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A TWO-WAY COUPLED MODEL OF VISCO-THERMO-ACOUSTIC EFFECTS IN PHOTOACOUSTIC TRACE GAS SENSORS
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| Pengarang | : | Mozumder, Ali,Safin, Artur,Minkoff, Susan E.,Zweck, John |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 3) |
| Halaman | : | 1074-1097 |
| Abstrak | : | We introduce the first two-way coupled model for the thermo-viscous damping of a mechanical structure (such as quartz tuning fork) that is forced by the weak acoustic and thermal waves generated when a laser source periodically interacts with a trace gas. The model is based on a Helmholtz system of thermo-visco-acoustic equations in the fluid, together with a system of equations for the temperature and the displacement of the structure. These two subsystems are coupled across the fluid-structure interface via several conditions. With this model, the user specifies the geometry of the structure and the viscous and thermal parameters of the fluid, and the model outputs an effective damping parameter and a signal strength that is proportional to the concentration of the trace gas. This new model is a significant improvement over existing one-way coupled models in which damping effects are incorporated via a priori laboratory measurements. Analytical solutions derived for an annular structure show reasonable agreement between the one-way and two-way coupled models at higher ambient pressures. However, at low ambient pressure the one-way coupled model does not adequately capture thermo-viscous effects. |
LOCALIZATION OF MOVING SOURCES: UNIQUENESS, STABILITY, AND BAYESIAN INFERENCE
| Pengarang | : | Suhada, Hendrata |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 3) |
| Halaman | : | 1049-1073 |
| Abstrak | : | We consider the subsonic moving point source problem for the scalar wave equation in \bfitR 3, proving a regularity result for the direct problem and uniqueness and stability results for the inverse problem. We then present and investigate numerically a Bayesian framework for the inference of the source trajectory and intensity from wave field measurements. The framework employs Gaussian process priors, the preconditioned Crank-Nicolson scheme with Markov chain Monte Carlo sampling, and conditioning on functionals to include prior information on the source trajectory |
COMPUTATIONAL TRANSLATION FRAMEWORK IDENTIFIES BIOCHEMICAL REACTION NETWORKS WITH SPECIAL TOPOLOGIES AND THEIR LONG-TERM DYNAMICS
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 3) |
| Halaman | : | 1025-1048 |
| Abstrak | : | Long-term behaviors of biochemical systems are described by steady states in deter ministic models and stationary distributions in stochastic models. Obtaining their analytic solutions can be done for limited cases, such as linear or finite-state systems, as it generally requires solving many coupled equations. Interestingly, analytic solutions can be easily obtained when underlying networks have special topologies, called weak reversibility (WR) and zero deficiency (ZD), and the kinetic law follows a generalized form of mass-action kinetics. However, such desired topological conditions do not hold for the majority of cases. Thus, translating networks to have WR and ZD while preserving the original dynamics was proposed. Yet, this approach is limited because manu ally obtaining the desired network translation among the large number of candidates is challenging. Here, we prove necessary conditions for having WR and ZD after translation, and based on these conditions, we develop a user-friendly computational package, TOWARDZ, that automatically and efficiently identifies translated networks with WR and ZD. This allows us to quantitatively examine how likely it is to obtain WR and ZD after translation depending on the number of species and reac tions. Importantly, we also describe how our package can be used to analytically derive steady states of deterministic models and stationary distributions of stochastic models. TOWARDZ provides an effective tool to analyze biochemical systems |
DENSITY FLUCTUATIONS IN STOCHASTIC KINEMATIC FLOWS
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 3) |
| Halaman | : | 1000-1024 |
| Abstrak | : | At the macroscopic scale, many important models of collective motion fall into the class of kinematic flows for which both velocity and diffusion terms depend only on particle density. When total particle numbers are fixed and finite, simulations of corresponding microscopic dynamics exhibit stochastic effects which can induce a variety of interesting behaviors not present in the large system limit. In this article we undertake a systematic examination of finite-size fluctuations in a general class of particle models whose statistics correspond to those of stochastic kinematic flows. Doing so, we are able to characterize phenomena including quasi-jams in models of traffic flow; stochastic pattern formation among spatially coupled oscillators; anomalous bulk subdiffusion in porous media; and travelling wave fluctuations in a model of bacterial swarming. |
ON THE OPTIMAL CONDUCTIVITY OF PACKED TWO-DIMENSIONAL DISPERSED COMPOSITES
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 3) |
| Halaman | : | 985-999 |
