Reaction-transport systems: mesoscopic foundations, fronts, and spatial instabilities
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin ; Heidelberg
Springer
[2010]
|
| Schriftenreihe: | Springer series in synergetics
Springer complexity |
| Schlagwörter: | |
| Links: | http://deposit.dnb.de/cgi-bin/dokserv?id=3493230&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029386496&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Literaturangaben |
| Umfang: | XXI, 454 Seiten Illustrationen, Diagramme 24 cm |
| ISBN: | 9783642114427 |
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| 245 | 1 | 0 | |a Reaction-transport systems |b mesoscopic foundations, fronts, and spatial instabilities |c Vicenç Méndez ; Sergei Fedotov ; Werner Horsthemke |
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Datensatz im Suchindex
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| adam_text | CONTENTS PART I GENERAL CONCEPTS 1 REACTION KINETICS 3 1.1 RATE
EQUATIONS 3 1.2 LINEAR STABILITY ANALYSIS 4 1.2.1 ONE-VARIABLE SYSTEMS 6
1.2.2 TWO-VARIABLE SYSTEMS 7 1.2.3 SYSTEMS WITH N 2 VARIABLES 10 1.3
CHEMICAL KINETICS 11 1.4 CHEMICAL AND BIOLOGICAL MODELS 14 1.4.1
BRANCHING-COALESCENCE MODEL 15 1.4.2 SCHLOEGL MODEL I 16 1.4.3 VERHULST
EQUATION 17 1.4.4 BRUSSELATOR 17 1.4.5 SCHNAKENBERG MODEL 19 1.4.6
GIERER-MEINHARDT MODEL 20 1.4.7 GRAY-SCOTT MODEL 20 1.4.8 OREGONATOR 24
1.4.9 LENGYEL-EPSTEIN MODEL 26 EXERCISES 30 2 REACTIONS AND TRANSPORT:
DIFFUSION, INERTIA, AND SUBDIFFUSION 33 2.1 REACTION-DIFFUSION EQUATION
33 2.1.1 PHENOMENOLOGICAL DERIVATION OF THE REACTION-DIFFUSION EQUATION
34 2.1.2 N-VARIABLE REACTION-DIFFUSION EQUATIONS 35 2.2
REACTION-TRANSPORT EQUATIONS WITH INERTIA 36 2.2.1 HYPERBOLIC
REACTION-DIFFUSION EQUATIONS 37 2.2.2 REACTION-CATTANEO SYSTEMS AND
REACTION-TELEGRAPH EQUATIONS 38 2.2.3 PERSISTENT RANDOM WALKS AND
REACTIONS 39 2.3 REACTIONS AND ANOMALOUS DIFFUSION 43 BIBLIOGRAFISCHE
INFORMATIONEN HTTP://D-NB.INFO/1003553613 DIGITALISIERT DURCH XII
CONTENTS 2.3.1 CONTINUOUS-TIME RANDOM WALKS 44 2.3.2
REACTION-SUBDIFFUSION EQUATIONS 48 EXERCISES 53 3 RANDOM WALKS AND
MESOSCOPIC REACTION-TRANSPORT EQUATIONS 55 3.1 DISCRETE-TIME RANDOM WALK
57 3.1.1 MESOSCOPIC EQUATION FOR THE PARTICLE DENSITY 58 3.1.2 RANDOM
WALK WITH TWO STATES AND THE SYSTEM OF TWO MESOSCOPIC EQUATIONS 59 3.2
CONTINUOUS-TIME RANDOM WALK 60 3.2.1 MESOSCOPIC EQUATION FOR THE
PARTICLE DENSITY 64 3.2.2 RANDOM WALK WITH DISCRETE STATES IN
CONTINUOUS-TIME .. 66 3.2.3 SEMI-MARKOV PROCESSES 67 3.3 MARKOV CTRW
