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| | There are many types of bike brakes for different applications. A little more than 30 miles, with a 5,200 foot elevation gain, and you'll ride over the finish line. The contemporary bikes for mountains are provided with stronger and lighter frame types in addition to pioneering form and design. There are more than 15 circuits in the sport of professional mountain biking. If you've ridden for years and years and know what you need, buying online does make sense. <br><br>Mountain cycling is some sort of rough sport, so these kind of bicycle parts are crafted accordingly. 750 the Ribble Winter Trainer provides fantastic features with a fantastic price tag. You can spend under $100 for a bargain bike at a department store, or lay down thousands for a professional model. From personal experience they can be not easy to maintain by yourself so a mechanical system may be better for you. It will be business as normal, very successful business as normal. <br><br>Mountain bikes in Arizona have two great rides in Sedona, Highline and the Dry Creek Loop. Mulberry Gap Mountain Bike Get-A-Way is located 12 miles from downtown Ellijay in the Chattahoochee National Forest with some of the best single track mountain bike trails including the Georgia Pinhoti trail system. The whole set-up, including your bag, should weigh no more than 20kgs (44lbs). Another way to classify brakes is by mounting style. If you have any inquiries regarding where and ways to make use of [http://www.freshwidewallpapers.com/profile/romaum Choosing the right ride for you mountain bike sizing.], you can call us at the web site. If you do, below is a list of items that you just would possibly wish to look at prior to shopping for a new mountain bike. <br><br>When discount sales are on, you need to be sure you understand the terms and conditions of your purchase, including warranty information. You can surpass your rivals if you participate in a match. Serious head injuries can be prevented with a helmet and today’s styles and designs make them more comfortable to wear. With a Shimano 105 groupset and FSA Gossamer chain set, it's a great choice for under. I've never been into cycling and wanted to give it a try for exercise. <br><br>So I should be looking for an 18 to 19 inch bike frame. Listed below are some of the common terms which you will come across. Something that sounds to me, to be nothing more than hard work. I've always been curious about this aspect of dating, because very few women have comparable experiences. It's about the journey and all that it entails, learning about yourself, making friends, being helped, and of course, helping others along the way". |
| |title = Movable cellular automaton method
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| |titlestyle =
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| |datastyle =
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| |headerstyle = background:#ccf;
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| |labelstyle = background:#ddf;
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| |image = [[File:MCA friction net.gif|300px|alt=modeling of contact interaction]]
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| |imagestyle =
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| |caption = Movable cellular automaton actively changed self neighbors by means switching neighbors state from linked to unlinked and vice versa (modeling of contact interaction)
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| |header1 = Method type
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| |label1 =
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| |data1 =
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| |label2 = Continuous/Discrete
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| |data2 = Discrete
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| |label3 = Analytical/Computational
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| |data3 = Computational
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| |header4 = Characteristics
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| |label4 =
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| |data4 =
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| |header5 =
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| |label5 = Influenced by
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| |data5 = [[cellular automaton]], [[discrete element method|discrete element]]
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| |label6 = Method in
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| |data6 = [[Computational mechanics|computational solid mechanics]]
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| }}
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| The '''Movable cellular automaton (MCA)''' method is a method in [[Computational mechanics|computational solid mechanics]] based on the discrete concept. It provides advantages both of classical [[cellular automaton]] and [[discrete element method|discrete element]] methods. Important advantage of the МСА method is a possibility of direct [[Computer simulation|simulation]] of materials fracture including damage generation, crack propagation, fragmentation and mass mixing. It is difficult to simulate these processes by means of [[continuum mechanics]] methods (For example: [[finite element method]], [[finite difference method]], etc.), so some new concepts like [[peridynamics]] are required. [[Discrete element method]] is very effective to simulate granular materials, but mutual forces among movable cellular automata provides simulating solids behavior. If size of automaton will be close to zero then MCA behavior becomes like classical [[continuum mechanics]] methods.
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| ==Keystone of the movable cellular automaton method==
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| [[File:MCA elements.png|thumb|left|<center>Object (at left) is described as set of interacted automata (at center). At right is shown velocity field of automata.</center>]]
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| In framework of the '''MCA''' approach an object under modeling is considered as a set of interacting elements/automata. The dynamics of the set of automata are defined by their mutual forces and rules for their relationships. This system exists and operates in time and space. Its evolution in time and space is governed by the equations of motion. The mutual forces and rules for inter-elements relationships are defined by the function of the automaton response. This function has to be specified for each automaton. Due to mobility of automata the following new parameters of cellular automata have to be included into consideration: ''R<sup>i</sup>'' – radius-vector of automaton; ''V<sup>i</sup>'' – velocity of automaton; '''ω<sup>i</sup>''' – rotation velocity of automaton; ''θ<sup>i</sup>'' – rotation vector of automaton; ''m<sup>i</sup>'' – mass of automaton; ''J<sup>i</sup>'' – moment of inertia of automaton.
