Applied and industrial mathematics in Italy III

CONTENTS......Page 10
Preface......Page 8
1. Introduction......Page 16
2. Multichannel MultiResolution Analysis and Multichannel Wavelet......Page 18
3. Experimental Results......Page 20
References......Page 26
1. Introduction......Page 28
2.1. Dirichlet problem......Page 29
2.2. Neumann problem......Page 31
3. Galerkin BEM discretization......Page 32
4. Numerical results......Page 34
References......Page 39
1. Introduction......Page 40
2.1. General Equations......Page 41
2.1.1. Treatment of the Coupling Term......Page 42
2.2. Solution of the Reactor Inventory Equations......Page 44
2.2.1. Solution by Laplace Transform......Page 45
2.2.2. Evaluation of the Precoe cients A......Page 46
2.3.2. Description of the Model......Page 47
3. Computer Implementation and Discussion of Results......Page 50
4. Conclusions......Page 51
References......Page 53
1. Introduction......Page 54
3. Mathematical Modeling......Page 55
3.1.1. CMM Measurement Errors......Page 56
3.2.1. Probe Head Errors......Page 57
3.4.1. Qualification Process Modeling......Page 58
3.4.2. Qualification Parameters Optimization......Page 61
4. Numerical Solution of Qualification Equations......Page 62
Acknowledgements......Page 64
References......Page 65
1. Introduction......Page 66
2. Basic Concepts......Page 68
3. Retarded Weighted Tra c Equilibrium Problem......Page 70
4. Existence of Equilibria......Page 73
5. Regularity of Equilibria......Page 74
References......Page 76
1. Introduction......Page 77
2. Equations governing the description of viscous-elastic field of vortices in the type-II superconductors......Page 80
3. A geometric model for type-II high-Tc superconductors......Page 83
References......Page 88
1. Introduction......Page 90
2. Evolution equations......Page 91
3. Well posedness of the problem......Page 96
References......Page 101
1. Introduction......Page 102
2. The method......Page 105
3. Convergence analysis......Page 108
4. Numerical experiments......Page 111
References......Page 113
1. Introduction......Page 114
2.1. Deformable Models: Snake......Page 116
3. Analysis of geometrical parameters and results......Page 117
3.2. Cluster analysis with 1-Pearson r......Page 120
4.1. Complete Linkage with 1-Pearson r......Page 121
4.4. Single Linkage with Euclidean distances......Page 122
4.5. Ward’s method with 1-Pearson r......Page 123
References......Page 124
1. Introduction.......Page 126
2. Buffon\'s type solutions and 2D raster classification applications for circles.......Page 127
3. Buffon\'s type solutions and 3D raster classification applications for spheres.......Page 129
References......Page 137
1. Introduction.......Page 138
2. Functional setting and notation.......Page 142
3. Global existence result.......Page 143
4. Exponential decay.......Page 146
References......Page 148
1. Introduction......Page 149
2. The MEG Inverse Problem......Page 150
3. A Joint Sparsity Constraint for the MEG Inverse Problem......Page 152
4. An Iterative Thresholding Algorithm for the MEG Inverse Problem......Page 154
5. Numerical Tests......Page 156
References......Page 160
No Sampling Linear Sampling for 3D Inverse Scattering Problems M. Brignone, R. Aramini, G. Bozza and M. Piana......Page 161
1. Introduction......Page 162
2. The linear sampling method......Page 163
3. The no-sampling approach......Page 166
4. Numerical results......Page 167
5. Conclusions......Page 168
References......Page 170
1. Introduction......Page 171
2. Analysis of extrema......Page 174
3. A test of serial independence......Page 176
5. Conclusions......Page 177
References......Page 178
1. Introduction.......Page 180
2. Scale irregular Koch curves......Page 182
3. Scale irregular fractal case......Page 184
4. Prefractal case......Page 185
References......Page 188
1. Introduction......Page 190
2. B acklund Transformations: background notions......Page 192
3. Operator Soliton Equations......Page 194
4. Burgers - Heat Operator B acklund Chart......Page 197
Acknowledgements......Page 198
References......Page 199
1. Introduction......Page 201
2. Liquid Penetrant Inspection......Page 202
3. General settings......Page 203
4. Alenia Aeronautics Approach......Page 204
4.1. PoD and process sensibility......Page 205
4.2. Standards manufacturing......Page 206
4.3. PoD and process sensibility determination......Page 207
4.4. A case study......Page 209
References......Page 210
1. Introduction......Page 211
2.1. Derivation of the scalar wave equations......Page 212
3. Integral-equation formulations......Page 214
4. Existence and uniqueness of ~ E......Page 215