MODELS 69 3.3.1 COMPOUND POISSON PROCESS 69 3.3.2 SYSTEM OF TWO
MESOSCOPIC EQUATIONS 71 3.3.3 CHARACTERISTIC FUNCTION AND TRANSPORT
EQUATION FOR THE PARTICLE DENSITY 72 3.3.4 LEVY PROCESSES 75 3.4
NON-MARKOVIAN CTRW MODELS WITH CHEMICAL REACTIONS 79 3.4.1 MODEL A 79
3.4.2 MODEL B 82 3.4.3 MODELC 83 3.5 RANDOM WALK IN RANDOM TIME AND
SUBORDINATION 85 3.5.1 SPACE-FRACTIONAL TRANSPORT EQUATION 87 3.5.2
INVERSE SUBORDINATION AND TIME-FRACTIONAL TRANSPORT EQUATION 90 3.6
MACROSCOPIC DESCRIPTION 91 3.6.1 SCALING PROCEDURE 92 3.6.2 ANOMALOUS
SCALING 94 3.6.3 SCALING AND CONVERGENCE TO THE DIFFUSION PROCESS 99 3.7
TRANSPORT EQUATIONS AND UNDERLYING STOCHASTIC PROCESSES 102 3.7.1
BROWNIAN MOTION, LEVY FLIGHT, AND THE DIFFUSION EQUATIONS 102 3.7.2
TRANSPORT EQUATIONS: FORWARD VS BACKWARD 104 3.7. CONTENTS 4.1.1 FRONTS
PROPAGATING INTO UNSTABLE STATES. PULLED VS PUSHED FRONTS 126 4.1.2
TRANSIENT DYNAMICS OF PULLED FRONTS 129 4.1.3 FRONT PROPAGATION INTO
METASTABLE STATES 130 4.2 FRONT VELOCITY SELECTION 132 4.2.1
HAMILTON-JACOBI FORMALISM 133 4.2.2 VARIATIONAL CHARACTERIZATION 135 4.3
EFFECT OF LOW CONCENTRATIONS 140 4.3.1 EFFECT ON PULLED FRONTS 140 4.3.2
EFFECT ON PUSHED FRONTS 141 4.3.3 VARIATIONAL PRINCIPLES AND THE CUTOFF
PROBLEM 142 4.4 EFFECT OF EXTERNAL NOISE 144 4.5 EFFECT OF TIME DELAY
AND AGE STRUCTURE 146 4.6 MULTI-COMPONENT REACTION-DIFFUSION SYSTEMS 148
4.6.1 TWO-COMPONENT RD SYSTEM 149 EXERCISES 150 REACTION-TRANSPORT
FRONTS PROPAGATING INTO UNSTABLE STATES 155 5.1 HYPERBOLIC SCALING AND
HAMILTON-JACOBI EQUATION FOR THE FRONT POSITION 157 5.1.1 DISCRETE-TIME
MODEL 157 5.2 CONTINUOUS-TIME MODEL WITH LONG-RANGE DISPERSAL 159 5.3
CTRW MODELS AND FRONT PROPAGATION 160 5.4 MEMORY EFFECTS IN RD EQUATION
164 5.5 FRONT PROPAGATION IN THE REACTION-TELEGRAPH EQUATION 166 5.5.1
RELATIVISTIC HAMILTON-JACOBI EQUATION 167 5.5.2 EXACT FORMULA FOR FRONT
VELOCITY 168 5.6 FRONT PROPAGATION IN PERSISTENT RANDOM WALKS WITH
REACTIONS .... 169 5.6.1 FRONTS IN DIRECTION-INDEPENDENT REACTION WALKS
169 5.6.2 FRONTS IN DIRECTION-DEPENDENT REACTION WALKS 172 5.7
REACTION-BIASED RANDOM WALKS. PROPAGATION FAILURE 175 EXERCISE XIV
CONTENTS 6.4.2 LOCAL VELOCITY APPROACH 203 6.4.3 HAMILTON-JACOBI
FORMALISM 204 EXERCISES 207 7 ECOLOGICAL APPLICATIONS 209 7. 1 HUMAN
MIGRATIONS 209 7.1.1 NEOLITHIC TRANSITION: SINGLE-SPECIES MODELS 209
7.1.2 HUNTER-GATHERERS INTERACTION: INDO-EUROPEAN NEOLITHIC TRANSITION
215 7.1.3 MODEL FOR HUMAN SETTLEMENTS 216 7.1.4 MODELS WITH DISPERSIVE
VARIABILITY 218 7.1.5 NEANDERTHAL EXTINCTION 227 7.1.6 US COLONIZATION:
