions kept in the dark. It appears that RAE solutions under solar light were suffering rapid degradation than those kept in the dark. Moreover, RAE samples at higher pH values showed faster rates of degradation than those with lower pH values. A mechanism for degradation was suggested through the formation of hydroxyl radical which is responsible for demineralization process. It is also appears that as the initial concentration of the dye increases, the requirement needed for degradation increased as well. The thermal degradation behavior of RAE at temperature range 25–60 °C under solar light showed first order kinetics with low activation energies.
DOI : 10.1016/j.bjbas.2015.06.001
Anahtar Kelimeler : Anthocyanin, Degradation, Solar light, Rosella extract
Cilt: 4
Sayı: 3
Sayfa: 262 - 268
Sınıflandırma :
Kimya %98
Yemek Bilimi %28
Kataliz %21
27
Earthquake waves in a random medium
Dergi Makalesi

Dergi Makalesi
Kaynak :
Wiley Online Library
Dergi:
International Journal for Numerical and Analytical Methods in Geomechanics
Yazar(lar) :
L. Chu , A. Askar , A. S. Cakmak
Konu :
Geotechnical Engineering and Engineering Geology, General Materials Science, Mechanics of Materials, Computational Mechanics
Yıl :
1981
A. Askar
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DOI : 10.1002/nag.1610050107
ISSN: 0363-9061
Sayı: 1
Cilt: 5
Sayfa: 79-96
28
ChemInform Abstract: NEW BIPHENYL DERIVATIVES. II: 1-(4-BIPHENYLYL)-1-HYDROXY-2-AMINOETHANES AND 1-(4-BIPHENYLYL)-1-CHLORO-2-AMINOETHANES AS POTENTIAL β-ADRENOCEPTOR BLOCKING AGENTS
Dergi Makalesi

Dergi Makalesi
Kaynak :
Wiley Online Library
Dergi:
Chemischer Informationsdienst
Yazar(lar) :
R. M. SHAFIK , A.-F. A. A. ASKAR
Yıl :
1979
A. ASKAR
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DOI : 10.1002/chin.197944176
ISSN: 0009-2975
Sayı: 44
Cilt: 10

29
Resonant non-linear vibrations in continuous systems—I. Undamped case
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Dergi Makalesi
Kaynak :
Science Direct
Dergi:
International Journal of Non-Linear Mechanics
Yayıncı:
Elsevier
Yazar(lar) :
M.J. Ablowitz , A. Askar , A.S. Cakmak , H. Engin
Yıl :
1979
A. Askar
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A method is presented for obtaining periodic solutions to forced oscillations of non-linear systems governed by equations of the form uss−uyy−εf(u,u,y,uyy…,s) = 0. The method is presented by application to the equation uss−uyy−εu2yuyy= 0 which governs the vibrations of a soil layer that is free on the top surface and is forced harmonically at the bedrock. It is shown that unlike the ODE case (Duffing equation), the PDE requires an infinite number of periodicity conditions to correctly characterize the resonant region and these conditions lead to an infinite number of branches in the dispersion spectrum. Calculations indicate that these branches tend to an envelope curve. The uniform approach presented by Millmann and Keller is discussed in order to determine in what sense it can be viewed as an effective approximation for the fundamental mode. Résumé On donne une methode pour obtenir des solutions periodiques aux oscillations forcees de systemes non lineaires regis par des equations de la forme uss− uyy− εf(u,uy,uyy,…,s) = 0. Cette methode est presentee en l' appliquant a l'equation uss − uyy − εu2yuyy = 0 qui regit les vibrations d'une couche de terrain libre a la surface superieure et forcee harmoniquement sur son assise. On montre que contrairement au cas de l'equation differentielle ordinaire (equation de Duffing), l'equation aux derivees partielles demande un nombre infini de conditions de periodicite pour caracteriser correctement la region de resonance et ces conditions conduisent a un nombre infini de branches dans le spectre de dispersion. Les calculs indiquent que ces branches tendent vers une courbe enveloppe. On discute l'approche uniforme presentee par Millmann et Keller pour determiner dans quel sens elle peut etre consideree comme une approximation effective du mode fondamental. Zusammenfassung Eine Methode zur Ermittelung periodixcher Losungen fur erzwungene Schwingungen nichtlinearer Systeme mit Gleichungen von der Form uss−uyy−εf(u,uy,uyy,…,s) = 0 wird angegeben. Die Methode wird auf die Gleichumg uss−uyy −εuy2uyy = 0 angewandt, welche die Schwingungen einer Bodenschicht mit freier Oberflache und harmonischer Erregung am Felsenuntergrund beschreibt. es wird gezeigt, dass im Gegensatz zum Fall mit gewohnlichen Differentialgleichungen (Duffing Gleichung) die partiellen Differentialgleichungen eine unendliche Anzahl von Periodizitats-bedingungen erfordern, um das Resonanzgebiet richtig zu charakterisieren. Diese Bedingungen fuhren zu unendlich vielen Abzweigungen im Dispersionsspektrum. Berechnungen deuten an, dass diese Abzweigungen zu einer einhullenden Kurve hin tendieren. Das einheitliche Verfahren nach Millmann und Keller wird diskutiert, um seine Nutzlichkeit als eine effektive Naherung fur die Grundschwingungs form zu bestimmen.
DOI : 10.1016/0020-7462(79)90011-8
ISSN: 0020-7462
Sayı: 4
Cilt: 14
Sayfa: 223-233
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