OPAC - Pencarian Artikel Jurnal & Majalah Library USD
Menampilkan semua artikel (Halaman 548 dari 34170, Total: 341698 data)
PB-STERIC EQUATIONS: A GENERAL MODEL OF POISSON-BOLTZMANN EQUATIONS
klik untuk membaca file PDF
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 4) |
| Halaman | : | 1603-1622 |
| Abstrak | : | When ions are crowded, the effect of steric repulsion between ions (which can produce oscillations in charge density profiles) becomes significant and the conventional Poisson-Boltzmann (PB) equation should be modified. Several modified PB equations were developed but the associated total ionic charge density has no oscillation. This motivates us to derive a general model of PB equations called the PB-steric equations with a parameter \Lambda , which not only include the conven tional and modified PB equations but also have oscillatory total ionic charge density under different assumptions of steric effects and chemical potentials. As \Lambda = 0, the PB-steric equation becomes the conventional PB equation, but as \Lambda > 0, the concentrations of ions and solvent molecules are determined by the Lambert type functions. To approach the modified PB equations, we study the asymptotic limit of PB-steric equations with the Robin boundary condition as \Lambda goes to infinity. Our theoretical results show that the PB-steric equations (for 0 \leq \Lambda \leq \infty ) may include the conventional and modified PB equations. On the other hand, we use the PB-steric equations to find oscillatory total ionic charge density which cannot be obtained in the conventional and modified PB equations. |
ANALYTICAL TIME-DEPENDENT DISTRIBUTIONS FOR GENE EXPRESSION MODELS WITH COMPLEX PROMOTER SWITCHING MECHANISMS
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 4) |
| Halaman | : | 1572-1602 |
| Abstrak | : | Classical gene expression models assume exponential switching time distributions between the active and inactive promoter states. However, recent experiments have shown that many genes in mammalian cells may produce nonexponential switching time distributions, implying the existence of multiple promoter states and molecular memory in the promoter switching dynamics. Here we analytically solve a gene expression model with random bursting and complex promoter switching, and derive the time-dependent distributions of the mRNA and protein copy numbers, generalizing the steady-state solution obtained in [T. Zhou and J. Zhang, SIAM J. Appl. Math., 72 (2012), pp. 789-818] and [U. Herbach, SIAM J. Appl. Math., 79 (2019), pp. 1007-1029]. Using multiscale simplification techniques, we find that molecular memory has no influence on the time-dependent distribution when promoter switching is very fast or very slow, while it significantly affects the distribution when promoter switching is neither too fast nor too slow. By analyzing the dynamical phase diagram of the system, we also find that molecular memory in the inactive gene state weakens transient and stationary bimodality of the copy number distribution, while molecular memory in the active gene state enhances such bimodality. |
DIRAC POINTS FOR THE HONEYCOMB LATTICE WITH IMPENETRABLE OBSTACLES
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 4) |
| Halaman | : | 1546-1571 |
| Abstrak | : | This work is concerned with the Dirac points for the honeycomb lattice with impene trable obstacles arranged periodically in a homogeneous medium. We consider both the Dirichlet and Neumann eigenvalue problems and prove the existence of Dirac points for both eigenvalue problems at crossing of the lower band surfaces as well as higher band surfaces. Furthermore, we perform quantitative analyses for the eigenvalues and the slopes of two conical dispersion surfaces near each Dirac point based on a combination of the layer potential technique and asymptotic analysis. It is shown that the eigenvalues are in the neighborhood of the singular frequencies associated with the Green's function for the honeycomb lattice, and the slopes of the dispersion surfaces are reciprocal to the eigenvalues. |
RENEWAL EQUATIONS FOR SINGLE-PARTICLE DIFFUSION IN MULTILAYERED MEDIA
| Pengarang | : | Bressloff, Paul C. |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 4) |
| Halaman | : | 1518-1545 |
| Abstrak | : | Diffusion in heterogeneous media partitioned by semipermeable interfaces has a wide range of applications in the physical and life sciences, ranging from thermal conduction in composite media, gas permeation in soils, diffusion magnetic resonance imaging, drug delivery, and intercellular gap junctions. Many of these systems involve three-dimensional diffusion in an array of parallel planes with homogeneity in the lateral directions, so that they can be reduced to effective one dimensional (1D) models. In this paper we develop a probabilistic model of single-particle diffusion in 1D multilayered media by constructing a multilayered version of so-called snapping out Brownian motion (BM). The latter sews together successive rounds of reflected BM, each of which is restricted to a single layer. Each round of reflected BM is killed when the local time at one end of the layer exceeds an independent, exponentially distributed random variable. (The local time specifies the amount of time a reflected Brownian