INVASIONS THROUGH FRACTAL RIVER NETWORKS 228 7.2 AVIAN RANGE EXPANSIONS
232 7.2.1 HOUSE FINCH 233 7.2.2 EURASIAN COLLARED DOVE 234 7.3 PLANT
INVASIONS 234 7.3.1 THE MODEL. INVASION THRESHOLD 236 7.3.2 APPLICATIONS
TO THE INVASION SUCCESS OF WEEDS 239 7.3.3 INVASION VELOCITY OF WEEDS
242 EXERCISES 244 8 BIOMEDICAL APPLICATIONS 245 8. 1 CANCER INVASION 245
8.1.1 TUMOR-HOST INTERACTION 245 8.1.2 TUMOR-HOST INTERACTION WITH
CONTACT INHIBITION 248 8.1.3 GLIOMA INVASION 250 8.2 VIRUS DISPERSAL IN
BACTERIAL COLONIES 255 8.3 PROPAGATION IN SPINY DENDRITES 259 8.3.1
MESOSCOPIC MODEL 261 8.3.2 BIOLOGICALLY INERT PARTICLES: ANOMALOUS
DIFFUSION 264 8.3.3 KINETICS OF PARTICLE DECAY IN SPINY DENDRITES 265
EXERCISES 266 PART III SPATIAL INSTABILITIES AND PATTERNS 9 CONTENTS XV
9.3.2 DEPENSATION GROWTH 280 9.3.3 CRITICAL DEPENSATION 281 9.4 EXACT
SOLUTIONS 283 EXERCISES 285 10 TURING INSTABILITIES IN HOMOGENEOUS
SYSTEMS 287 10.1 TURING INSTABILITIES IN STANDARD REACTION-DIFFUSION
SYSTEMS 287 10.1.1 -VARIABLE REACTION-DIFFUSION SYSTEMS 288 10.1.2
TWO-VARIABLE REACTION-DIFFUSION SYSTEMS 292 10.1.3 TURING INSTABILITY IN
THE STANDARD BRUSSELATOR REACTION-DIFFUSION SYSTEM 296 10.2 TURING
INSTABILITIES IN HRDES AND REACTION-CATTANEO SYSTEMS .... 297 10.2.1
TURING INSTABILITIES IN HYPERBOLIC REACTION-DIFFUSION EQUATIONS 297
10.2.2 TURING INSTABILITIES IN REACTION-CATTANEO SYSTEMS 299 10.3 TURING
INSTABILITIES IN PERSISTENT RANDOM WALKS WITH REACTIONS ... 300 10.3.1
TURING INSTABILITIES IN DIRECTION-INDEPENDENT REACTION WALKS 301 10.3.2
SPATIAL HOPF INSTABILITIES IN DIRECTION-INDEPENDENT REACTION WALKS 306
10.3.3 SPATIAL INSTABILITIES IN ONE-VARIABLE SYSTEMS 310 10.3.4 TURING
INSTABILITIES IN DIRECTION-DEPENDENT REACTION WALKS 312 10.4 TURING
INSTABILITIES AND ANOMALOUS DIFFUSION 316 10.4.1 TURING INSTABILITIES IN
REACTION-SUBDIFFUSION SYSTEMS: MODEL B 316 10.4.2 TURING INSTABILITIES
IN REACTION-SUBDIFFUSION SYSTEMS: MODEL A AND OTHER APPROACHES 326
10.4.3 TURING INSTABILITY IN THE SUPERDIFFUSIVE BRUSSELATOR 327
EXERCISES 329 11 TURING INSTABILITIES IN REACTION-DIFFUSION SYSTEMS WITH
TEMPORALLY O XVI CONTENTS 12.1.4 THEORY OF TURING PATTERNS IN THE CIMA
AND CDIMA REACTIONS: 2+1 MODEL 351 12.1.5 TURING PATTERNS IN THE
BZ-AOT REACTION: EXPERIMENTS ... 356 12.1.6 TURING PATTERNS IN THE
BZ-AOT REACTION: THEORY 357 12.2 TURING MECHANISM IN BIOLOGICAL PATTERN
FORMATION 360 12.2.1 HAIR-FOLLICLE PATTERNING 360 12.2.2 LEFT-RIGHT
ASYMMETRY IN THE MOUSE EMBRYO 362 EXERCISES 363 13 PATTERN FORMATION IN
SPATIALLY DISCRETE SYSTEMS 365 13.1 LINEAR STABILITY ANALYSIS 366 13.1.1
ROUTH-HURWITZ ANALYSIS 367 13.1.2 STRUCTURAL MODE ANALYSIS 368 13.2
INSTABILITIES IN DIFFUSIVELY COUPLED REACTOR NETWORKS 372 13.3 NETWORKS
OF DIFFUSIVELY COUPLED REACTORS WITH LENGYEL-EPSTEIN KINETICS 375 13.3.1
TURING THRESHOLD 375 13.3.2 TURING INSTABILITY IN SMALL ARRAYS 378 13.4
LOCALIZED PATTERNS IN HOMOGENEOUS NETWORKS OF DIFFUSIVELY COUPLED
REACTORS 387 13.4.1 THEORETICAL TOOLS 389 13.4.2 LOCALIZED PATTERN IN
NETWORKS WITH LENGYEL-EPSTEIN KINETICS 393 13.5 TURING INSTABILITY IN
LARGE ARRAYS 401 13.6 TURING INSTABILITY IN SMALL INHOMOGENEOUS ARRAYS
402 13.6.1 TWO COUPLED REACTORS 404 13.6.2 THREE COUPLED REACTORS 406
13.6.3 FOUR COUPLED REACTORS 409 13.7 NETWORKS OF PHOTOCHEMICALLY
COUPLED REACTORS 410 13.7.1 PHOTOSENSITIVE BZ AND CDIMA REACTIONS 411