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| ==New concept: neighbours==
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| [[File:MCA neighbors.gif|thumb|<center>Each automaton has some neighbors</center>]]
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| The new concept of the MCA method is based on the introducing of the '''state of the pair of automata''' (relation of interacting pairs of automata) in addition to the conventional one – the state of a separate automaton. Note that the introduction of this definition allows to go from the static net concept to the '''concept of neighbours'''. As a result of this, the automata have the ability to change their neighbors by switching the states (relationships) of the pairs.
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| ==Definition of the parameter of pair state==
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| The introducing of new type of states leads to new parameter to use it as criteria for '''switching relationships'''. It is defined as an automaton overlapping parameters ''h<sup>ij</sup>''. So the relationship of the cellular automata is characterised by the value of their '''overlapping'''.
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| [[File:MCA sh1.gif]] [[File:MCA sh2.gif]]
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| The initial structure is formed by setting up certain relationships among each pair of neighboring elements.
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| ==Criterion of switching of the state of pair relationships==
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| [[File:MCA switch.gif|thumb|<center>At left pair of automata ij is linked. At right pair of automata ij is unlinked.</center>]]
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| In contrast to the classical cellular automaton method in the MCA method not only a single automaton but also a '''relationship of pair of automata can be switched'''. According with the bistable automata concept there are two types of the pair states (relationships):
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|
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| {| class="wikitable" border="1"
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| |-
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| | '''linked'''
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| | – both automata belong to a solid
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| |-
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| | '''unlinked'''
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| | – each automaton of the pair belongs to different bodies or parts of damaged body.
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| |}
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| So the '''changing of the state of pair relationships''' is controlled by relative movements of the automata and the media formed by such pairs can be considered as bistable media.
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| ==Equations of MCA motion==
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| The evolution of MCA media is described by the following '''equations of motion for translation''': | |
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| :<math>{d^2 h^{ij} \over dt^2} = \left( {1 \over m^i} + {1 \over m^j} \right) p^{ij} + \sum_{k\neq j} C(ij,ik) \psi(\alpha_{ij,ik}) {1 \over m^i} p^{ik} + \sum_{l \neq i} C(ij,jl) \psi(\alpha_{ij,jl}) {1 \over m^j} p^{jl}</math>
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| [[File:MCA neighbour in pair.png|thumb|<center>Forces between automata ij coming from their neighbors.</center>]]
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| Here m<sup>i</sup> is the mass of automaton i, p<sup>ij</sup> is central force acting between automata i and j, C(ij,ik) is certain coefficient associated with transferring the h parameter from pair '''ij''' to pair '''ik''', ψ(α<sub>ij,ik</sub>) is angle between directions '''ij''' and '''ik'''.
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| Due to finite size of movable automata the rotation effects have to be taken into account. The '''equations of motion for rotation''' can be written as follows:
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| :<math>{d^2 \theta^{ij} \over dt^2} = \left( {q^{ij} \over J^i} + {q^{ji} \over J^j} \right) \tau^{ij} + \sum_{k\neq j} S(ij,ik) {q^{ik} \over J^i} \tau^{ik} + \sum_{l\neq j} S(ij,jl) {q^{jl} \over J^j} \tau^{jl}</math>
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| Here Θ<sup>ij</sup> is the angle of relative rotation (it is a switching parameter like h<sup>ij</sup> for translation), q<sup>ij</sup> is the distance from center of automaton '''i''' to contact point of automaton '''j''' (moment arm), τ<sup>ij</sup> is the pair tangential interaction, S(ij,ik) is certain coefficient associated with transferring the Θ parameter from one pair to other (it is similar to C(ij,ik) from the equation for translation).
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| It should be noted that these equations are completely similar to the equations of motion for the many–particle approach.
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| ==Definition of deformation in pair of automata==
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| [[File:MCA Deformation in Pair of Automata.gif|thumb|left|<center>Rotation of body as whole not caused to deformation in pair of automata</center>]]
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| '''Translation of the pair automata'''
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| The dimensionless deformation parameter for translation of the '''i j''' automata pair can be presented as:
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| :<math> \varepsilon^{ij} = {h^{ij} \over r_{0}^{ij}} = { \left( q^{ij} + q^{ji} \right) - \left( d^{i} + d^{j} \right) \big / 2 \over \left( d^{i} + d^{j} \right) \big / 2 }</math>
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| In this case:
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| :<math>\left( \Delta{\varepsilon^{i(j)}} + \Delta{\varepsilon^{j(i)}} \right)
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| { \left( d^{i} + d^{j} \right) \over 2} = V_{n}^{ij} \Delta{t}</math>
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| where '''Δt''' time step, '''V<sub>n</sub><sup>ij</sup>''' – relative velocity.