5. Jump conditions......Page 217
6. Reflection-transmission of TE waves......Page 218
7.1. Uniform layer......Page 219
7.2. Low frequencies......Page 220
References......Page 221
1. Introduction......Page 223
2. The Blume–Capel model......Page 225
3. Probabilistic cellular automata with self–interaction......Page 232
References......Page 234
Mathematical Models for Bio lms on the Surface of Monuments F. Clarelli, C. Di Russo, R. Natalini and M. Ribot......Page 235
2.1. Previous models.......Page 236
2.2. The new hydrodynamical model.......Page 238
2.3. Inuence of light, temperature and nutrients.......Page 241
2.3.2. Temperature dependence......Page 242
3. Numerical approximation and simulations.......Page 243
Acknowledgements.......Page 245
References......Page 246
1. Introduction......Page 247
2. A mathematical model for consolidation of building stones......Page 248
3. Fitting the model with the experiments......Page 251
3.2. Fitting the function B......Page 253
4. Numerical tests for the consolidation model......Page 254
References......Page 258
1. Introduction......Page 259
2. Analytical Results......Page 260
3. Passing through a Toll Gate......Page 264
4. Pedestrian Evacuation and Braess Paradox......Page 266
References......Page 269
1. Introduction......Page 271
2. Statement of the problem......Page 274
3. Previous results......Page 277
4. Regularity and weak solutions......Page 280
References......Page 281
1. Introduction......Page 283
2. Construction of the methods and order conditions......Page 284
3. Linear stability analysis......Page 287
4. Examples of methods......Page 289
References......Page 290
1. Introduction......Page 293
2. General two–step collocation methods......Page 295
3. Order conditions......Page 296
4. Linear stability analysis......Page 298
5. Examples of methods......Page 299
6. Numerical evidences......Page 300
7. Conclusions and future work......Page 301
References......Page 302
1. Introduction......Page 304
2. The general linear interpolation problem......Page 305
3. The method......Page 306
4. Global error......Page 307
5. The numerical algorithm and numerical comparison......Page 308
References......Page 312
1. Introduction......Page 313
2. Mathematical models for blood ow and drug release......Page 314
2.1. Blood flow models......Page 315
2.2. Reduced 1D-3D models for drug release by thin DES......Page 316
3.1. Coupled fluid-dynamics......Page 318
3.2. Coupled mass transport......Page 321
4. Numerical results......Page 323
Acknowledgements......Page 324
References......Page 325
1. Introduction......Page 326
2. Equations of the model......Page 327
3. Stability analysis of the \"limiting system\"......Page 333
4. Comparison between numerical solution and stability analysis......Page 335
Acknowledgments......Page 336
References......Page 337
1. Introduction and Motivation......Page 338
1.1. Filippov sliding modes......Page 339
1.2. Utkin sliding modes......Page 340
2. Reinterpretation......Page 342
References......Page 345
1. Introduction......Page 346
2. Translation of the independent variable......Page 348
2.1. Length estimation for tubular ow reactors......Page 349
3. Translation of the dependent variable......Page 351
3.1. An application to a parachute model......Page 352
4. Conclusion......Page 353
References......Page 355
1. Introduction......Page 356
2. Mathematical modeling......Page 357
3. Extended scaling invariance......Page 358
4.1. The viscous case......Page 359
4.2. The case of approximately invariant parameters......Page 361
4.3. The classical scaling invariance strategy......Page 365
4.4. Numerical method and adaptive criteria......Page 366
References......Page 367
1. Introduction......Page 368
2. Ill and Well-Posed One-Dimensional Models......Page 369
3. Academic test case......Page 371
3.2. Budd and Huang asymptotic analysis......Page 372
4. Validation of numerical results......Page 373
5. Numerical method and adaptive procedure......Page 376
References......Page 379
1. Introduction......Page 380
2. A non conventional model for piezoelectric crystals with dislocations......Page 383
3. Clausius-Duhem inequality analysis and heat equation......Page 387
References......Page 390
1. The problem......Page 392
2. The monotone structure......Page 395
3. The representation of......Page 396
4. The V -problem......Page 398
5. Existence and uniqueness of solutions......Page 399
6. Outline of the proofs......Page 401
References......Page 403
Numerical Simulation of Capillary Flows through Molecular Dynamics S. Iacono......Page 404
1. Continuous model......Page 405