13.7.2 STABILITY ANALYSIS OF PHOTOCHEMICALLY COUPLED REACTORS .412
13.7.3 INSTABILITY THRESHOLDS 414 13.7.
|
| any_adam_object | 1 |
| author | Méndez, Vicenç Fedotov, Sergei Horsthemke, Werner |
| author_facet | Méndez, Vicenç Fedotov, Sergei Horsthemke, Werner |
| author_role | aut aut aut |
| author_sort | Méndez, Vicenç |
| author_variant | v m vm s f sf w h wh |
| building | Verbundindex |
| bvnumber | BV043978051 |
| ctrlnum | (OCoLC)699804041 (DE-599)DNB1003553613 |
| dewey-full | 530.15 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.15 |
| dewey-search | 530.15 |
| dewey-sort | 3530.15 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV043978051 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T17:50:16Z |
| institution | BVB |
| isbn | 9783642114427 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029386496 |
| oclc_num | 699804041 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM |
| owner_facet | DE-19 DE-BY-UBM |
| physical | XXI, 454 Seiten Illustrationen, Diagramme 24 cm |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in synergetics Springer complexity |
| spellingShingle | Méndez, Vicenç Fedotov, Sergei Horsthemke, Werner Reaction-transport systems mesoscopic foundations, fronts, and spatial instabilities Turing-System (DE-588)4814930-5 gnd Anomale Diffusion (DE-588)4532384-7 gnd Inhomogenes Medium (DE-588)4228459-4 gnd Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd Mesoskopisches System (DE-588)4280799-2 gnd |
| subject_GND | (DE-588)4814930-5 (DE-588)4532384-7 (DE-588)4228459-4 (DE-588)4323967-5 (DE-588)4280799-2 |
| title | Reaction-transport systems mesoscopic foundations, fronts, and spatial instabilities |
| title_auth | Reaction-transport systems mesoscopic foundations, fronts, and spatial instabilities |
| title_exact_search | Reaction-transport systems mesoscopic foundations, fronts, and spatial instabilities |
| title_full | Reaction-transport systems mesoscopic foundations, fronts, and spatial instabilities Vicenç Méndez ; Sergei Fedotov ; Werner Horsthemke |
| title_fullStr | Reaction-transport systems mesoscopic foundations, fronts, and spatial instabilities Vicenç Méndez ; Sergei Fedotov ; Werner Horsthemke |
| title_full_unstemmed | Reaction-transport systems mesoscopic foundations, fronts, and spatial instabilities Vicenç Méndez ; Sergei Fedotov ; Werner Horsthemke |
| title_short | Reaction-transport systems |
| title_sort | reaction transport systems mesoscopic foundations fronts and spatial instabilities |
| title_sub | mesoscopic foundations, fronts, and spatial instabilities |
| topic | Turing-System (DE-588)4814930-5 gnd Anomale Diffusion (DE-588)4532384-7 gnd Inhomogenes Medium (DE-588)4228459-4 gnd Reaktions-Diffusionsgleichung (DE-588)4323967-5 gnd Mesoskopisches System (DE-588)4280799-2 gnd |
| topic_facet | Turing-System Anomale Diffusion Inhomogenes Medium Reaktions-Diffusionsgleichung Mesoskopisches System |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3493230&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029386496&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT mendezvicenc reactiontransportsystemsmesoscopicfoundationsfrontsandspatialinstabilities AT fedotovsergei reactiontransportsystemsmesoscopicfoundationsfrontsandspatialinstabilities AT horsthemkewerner reactiontransportsystemsmesoscopicfoundationsfrontsandspatialinstabilities |