particle spends in a neighborhood of a boundary.) The particle then immediately resumes reflected BM in the same layer or the layer on the other side of the boundary with equal probability, and the process is iterated We proceed by constructing a last renewal equation for multilayered snapping out BM that relates the full probability density to the probability densities of partially reflected BM in each layer. We then show how transfer matrices can be used to solve the Laplace transformed renewal equation, and prove that the renewal equation and corresponding multilayer diffusion equation are equivalent. We illustrate the theory by analyzing the first passage time (FPT) problem for escape at the exterior boundaries of the domain. Finally, we use the renewal approach to incorporate a generalization of snapping out BM based on the encounter-based method for surface absorption; each round of reflected BM is now killed according to a nonexponential distribution for each local time threshold. This is achieved by considering a corresponding first renewal equation that relates the full probability density to the FPT densities for killing each round of reflected BM. We show that for certain configurations, nonexponential killing leads to an effective time-dependent permeability that is normalizable but heavy-tailed. |
INVERSE PROBLEMS FOR SUBDIFFUSION FROM OBSERVATION AT AN UNKNOWNTERMINAL TIME
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 4) |
| Halaman | : | 1496-1517 |
| Abstrak | : | Inverse problems of recovering space-dependent parameters, e.g., initial condition, space-dependent source, or potential coefficient in a subdiffusion model from the terminal observation have been extensively studied in recent years. However, all existing studies have assumed that the terminal time at which one takes the observation is exactly known. In this work, we present uniqueness and stability results for three canonical inverse problems, e.g., backward problem, inverse source, and inverse potential problems from the terminal observation at an unknown time. The subdiffusive nature of the problem indicates that one can simultaneously determine the terminal time and space-dependent parameter. The analysis is based on explicit solution representations, asymptotic behavior of the Mittag-Leffler function, and mild regularity conditions on the problem data. Further, we present several one- and two-dimensional numerical experiments to illustrate the feasibility of the approach. |
PARTISIPASI POLITIK PEREMPUAN: ANTARA KEWAJIBAN DAN PERJUANGAN MEMPEROLEH HAK
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Bina Darma |
| Volume / Edisi | : | 15-54 (No. 54) |
| Halaman | : | 89-96 |
| Abstrak | : | - |
FRAME HYDRODYNAMICS OF BIAXIAL NEMATICS FROM MOLECULAR-THEORY-BASED TENSOR MODELS
| Pengarang | : | Li, Sirui,Xu, Jie |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 4) |
| Halaman | : | 1467-1495 |
| Abstrak | : | Starting from a dynamic tensor model about two second-order tensors, we derive the frame hydrodynamics for the biaxial nematic phase using the Hilbert expansion. The coefficients in the frame model are derived from those in the tensor model. The energy dissipation of the tensor model is maintained in the frame model. The model is reduced to the Ericksen-Leslie model if the biaxial bulk energy minimum of the tensor model is reduced to a uniaxial one. |
DARI KERUSUHAN MENUJU KE KERUKUNAN
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Bina Darma |
| Volume / Edisi | : | 15-54 (No. 54) |
| Halaman | : | 77-88 |
| Abstrak | : | - |
SENSITIVITY OF STEADY STATES IN NETWORKS WITH APPLICATION TO MARKOV CHAINS AND CHEMICAL REACTION NETWORKS
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 4) |
| Halaman | : | 1444-1466 |
| Abstrak | : | We consider steady states of dynamics that have an underlying network structure. We study how a steady state responds to small perturbations in the network parameters and how this sensitivity is connected to the network structure. We introduce a prototypical linear response equation and determine its sensitivity. This abstract result is applied to study the sensitivity of steady states in two common dynamics on networks: continuous-time Markov chains and deterministically modeled chemical reaction networks. For continuous-time Markov chains, we are able to efficiently compute the signs of the response in terms of the underlying network structure. The study of chemical reaction networks extends the sensitivity analysis to open systems with more complex network structures |
INSTABILITY OF HYSTERETIC PHASE INTERFACES IN A MEAN-FIELD MODEL WITH INHOMOGENEITIES
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 4) |
| Halaman | : | 1422-1443 |
| Abstrak | : | We study a system of nonidentical bistable particles that is driven by a dynamical constraint and coupled through a nonlocal mean-field. Assuming piecewise affine constitutive laws we prove the existence of traveling wave solutions and characterize their dynamical stability. Our f indings explain the two dynamical regimes for phase interface that can be observed in numerical simulations with different parameters. We further discuss the convergence to a rate-independent model with strong hysteresis in the limit of vanishing relaxation time. |