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AN ASYMPTOTIC MODEL FOR GAS-SOLID FLOW IN A COUNTERCURRENT MOVING BED REACTOR
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| Pengarang | : | Vynnycky, Michael,Rangavittal, Bharath V.,Glaser, Bjorn |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 2) |
| Halaman | : | 882-908 |
| Abstrak | : | Asymptotic methods are employed to analyze earlier two-phase steady-state Euler Euler models that were originally intended as simplified representations for gas-solid flow in an ironmaking blast furnace; more generally, however, they can be thought of as models for two-phase f low in countercurrent moving bed reactors. A scaling analysis, based around the fact that the solid velocity is typically several orders of magnitude smaller than the gas velocity, indicates that the effects of viscosity and inertia are basically negligible compared with those of gravity and interphase momentum transfer. The resulting reduced model yields quasi-analytical expressions for the solid fraction and the gas velocity, with the former being directly related to the shapes of the reactor and any stagnant zone that may form as a consequence of solids or granular materials being able to withstand substantial amounts of shear; in ironmaking blast furnaces, this occurs near the bottom of the reactor, and the zone is commonly known as the deadman. On the other hand, the solid velocity can be found via a numerical solution of Laplace's equation; nevertheless, the solution is different to that obtained from earlier potential flow models in blast furnace modeling. Most significantly, the current model would form the basis of a computationally efficient approach for modeling transient heat and mass transfer with chemical reactions in a countercurrent moving bed reactor. |
ACCUMULATION TIME OF DIFFUSION IN A 3D SINGULARLY PERTURBED DOMAIN
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 2) |
| Halaman | : | 862-881 |
| Abstrak | : | Boundary value problems for diffusion in singularly perturbed domains is a topic of considerable current interest. Applications include intracellular diffusive transport and the spread of pollutants or heat from localized sources. In a previous paper, we introduced a new method for characterizing the approach to steady state in the case of two-dimensional (2D) diffusion. This was based on a local measure of the relaxation rate known as the accumulation time T(x). The latter was calculated by solving the diffusion equation in Laplace space using a combination of matched asymptotics and Green's function methods. We thus obtained an asymptotic expansion of T(x) in powers of \nu = - 1/ln\epsilon , where \epsilon specifies the relative size of the holes. In this paper, we develop the corresponding theory for three-dimensional (3D) diffusion. The analysis is a nontrivial extension of the 2D case due to differences in the singular nature of the Laplace transformed Green's function. In particular, the asymptotic expansion of the solution of the 3D diffusion equation in Laplace space involves terms of order O((\epsilon /s)n), where s is the Laplace variable. These s-singularities have to be removed by partial series resummations in order to obtain an asymptotic expansion of T(x) in powers of \epsilon |
A ROUTE TO THE HYDRODYNAMIC LIMIT OF A REACTION-DIFFUSION MASTER EQUATION USING GRADIENT STRUCTURES
| Pengarang | : | Montefusco, Alberto,Schutte, Christof,Winkelmann, Stefanie |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 2) |
| Halaman | : | 837-861 |
| Abstrak | : | The reaction-diffusion master equation (RDME) is a lattice-based stochastic model for spatially resolved cellular processes. It is often interpreted as an approximation to spatially continuous reaction-diffusion models, which, in the limit of an infinitely large population, may be described by means of reaction-diffusion partial differential equations. Analyzing and understanding the relation between different mathematical models for reaction-diffusion dynamics is a research topic of steady interest. In this work, we explore a route to the hydrodynamic limit of the RDME which uses gradient structures. Specifically, we elaborate on a method introduced in [J. Maas and A. Mielke, J. Stat. Phys., 181 (2020), pp. 2257-2303] in the context of well-mixed reaction networks by showing that, once it is complemented with an appropriate limit procedure, it can be applied to spatially extended systems with diffusion. Under the assumption of detailed balance, we write down a gradient structure for the RDME and use the method in order to produce a gradient structure for its hydrodynamic limit, namely, for the corresponding RDPDE. |
PEMBANGUNAN EKONOMI DI PEDESAAN: MENCARI SUATU POLA YANG TEPAT
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Bina Darma |
| Volume / Edisi | : | 13-51 (No. 51) |
| Halaman | : | 98-112 |
| Abstrak | : | - |
NORMAL FORMS, DIFFERENTIABLE CONJUGACIES, AND ELEMENTARY BIFURCATIONS OF MAPS
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 2) |
| Halaman | : | 816-836 |
| Abstrak | : | Westrengthen the standard bifurcation theorems for saddle-node, transcritical, pitch fork, and period-doubling bifurcations of maps. Our new formulation involves adding one or two extra terms to the standard truncated normal forms with coefficients determined by algebraic equations. These extended normal forms are differentiably conjugate to the original maps on basins of attrac tion and repulsion of fixed points or periodic orbits. This reflects common assumptions about the additional information in normal forms despite standard bifurcation theorems being formulated only in terms of topological equivalence. |
GEREJA DAN KEGIATAN EKONOMI-BISNIS: PERLU DAN BOLEHKAH?