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| Rotation of the pair automata can be calculated by analogy with the last translation relationships.
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| ==Modeling of irreversible deformation in the MCA method==
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| [[File:MCA Irreversible Deformation.gif|thumb|<center>Deformation is determine by value of distance from the center of automaton</center>]]
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| [[File:MCA response function of automata.gif|thumb|<center>There are two types of the response function of automata</center>]]
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| The '''ε<sup>ij</sup>''' parameter is used as a measure of deformation of automaton '''i''' under its interaction with automaton '''j'''. Where '''q<sup>ij</sup>''' – is a distance from the center of automaton '''i''' to its contact point with automaton '''j'''; '''R<sup>i</sup> = d<sup>i</sup>/2''' ('''d<sup>i</sup>''' – is the size of automaton '''i''').
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| '''As an example''' the titanium specimen under cyclic loading (tension – compression) is considered. The loading diagram is shown in the next figure:
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| {| class="wikitable" border="1"
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| |-
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| ! Scheme of loading
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| ! Loading diagram
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| |-
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| | [[File:MCA cyclic schem.gif]]
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| | [[File:MCA cyclic diag.gif]]
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| |-
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| | ('''Red marks''' are the experimental data)
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| |}
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| ==Advantages of MCA method==
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| Due to mobility of each automaton the MCA method allows to take into account directly such actions as:
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| * mass mixing
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| * penetration effects
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| * chemical reactions
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| * intensive deformation
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| * phase transformations
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| * accumulation of damages
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| * fragmentation and fracture
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| * cracks generation and development
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| Using boundary conditions of different types (fixed, elastic, viscous-elastic, etc.) it is possible to imitate different properties of surrounding medium, containing the simulated system. It is possible to model different modes of mechanical loading (tension, compression, shear strain, etc.) by setting up additional conditions at the boundaries.
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| ==References==
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| *{{cite journal|last =Psakhie| first=S.G.| authorlink=| coauthors=Horie, Y.; Korostelev, S.Yu.; Smolin, A.Yu.; Dmitriev, A.I.; Shilko, E.V.; Alekseev, S.V.| title=Method of movable cellular automata as a tool for simulation within the framework of mesomechanics| journal=Russian Physics Journal| volume=38| issue=11| pages=1157–1168| publisher=Springer New York| location = | date = November. - 1995| url=| doi=10.1007/BF00559396| id=| accessdate=}}
| |
| *{{cite journal|last =Psakhie| first=S.G.| authorlink=| coauthors=Korostelev, S.Y.; Smolin, A.Y.; Dmitriev, A.I.; Shilko, E.V.; Moiseenko D.D.; Tatarincev E.M.; Alekseev, S.V.| title=Movable cellular automata method as a tool for physical mesomechanics of materials| journal=Physical mesomechanics| volume=1| issue=1| pages=95–108| publisher=The Organization of the Russian Academy of Sciences, Institute of Strength Physics and Materials Science of the Siberian Branch of RAS (ISPMS SB RAS)| location = | year = 1998| url=| doi = | id =| accessdate=}} ({{lang-ru|{{cite journal|last =Псахье| first=С.Г.| authorlink=| coauthors=Коростелев, С.Ю.; Смолин, А.Ю.; Дмитриев, А.И.; Шилько, Е.В.; Моисеенко, Д.Д.; Татаринцев, Е.М.; Алексеев, С.В.| title=Метод подвижных клеточных автоматов как инструмент физической мезомеханики материалов| journal=Физическая мезомеханика| volume=1| issue=1| pages=95–108| publisher=Учреждение Российской академии наук Институт физики прочности и материаловедения Сибирского отделения РАН (ИФПМ СО РАН)| location = | year = 1998| url = http://elibrary.ru/item.asp?id=12913617| doi = | id =| accessdate = 2010-03-03}}}})
