Based on some known loop algebras with finite dimensions, two different negative-order integrable couplings of the negative-order Korteweg-de Vries (KdV) hierarchy of evolution equations are generated by making use of the Tu scheme, from which the corresponding negative-order integrable couplings of the negative-order KdV equations are followed to be obtained. The resulting Hamiltonian structure of one negative integrable coupling is
derived from the variational identity.

Binlu Feng

Yufeng Zhang

Two Kinds of New Integrable Couplings of the Negative-Order Korteweg-de Vries Equation

Magnetic particle imaging (MPI) is a quantitative method for determining the spatial distribution of magnetic nanoparticles, which can be used as tracers for cardiovascular imaging. For reconstructing a spatial map of the particle distribution, the system matrix describing the magnetic particle imaging equation has to be known. Due to the complex dynamic behavior of the magnetic particles, the system matrix is commonly measured in a calibration procedure. In order to speed up the reconstruction process, recently, a matrix compression technique has been proposed that makes use of a basis transformation in order to compress the MPI system matrix. By thresholding the resulting matrix and storing the remaining entries in compressed row storage format, only a fraction of the data has to be processed when reconstructing the particle distribution. In the present work, it is shown that the image quality of the algorithm can be considerably improved by using a local threshold for each matrix row instead of a global threshold for the entire system matrix.

T. Knopp

A. Weber

Local System Matrix Compression for Efficient Reconstruction in Magnetic Particle Imaging

We investigate properties of algorithms that are used to solve coupled evolutionary partial differential equations posed on neighboring, nonoverlapping domains, where the solutions are coupled by continuity of state and normal flux through a shared boundary. The algorithms considered are based on the widely used approach of iteratively exchanging boundary condition data on the shared boundary at each time step. There exists a significant and sophisticated numerical analysis of such methods. However, computations for practical applications are often carried out under conditions under which it is unclear if rigorous results apply while relatively few iterations are used per time step. To examine this situation, we derive exact matrix expressions for the propagation of the error due to incomplete iteration that can be readily evaluated for specific discretization parameters. Using the formulas, we show that the universal validity of several tenants of the practitioner&#x2019;s conventional wisdom are not universally valid.

B. Sheehan

D. Estep

S. Tavener

J. Cary

S. Kruger

A. Hakim

A. Pletzer

J. Carlsson

S. Vadlamani

The Interaction of Iteration Error and Stability for Linear Partial Differential Equations Coupled through an Interface