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Bina Darma |
| Volume / Edisi | : | 13-51 (No. 51) |
| Halaman | : | 86-97 |
| Abstrak | : | - |
WHYINCREASE OF HETEROGENEITY SIGNALS PRE-DETERIORATION DURING TUMOR PROGRESSION: A UNIFIED MATHEMATICAL MODEL
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 2) |
| Halaman | : | 791-815 |
| Abstrak | : | Heterogeneity plays an important role in cancer genesis and progression. In this paper, we theoretically and computationally show that the increase of heterogeneity signals prede terioration during tumor progression by unified random ordinary differential equations (RODEs). Tumor formation results from a systematic change in organisms, and its causality is complex. Het erogeneity may be one of the key factors under some conditions. Specifically, the interactions between cell populations are modeled by random community matrices in normal tissues, benign tumors, and malignant tumors, and then we prove that the RODEs system describing the cell density of normal tissues or benign tumors becomes unstable as heterogeneity of cell populations or species increases. The increase of heterogeneity is an important signal. Heterogeneity can be viewed as a feature to dis tinguish benign tumors from malignant tumors under certain circumstances. Furthermore, we show that with the increase of heterogeneity, the divergence speed of the RODEs system becomes faster, which implies that malignant tumors with higher heterogeneity may develop faster and have poorer prognoses. Our theoretical findings can explain some noteworthy phenomena in various datasets in tumor patients and our biological experiments in mice from a mathematical viewpoint. Particularly, clinical data and mutation information from the cancer genome atlas and our experiments in mice revealed that tumors with higher heterogeneity usually show shorter survival time, whereas tumors with lower heterogeneity tend to have better prognosis, which also indicates that heterogeneity can be used as a potential biomarker in future clinical diagnosis. Targeting the heterogeneity may be a potential strategy for the cancer treatment. |
MENCARI FORMAT KETERLIBATAN SOSIAL GENERASI MUDA KRISTEN INDONESIA
| Pengarang | : | Saptono |
| Nama Majalah/Jurnal | : | Bina Darma |
| Volume / Edisi | : | 13-51 (No. 51) |
| Halaman | : | 77-85 |
| Abstrak | : | - |
SOME ELECTRIC, THERMAL, AND THERMOELECTRIC PROPERTIES OF SUSPENDED MONOLAYER GRAPHENE
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 2) |
| Halaman | : | 770-790 |
| Abstrak | : | In this paper we investigate some electric, thermal, and thermoelectric properties of suspended monolayer graphene. By means of a numerical experiment, which was made employing a previously developed macroscopic model for charge and energy transport in graphene, we analyze how fast a suspended graphene sheet heats up when it is subject to a constant homogeneous electric field and how it reaches the equilibrium state once the electric field is turned off. We consider electrons and all phonon branches and show that the influence of the out-of-plane acoustical phonons on the f inal equilibrium temperature is notable due to their great surface heat capacity. The influence of the electrons on the equilibrium temperature depends on their density; in fact the higher it is, the more energy they gain from the electric field. The behavior of the system can be theoretically justified on the basis of two important physical properties: the conservation of the total energy and the increase of the total entropy of the electron-phonon system; of the latter we give an almost explicit expression. After that, we study the electronic thermal and electric conductivity and the thermopower by finding formulas which express them as functions of the electron and phonon temperatures and the electron density by using a suitable recasting of the macroscopic model in the framework of linear irreversible thermodynamics. |
SPLITTING REACTIONS PRESERVES NONDEGENERATE BEHAVIORS IN CHEMICAL REACTION NETWORKS
| Pengarang | : | Banaji, Murad |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 2) |
| Halaman | : | 748-769 |
| Abstrak | : | A family of results, referred to as inheritance results, tell us which enlargements of a chemical reaction network (CRN) preserve its capacity for nontrivial behaviours such as multista tionarity and oscillation. In this paper, the following inheritance result is proved: under mild as sumptions, splitting chemical reactions and inserting complexes involving some new chemical species preserves the capacity of a mass action CRN for multiple nondegenerate equilibria and/or periodic orbits. The claim has been proved previously for equilibria alone; however, the generalisation to include oscillation involves extensive development of rather different techniques. Several inheritance results for multistationarity and oscillation in mass action CRNs, including the main result of this paper, are gathered into a single theorem. Examples are presented showing how these results can be used together to make claims about reaction networks based on knowledge of their subnetworks. The examples include some networks of biological importance. |