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| *{{cite journal|last =Psakhie| first=S.G.| authorlink=| coauthors=Ostermeyer, G.P.; Dmitriev, A.I.; Shilko, E.V.; Smolin, A.Y.; Korostelev, S.Y.| title=Movable cellular automata method as new direction in numerical discrete mechanics. I. Theoretical description| journal=Physical mesomechanics| volume=3| issue=2| pages=5–13| publisher=The Organization of the Russian Academy of Sciences, Institute of Strength Physics and Materials Science of the Siberian Branch of RAS (ISPMS SB RAS)| location = | year=2000| url=| doi = | id = | accessdate = }} ({{lang-ru|{{cite journal|last =Псахье| first=С.Г.| authorlink=| coauthors=Остермайер, Г.П.; Дмитриев, А.И.; Шилько, Е.В.; Смолин, А.Ю.; Коростелев, С.Ю.| title=Метод подвижных клеточных автоматов как новое направление дискретной вычислительной механики. I. Теоретическое описание| journal=Физическая мезомеханика| volume=3| issue=2| pages=5–13| publisher=Учреждение Российской академии наук Институт физики прочности и материаловедения Сибирского отделения РАН (ИФПМ СО РАН)| location = | year=2000 | url=http://elibrary.ru/item.asp?id=12913646| doi = | id = | accessdate = 2010-03-03}}}})
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| *{{cite journal|last =Psakhie| first=S.G.| authorlink=| coauthors=Horie, Y.; Ostermeyer, G.P.; Korostelev, S.Yu.; Smolin, A.Yu.; Shilko, E.V.; Dmitriev, A.I.; Blatnik, S.; Spegel, M.; Zavsek, S.| title=Movable cellular automata method for simulating materials with mesostructure| journal=Theoretical and Applied Fracture Mechanics| volume=37| issue=1-3| pages=311–334| publisher=Elsevier Science Ltd.| location = | date=December 2001| url = http://mechanik.tu-berlin.de/popov/software/mca/TAFMEC.pdf| doi=10.1016/S0167-8442(01)00079-9| id = | accessdate = }}
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| *{{cite journal|last =Psakhie| first=S.G.| authorlink=| coauthors=Smolin, A.Y.; Stefanov, Y.P.; Makarov, P.V.; Chertov, M.A.| title=Modeling the behavior of complex media by jointly using discrete and continuum approaches| journal=Technical Physics Letters| volume=30| issue=9| pages=712–714| publisher=MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.| location = | year = 2004| url = | doi=10.1134/1.1804572| id = | accessdate = }}
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| *{{cite book| last=Shimizu| first=Y.| authorlink = | coauthors=Hart, R.; Cundall, P.| title=Numerical modeling in Micromechanics via Particle Methods| publisher = | year=2004| location = | page = | url=http://books.google.com/books?id=GVAUH98Yr6oC&lpg=PA242&dq=%22Movable%20cellular%20automaton%22%20-inpublisher%3Aicon&as_brr=0&hl=ru&pg=PR4#v=onepage&q=%22Movable%20cellular%20automaton%22%20-inpublisher:icon&f=false| doi = | id = | isbn=90-5809-679-3 | accessdate = 2010-03-03}}
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| *{{cite book| last=Gnecco| first=E.| authorlink = | coauthors=Meyer E. (Eds.)| title=Fundamentals of friction and wear on the Nanoscale| publisher = | year=2007| location = | page = | url=http://books.google.com/books?id=v2Pe5thhNiwC&lpg=PP1&hl=ru&pg=PP1#v=onepage&q=&f=false| doi = | id = | isbn=978-3-540-36806-9 | accessdate = 2010-03-03}}
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| *{{cite journal|last =Yunliang| first=Tan| authorlink =| coauthors=Guirong, Teng; Haitao, Li|title=MCA Model for Simulating the Failure of Microinhomogeneous Materials| journal=Journal of Nanomaterials | volume=2008 | issue=| pages=1–7 | publisher=Hindawi Publishing Corporation| location = | date = | url = | doi = 10.1155/2008/946038 | id = 946038| accessdate = }}