We consider the Thomas-Fermi-Dirac-von Weizs&#xe4;cker equation <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.3616pt" id="M1" height="14.4397pt" version="1.1" viewBox="-0.0498162 -12.0781 165.674 14.4397" width="165.674pt"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path id="g117-33" d="M535 230V280H52V230H535Z"/></g><g transform="matrix(.0135,0,0,-0.0135,7.953,0)"><path id="g113-133" d="M600 0V24L339 665L311 657L43 24V0H600ZM497 50H107L303 539L497 50Z"/></g><g transform="matrix(.0135,0,0,-0.0135,16.631,0)"><path id="g113-118" d="M515 96L502 119C471 88 431 62 423 62C416 62 411 70 417 101C440 223 469 341 497 448H486L412 422L380 277C330 188 210 57 152 57C137 57 126 69 139 124L195 366C210 431 205 448 182 448C155 448 89 413 23 350L36 326C73 354 103 376 112 376C118 376 118 365 113 340L61 118C54 90 52 68 52 51C52 0 75 -12 98 -12S151 -3 181 17C242 58 305 119 362 193H364L345 104C323 3 339 -12 359 -12C390 -12 464 35 515 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12.5699" width="51.7303pt"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path id="g113-107" d="M394 607C394 634 378 655 350 655C315 655 294 620 294 594C294 564 314 546 339 546C372 546 394 574 394 607ZM360 349C373 414 374 448 351 448C321 448 249 404 183 338L197 313C223 336 265 367 276 367C285 367 283 355 275 313C241 129 220 23 189 -102C175 -158 153 -197 124 -197C106 -197 85 -187 70 -177C64 -173 51 -177 44 -183C34 -193 23 -209 23 -228C23 -244 46 -261 67 -261C86 -261 127 -245 181 -197C237 -147 279 -52 303 66L360 349Z"/></g><g transform="matrix(.0135,0,0,-0.0135,9.517,0)"><path id="g117-34" d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"/></g><g transform="matrix(.0135,0,0,-0.0135,21.255,0)"><use xlink:href="#g113-50"/></g><g transform="matrix(.0135,0,0,-0.0135,27.758,0)"><path id="g113-45" d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"/></g><g transform="matrix(.0135,0,0,-0.0135,33.118,0)"><use xlink:href="#g113-51"/></g><g transform="matrix(.0135,0,0,-0.0135,39.621,0)"><use xlink:href="#g113-45"/></g><g transform="matrix(.0135,0,0,-0.0135,44.981,0)"><path id="g113-52" d="M285 378C315 398 338 416 353 432C373 451 384 474 384 503C384 579 325 635 236 635H235C182 635 136 610 108 579L65 516L85 496C110 533 150 575 205 575C258 575 300 543 300 481C300 407 232 369 141 339L147 310C163 315 188 321 211 321C268 321 338 284 338 192C338 94 288 40 217 40C160 40 119 68 93 91C85 98 77 97 69 91C60 84 47 71 46 58C44 46 48 35 62 22C75 10 116 -12 162 -12C234 -12 424 62 424 224C424 297 373 359 285 376V378Z"/></g></svg>, and 0 is in a spectral gap of the operator <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.3625803pt" id="M9" height="9.36053pt" version="1.1" viewBox="-0.0498162 -8.99795 40.4795 9.36053" width="40.4795pt"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><use xlink:href="#g117-33"/></g><g transform="matrix(.0135,0,0,-0.0135,7.953,0)"><use xlink:href="#g113-133"/></g><g transform="matrix(.0135,0,0,-0.0135,19.659,0)"><use xlink:href="#g117-36"/></g><g transform="matrix(.0135,0,0,-0.0135,30.64,0)"><use xlink:href="#g113-87"/></g></svg>. Using a new infinite-dimensional linking theorem, we prove that, for sufficiently small <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.6617994pt" id="M10" height="10.3397pt" version="1.1" viewBox="-0.0498162 -9.6779 29.6864 10.3397" width="29.6864pt"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><use xlink:href="#g113-233"/></g><g transform="matrix(.0135,0,0,-0.0135,11.261,0)"><use xlink:href="#g117-92"/></g><g transform="matrix(.0135,0,0,-0.0135,22.999,0)"><use xlink:href="#g113-49"/></g></svg>, this equation has a nontrivial solution.

Shaowei Chen

Lishan Lin

Liqin Xiao

Existence Results for the Periodic Thomas-Fermi-Dirac-von Weizs&#xe4;cker Equations

The main goal of this work is to explore the symmetries and develop the dynamics associated with a 3D Abelian <i>BF</i> model coupled to scalar fields submitted to a sigma model like constraint, at the classical and quantum levels. Background independence, on which the model is founded, strongly constrains its nature. We adapt to the present model the techniques of Loop Quantum Gravity in order to construct its physical Hilbert space and its observables.

Diego C. M. Mendon&#xe7;a

Olivier Piguet

Loop Quantization of a 3D Abelian <i>BF</i> Model with <i>&#x3c3;</i>-Model Matter

This paper defines the concepts of region representative vehicle and driver and region representative safe driving awareness and its heterogeneity, and, based on these concepts and a new car-following model proposed, it proposes a new continuum model for traffic flow considering region representative safe driving awareness heterogeneity. Analyses show that the new continuum model follows traffic flow anisotropy principle, and the following insights can be gotten: (1) the bigger the difference of the preceding region representative safe driving awareness coefficient minus the following region representative safe driving awareness coefficient is, the less the probability of the wrong-way travel (the negative velocity) problem in the new continuum model is; (2) when the preceding region representative safe driving awareness coefficient is not less than the following region representative safe driving awareness coefficient, there is no wrong-way travel problem in the new continuum model, and vice versa.

Youzhi Zeng

Ning Zhang

Continuum Model for Traffic Flow considering Safe Driving Awareness Heterogeneity

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<p><em>Advances in Mathematical Physics</em> publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches.</p>


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<p>Chief Editor, Prof Di Matteo (Department of Mathematics, King’s College London), engages in world-leading multidisciplinary and data-driven research focussed on the analysis of complex data from the perspective of a statistical physicist.</p>


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Advances in Mathematical Physics - Table of contents 2015

Advances in Mathematical Physics | Hindawi

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Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches.

Advances in Mathematical Physics