Simulating Nonhomogeneous Non-Gaussian Field by Using Iterative Rank-Dependent Reordering versus Translation Process-Based Procedure

<div>Comparison of the autocorrelation function for Cases 1 to 4 (<svg height="14.8173pt" id="M220" style="vertical-align:-5.52897pt" version="1.1" viewbox="-0.0498162 -9.28833 29.4928 14.8173" width="29.4928pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M290 -163V-135C183 -126 181 -122 181 -44V583C181 662 184 666 290 675V703H120V-163H290Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.485,0)"><path d="M625 186C574 85 512 32 429 32C293 32 194 153 194 337C194 485 274 621 419 621C496 621 573 586 606 468L643 475C636 537 629 583 620 638C593 644 519 665 438 665C199 665 42 523 42 317C42 158 152 -15 418 -15C486 -15 578 5 604 11C621 46 647 122 660 171L625 186Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,13.306,3.132)"><path d="M525 275C525 381 464 451 380 451C338 451 289 439 241 405C158 347 127 277 106 152C51 -168 37 -216 24 -242L28 -257C42 -256 92 -247 117 -222C126 -213 134 -193 150 -69L166 32C184 10 211 -12 245 -12C276 -12 332 8 384 46C458 100 525 176 525 275ZM436 260C436 131 366 41 267 41C246 41 208 51 175 82C181 125 187 162 195 200C220 322 257 400 328 400C398 400 436 338 436 260Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,18.304,3.132)"><path d="M679 650H432L424 619L456 615C499 610 507 601 486 568C442 499 366 400 315 336C281 403 229 526 211 570C199 600 202 610 239 614C239 614 281 618 281 619L288 650H33L24 619C98 612 106 606 129 552L226 325C238 297 238 282 234 259L211 136C193 42 184 38 97 32L86 0H375L382 32C285 39 277 45 296 136L324 267C329 290 337 304 350 322C420 416 479 489 523 539C582 607 595 613 668 619L679 650Z"></path></g><g transform="matrix(.013,0,0,-0.013,24.875,0)"><path d="M226 -163V703H56V676C162 667 165 662 165 584V-43C165 -122 162 -126 56 -136V-163H226Z"></path></g></svg> for Cases 2 and 4 is replaced by <span class="nowrap"><svg height="17.4597pt" id="M221" style="vertical-align:-5.528999pt" version="1.1" viewbox="-0.0498162 -11.9307 29.4928 17.4597" width="29.4928pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M290 -163V-135C183 -126 181 -122 181 -44V583C181 662 184 666 290 675V703H120V-163H290Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.602,-2.903)"><path d="M658 624L641 649C599 612 554 595 493 595C444 595 402 603 342 615C268 634 232 641 184 641C129 641 57 621 0 557L17 532C67 566 113 586 176 586C230 586 265 577 316 565C380 550 430 540 482 540C540 540 611 558 658 624Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.485,0)"><path d="M625 186C574 85 512 32 429 32C293 32 194 153 194 337C194 485 274 621 419 621C496 621 573 586 606 468L643 475C636 537 629 583 620 638C593 644 519 665 438 665C199 665 42 523 42 317C42 158 152 -15 418 -15C486 -15 578 5 604 11C621 46 647 122 660 171L625 186Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,13.306,3.132)"><path d="M525 275C525 381 464 451 380 451C338 451 289 439 241 405C158 347 127 277 106 152C51 -168 37 -216 24 -242L28 -257C42 -256 92 -247 117 -222C126 -213 134 -193 150 -69L166 32C184 10 211 -12 245 -12C276 -12 332 8 384 46C458 100 525 176 525 275ZM436 260C436 131 366 41 267 41C246 41 208 51 175 82C181 125 187 162 195 200C220 322 257 400 328 400C398 400 436 338 436 260Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,18.304,3.132)"><path d="M679 650H432L424 619L456 615C499 610 507 601 486 568C442 499 366 400 315 336C281 403 229 526 211 570C199 600 202 610 239 614C239 614 281 618 281 619L288 650H33L24 619C98 612 106 606 129 552L226 325C238 297 238 282 234 259L211 136C193 42 184 38 97 32L86 0H375L382 32C285 39 277 45 296 136L324 267C329 290 337 304 350 322C420 416 479 489 523 539C582 607 595 613 668 619L679 650Z"></path></g><g transform="matrix(.013,0,0,-0.013,24.875,0)"><path d="M226 -163V703H56V676C162 667 165 662 165 584V-43C165 -122 162 -126 56 -136V-163H226Z"></path></g></svg>).</span></div>

Mathematical Problems in Engineering

fig4

Figure 4

Figure 4: Simulating Nonhomogeneous Non-Gaussian Field by Using Iterative Rank-Dependent Reordering versus Translation Process-Based Procedure 