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| *{{cite book| last=Fomin| first=V.M.| authorlink = | coauthors=Andreev, A.N. and al| title=Mechanics - from discrete to continuous| publisher=Russian academy of science, Siberian branch, Institute of theoretical and applied mechanics (named S.A. Khristianovich)| year=2008| location = | page=344| url=| doi = | id = | isbn=978-5-7692-0974-1}} ({{lang-ru|{{cite book| last=Фомин| first=В.М.| authorlink = | coauthors=Андреев А.Н. и др.| title=Механика - от дискретного к сплошному| publisher=Рос. акад наук, Сиб. отд-ние, Ин-т теоретической и прикладной механики им. С.А. Христиановича| year=2008| location = | page=344| url=http://www.sibran.ru/psb/books/show_text.phtml?rus+1880+psb| doi=| id=| isbn=978-5-7692-0974-1| accessdate = 3.03.2010}}}})
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| *{{cite journal| last=Smolin| first=A.Y.| authorlink=| coauthors=Roman, N.V.; Dobrynin, S.A.; Psakhie, S.G.| title=On rotation in the movable cellular automaton method| journal=Physical Mesomechanics| volume=12| issue=3-4| pages=124–129| publisher=Elsevier B.V.| location = | date=May–August. - 2009| url = | doi=10.1016/j.physme.2009.07.004| id = | accessdate = }}
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| *{{cite book| last=Popov| first=Valentin L.| authorlink = | coauthors = | title= Kontaktmechanik und Reibung (Ein Lehr- und Anwendungsbuch von der Nanotribologie bis zur numerischen Simulation)| publisher=Springer Berlin Heidelberg| year=2009| location = | page = | url=| doi=10.1007/978-3-540-88837-6| id = | isbn=978-3-540-88836-9| accessdate=}}
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| *{{cite book| last=Dobrynin| first=S.A.| authorlink = | coauthors = | title=Development of movable cellular atomaton method for modeling generation and propagation of elastic waves under contact interaction of solids| publisher=PhD thesis in physics and mathematics| year=2010| location=Tomsk| page=130| url = | doi=| id = | isbn = }} ({{lang-ru|{{cite book| last=Добрынин| first=С.А.| authorlink = | coauthors = | title=Развитие метода подвижных клеточных автоматов для моделирования генерации и распространения упругих волн при контактном взаимодействии твердых тел| publisher=Диссертация … кандидата физико-математических наук| year=2010| location=Томск| page=130| url=http://serg-dobrinin.narod.ru/disert/index.html| doi = | id = | isbn = | accessdate = 3.03.2010}}}})
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| * {{cite book| last=Dobrynin| first=Sergey| authorlink = | coauthors = | title=Computer simulation by movable cellular automaton method| publisher=LAP LAMBERT Academic Publishing| year=2011| location=Saarbrücken Germany| page=132| url= | doi = | id = | isbn = 978-3-8443-5954-1| accessdate = 19.11.2011}} ({{lang-ru|{{cite book| last=Добрынин| first=Сергей| authorlink = | coauthors = | title=Компьютерное моделирование методом подвижных клеточных автоматов| publisher=LAP LAMBERT Academic Publishing| year=2011| location=Saarbrücken Germany| page=132| url=https://www.lap-publishing.com/catalog/details/store/gb/book/978-3-8443-5954-1/%D0%9A%D0%BE%D0%BC%D0%BF%D1%8C%D1%8E%D1%82%D0%B5%D1%80%D0%BD%D0%BE%D0%B5-%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB%D0%B8%D1%80%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5-%D0%BC%D0%B5%D1%82%D0%BE%D0%B4%D0%BE%D0%BC-%D0%BF%D0%BE%D0%B4%D0%B2%D0%B8%D0%B6%D0%BD%D1%8B%D1%85-%D0%BA%D0%BB%D0%B5%D1%82%D0%BE%D1%87%D0%BD%D1%8B%D1%85-%D0%B0%D0%B2%D1%82%D0%BE%D0%BC%D0%B0%D1%82%D0%BE%D0%B2| doi = | id = | isbn = 978-3-8443-5954-1| accessdate = 19.11.2011}}}})
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| | |
| ==Software==
| |
| * [http://mechanik.tu-berlin.de/popov/software/mca/mca.htm MCA software package]
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| * Software for simulation of materials in discrete-continuous approach «FEM+MCA»: Number of state registration in Applied Research Foundation of Algorithms and Software (AFAS): 50208802297 / Smolin A.Y., Zelepugin S.A., Dobrynin S.A.; applicant and development center is Tomsk State University. – register date 28.11.2008; [http://serg-dobrinin.narod.ru/mydiploms/reg_program.jpg certificate AFAS N 11826 date 01.12.2008.]
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| ==See also==
| |
| *[[Continuum mechanics]]
| |
| *[[Solid mechanics]]
| |
| *[[Fracture mechanics]]
| |
| *[[Peridynamics]]
| |
| *[[Computer simulation]]
| |
| *[[Discrete element method]]
| |
| *[[Cellular automaton]]
| |
| *[[Finite element method]]
| |
| *[[Finite difference method]]
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| | |
| [[Category:Solid mechanics]]
| |
| [[Category:Numerical analysis]]
| |
| [[Category:Cellular automata]]
| |
| [[Category:Condensed matter physics]]
| |
| [[Category:Mathematical modeling]]
| |
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