| Abstrak | : | Optimal packing is applied in physics for investigation of macroscopic properties of composites and porous media. The present paper demonstrates that the optimal packing of perfectly conducting disks on the plane corresponds to the minimal effective conductivity for macroscopically isotropic composites. Such an optimal location is studied and compared to the pure geometric problem for N \leq 8 disks packing on the flat torus. The hexagonal (triangular) array of disks solves the problem for the triangle lattice numbers N =1,3,4,7,.... The rest of the cases N =2,5,6,8 are investigated separately by minimization of structural sums constructed by means of the Eisenstein functions. |
GENERALIZED SCHWARZ INTEGRAL FORMULAS FOR MULTIPLY CONNECTED DOMAINS
| Pengarang | : | Miyoshi, Hiroyuki,Crowdy, Darren G. |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 3) |
| Halaman | : | 966-984 |
| Abstrak | : | A generalization of the Schwarz integral formula in the class of multiply connected circular domains is constructed. A classical Schwarz integral formula retrieves, up to an imaginary constant, an analytic function in a domain given its real part on the boundary of a domain; Poisson integral formulas are well-known examples for simply connected domains. The generalized integral formulas derived here retrieve an analytic function given more general linear combinations of its real and imaginary parts on each boundary component of a multiply connected domain. Those linear combinations can be different on each boundary component. The chief mathematical tool is the prime function of a multiply connected circular domain. A Schwarz integral formula for such domains, retrieving an analytic function given its real part on all boundary components, was derived in terms of the prime function by Crowdy [Complex Var. Elliptic Equ., 53 (2008), pp. 221-236]. The present paper combines those formulas with use of radial-slit conformal mappings, also expressible in terms of the prime function, to produce integral expressions for analytic functions where more general linear combinations of their real and imaginary parts are specified on the boundary components of a multiply connected domain. We refer to the resulting expressions as generalized Schwarz integral formulas. Their usefulness and versatility are showcased by application to three topical problems: f inding the potential around periodic interdigitated electrodes, solving the free boundary problem for hollow vortex wakes behind a bluff body, and determining the two-phase flow over a so-called liquid-infused surface. |
NONLINEAR SHALLOW-WATER WAVES WITH VERTICAL ODD VISCOSITY
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 3) |
| Halaman | : | 938-965 |
| Abstrak | : | The breaking of a detailed balance in fluids through Coriolis forces or odd-viscous stresses has profound effects on the dynamics of surface waves. Here we explore both weakly and strongly nonlinear waves in a three-dimensional fluid with vertical odd viscosity with and without the Coriolis effect. Our model describes the free surface of a shallow fluid composed of nearly vertical vortex filaments, which all stand perpendicular to the surface. We find that the odd viscosity in this configuration induces previously unexplored nonlinear effects in shallow-water waves, arising from both stresses on the surface and stress gradients in the bulk. By assuming weak nonlinearity, we find reduced equations including Korteweg-de Vries, Ostrovsky, and Kadomtsev-Petviashvilli equations with modified coefficients. At sufficiently large odd viscosity, the dispersion changes sign, allowing for compact two-dimensional solitary waves. We show that odd viscosity and surface tension have the same effect on the free surface, but distinct signatures in the fluid flow. Our results describe the collective dynamics of many-vortex systems, which can also occur in oceanic and atmospheric geophysics. |
"MAYORITAS TUNGGAL, TIDAK BOLEH"
| Pengarang | : | Theo Syafei |
| Nama Majalah/Jurnal | : | Bina Darma |
| Volume / Edisi | : | 14-53 (No. 53) |
| Halaman | : | 59-65 |
| Abstrak | : | - |
DISSIPATION OF TRAFFIC JAMS USING A SINGLE AUTONOMOUS VEHICLE ON A RING ROAD
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 3) |
| Halaman | : | 909-937 |
| Abstrak | : | In this article, we study the problem of stabilizing the traffic flow on a ring road to a uniform steady-state using autonomous vehicles (AV). Traffic is represented at a microscopic level via a Bando-Follow-the-Leader model capable of reproducing phantom jams. For the single-lane case, a single AV can stabilize an arbitrary large ring road with an arbitrary large number of cars. Moreover, this stabilization is exponentially quick with a decay rate independent of the number of cars and a control gain also independent of the number of cars. On the other side, the stabilization domain and stabilization time depend on the number of cars. Two types of controller algorithms are proposed: a proportional control and a proportional-integral control. In both cases, the measurements used by the controller only depend on the local data around the AV, enabling an easy implementation. After numerical tests of the single-lane case, a multilane model is described using a safety-incentive mechanism for lane change. Numerical simulations for the multilane ring road suggest that the control strategy is also very efficient in such a setting, even with a single AV. |
"KENAPA TIDAK MEMAKAI KOMBINASI YANG IMBANG?"
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Bina Darma |
| Volume / Edisi | : | 14-53 (No. 53) |
| Halaman | : | 40-49 |
| Abstrak | : | - |