2. Molecular Dynamics model......Page 406
3. Numerical methods......Page 408
4. Capillary ows MD simulation......Page 409
5. Results......Page 410
6. Conclusions......Page 412
References......Page 415
1. Introduction......Page 416
2. Material symmetries for  ber-reinforced materials: Rychlewski\'s theorem......Page 417
3. Four basic structures for surfaces formed by two families of yarns......Page 420
4. Application to a  bered surface with bending stiffness......Page 422
5. Discussion......Page 424
Acknowledgements......Page 425
References......Page 426
1. Introduction......Page 428
2. Kinetic Transport Model......Page 429
3. Numerical Approach......Page 432
4. Results......Page 434
References......Page 438
1. Introduction......Page 440
2. Mathematical model of dissolution......Page 442
3. Mathematical model of dissolution and surface erosion......Page 445
4. Numerical method......Page 446
5. Results and Discussion......Page 447
References......Page 451
1. Introduction......Page 452
2.1. Microscopic description of Fns and T......Page 455
2.2. Mutual friction and vortex tension in the HVBK model......Page 456
2.3. Limit of validity of HVBK\'s equations......Page 457
2.4. Generalized expressions for Fns and T......Page 458
2.5. Application to counter flow in rotation......Page 459
3.1. Onsager-Casimir reciprocity relation......Page 460
4. Conclusions......Page 461
References......Page 462
1. Introduction.......Page 464
2. Carbon nanotubes and chirality......Page 465
3.1. Lattice modeling......Page 466
3.2. Empiric potential......Page 468
3.3. The atomic{scale  nite element method......Page 469
4.1. Diameters and Lengths at the Energy Ground......Page 470
4.2. Young\'s Modulus......Page 471
4.3. Poisson\'s Ratio and Shear modulus......Page 472
References......Page 474
1. Introduction......Page 476
2. Code design......Page 478
References......Page 487
1. Introduction......Page 488
2. Formulation of ULBE method......Page 490
3. ULBE for Non-Newtonian .ows......Page 492
4. Flow through a stenosed vessel......Page 493
5. Results and discussion......Page 496
References......Page 498
1. Introduction......Page 500
2. A non conventional model for porous solids filled by fluid flow......Page 502
3. Balance and evolution equations......Page 504
4. Entropy inequality analysis......Page 506
5. Constitutive theory......Page 507
References......Page 510
1. Introduction......Page 511
2. Schwarz function dynamics......Page 513
4. An integral approach to vortex dynamics......Page 514
5. Application to the sample vortices......Page 515
6. Conclusions and future work......Page 518
Appendix A. Kinematics of vortices having Schwarz functions with two simple poles......Page 519
Appendix B. First integrals of motion......Page 520
References......Page 522
1. Introduction......Page 523
2. Problem definition......Page 524
3. Reduced basis method......Page 525
4. Lower bounds for the coercivity constant......Page 526
5. A posteriori error estimation......Page 527
5.1. Offline-online computational procedures......Page 528
6.1. Bulb and keel......Page 529
6.2. A more complex example: several parametrized bodies......Page 532
References......Page 534
1. Introduction......Page 535
2. Preliminaries......Page 537
3. Approximation of surfaces and their support functions......Page 538
3.1. Quadratic spline approximation......Page 540
3.2. Support function approximation......Page 541
4. Curvature-dependent sampling......Page 542
4.1. The curve case......Page 543
5. Conclusion......Page 544
References......Page 545
1. Introduction......Page 547
2.1. Deformation model......Page 548
2.2. Thermal model......Page 550
2.3. Discussion and conclusions......Page 554
References......Page 555
1. Introduction......Page 557
2. Walrasian price equilibrium problem......Page 558
2.1. Existence results......Page 559
2.3. Sensitivity analysis......Page 560
3. Qualitative analysis: Parametric variational approach......Page 561
3.1. Existence and uniqueness results......Page 562
3.2. Parametric sensitivity analysis......Page 563
4. Example......Page 564
References......Page 567
1. Introduction......Page 569
2. A stratified fluid model......Page 570
3. Modeling generation and expulsion of hydrocarbons......Page 574
References......Page 579
1. Introduction......Page 581
2. The model......Page 582
2.1. The Lattice Boltzmann scheme and the calculation of the forcing term......Page 583
2.2. Numerical implementation of the convection-di usion equation......Page 585
3. Results and discussion......Page 586
4. Conclusions......Page 588
References......Page 589