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Doering CR, Toppaladoddi S, Wettlaufer JS. Absence of Evidence for the Ultimate Regime in Two-Dimensional Rayleigh-Bénard Convection. Phys Rev Lett 2019; 123:259401. [PMID: 31922771 DOI: 10.1103/physrevlett.123.259401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2018] [Indexed: 06/10/2023]
Affiliation(s)
- C R Doering
- University of Michigan, Ann Arbor, Michigan 48109-1043, USA
| | | | - J S Wettlaufer
- University of Oxford, Oxford OX2 6GG, United Kingdom
- Yale University, New Haven, Connecticut 06520-8109, USA
- Nordita, Royal Institute of Technology and Stockholm University, SE-10691 Stockholm, Sweden
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Ödman D, Werner E, Dorfman KD, Doering CR, Mehlig B. Distribution of label spacings for genome mapping in nanochannels. Biomicrofluidics 2018; 12:034115. [PMID: 30018694 PMCID: PMC6019347 DOI: 10.1063/1.5038417] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2018] [Accepted: 06/06/2018] [Indexed: 05/27/2023]
Abstract
In genome mapping experiments, long DNA molecules are stretched by confining them to very narrow channels, so that the locations of sequence-specific fluorescent labels along the channel axis provide large-scale genomic information. It is difficult, however, to make the channels narrow enough so that the DNA molecule is fully stretched. In practice, its conformations may form hairpins that change the spacings between internal segments of the DNA molecule, and thus the label locations along the channel axis. Here, we describe a theory for the distribution of label spacings that explains the heavy tails observed in distributions of label spacings in genome mapping experiments.
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Affiliation(s)
- D Ödman
- Department of Physics, University of Gothenburg, 41296 Gothenburg, Sweden
| | - E Werner
- Department of Physics, University of Gothenburg, 41296 Gothenburg, Sweden
| | - K D Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - C R Doering
- Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48109-1042, USA
| | - B Mehlig
- Department of Physics, University of Gothenburg, 41296 Gothenburg, Sweden
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Affiliation(s)
- E B Wilson
- Harvard School of Public Health, Harvard University
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Affiliation(s)
- C R Doering
- Department of Vital Statistics, Harvard School of Public Health
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Lombard HL, Doering CR. Cancer Studies in Massachusetts: 1. The Relationship between Cancer and Density of Population in Massachusetts. Proc Natl Acad Sci U S A 2006; 13:728-35. [PMID: 16587265 PMCID: PMC1085204 DOI: 10.1073/pnas.13.10.728] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Affiliation(s)
- H L Lombard
- Massachusetts Department of Public Health and Harvard School of Public Health
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Affiliation(s)
- C R Doering
- Harvard School of Public Health, Department of Vital Statistics
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Calzavarini E, Doering CR, Gibbon JD, Lohse D, Tanabe A, Toschi F. Exponentially growing solutions in homogeneous Rayleigh-Bénard convection. Phys Rev E Stat Nonlin Soft Matter Phys 2006; 73:035301. [PMID: 16605590 DOI: 10.1103/physreve.73.035301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/23/2005] [Indexed: 05/08/2023]
Abstract
It is shown that homogeneous Rayleigh-Bénard flow, i.e., Rayleigh-Bénard turbulence with periodic boundary conditions in all directions and a volume forcing of the temperature field by a mean gradient, has a family of exact, exponentially growing, separable solutions of the full nonlinear system of equations. These solutions are clearly manifest in numerical simulations above a computable critical value of the Rayleigh number. In our numerical simulations they are subject to secondary numerical noise and resolution dependent instabilities that limit their growth to produce statistically steady turbulent transport.
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Affiliation(s)
- E Calzavarini
- Department of Applied Physics, University of Twente, 7500 AE Enschede, The Netherlands
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Abstract
The immune response to Mycobacterium tuberculosis (Mtb) infection is the formation of multicellular lesions, or granolomas, in the lung of the individual. However, the structure of the granulomas and the spatial distribution of the immune cells within is not well understood. In this paper we develop a mathematical model investigating the early and initial immune response to Mtb. The model consists of coupled reaction-diffusion-advection partial differential equations governing the dynamics of the relevant macrophage and bacteria populations and a bacteria-produced chemokine. Our novel application of mathematical concepts of internal states and internal velocity allows us to begin to study this unique immunological structure. Volume changes resulting from proliferation and death terms generate a velocity field by which all cells are transported within the forming granuloma. We present numerical results for two distinct infection outcomes: controlled and uncontrolled granuloma growth. Using a simplified model we are able to analytically determine conditions under which the bacteria population decreases, representing early clearance of infection, or grows, representing the initial stages of granuloma formation.
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Affiliation(s)
- D Gammack
- Department of Microbiology and Immunology, University of Michigan Medical School, Ann Arbor, MI 49109, USA
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Doering CR, Constantin P. Variational bounds on energy dissipation in incompressible flows. III. Convection. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1996; 53:5957-5981. [PMID: 9964954 DOI: 10.1103/physreve.53.5957] [Citation(s) in RCA: 152] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Bulsara AR, Elston TC, Doering CR, Lowen SB, Lindenberg K. Cooperative behavior in periodically driven noisy integrate-fire models of neuronal dynamics. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1996; 53:3958-3969. [PMID: 9964707 DOI: 10.1103/physreve.53.3958] [Citation(s) in RCA: 42] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Constantin P, Doering CR. Variational bounds on energy dissipation in incompressible flows. II. Channel flow. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1995; 51:3192-3198. [PMID: 9962998 DOI: 10.1103/physreve.51.3192] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Doering CR, Constantin P. Variational bounds on energy dissipation in incompressible flows: Shear flow. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1994; 49:4087-4099. [PMID: 9961698 DOI: 10.1103/physreve.49.4087] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Privman V, Doering CR, Frisch HL. Crossover from rate-equation to diffusion-controlled kinetics in two-particle coagulation. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1993; 48:846-851. [PMID: 9960667 DOI: 10.1103/physreve.48.846] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Zürcher U, Doering CR. Thermally activated escape over fluctuating barriers. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1993; 47:3862-3869. [PMID: 9960458 DOI: 10.1103/physreve.47.3862] [Citation(s) in RCA: 29] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Ray TS, Glasser ML, Doering CR. Anomalous transmission-time moments in the ballistic limit of isotropic scattering. Phys Rev A 1992; 45:8573-8579. [PMID: 9906957 DOI: 10.1103/physreva.45.8573] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Horsthemke W, Doering CR, Ray TS, Burschka MA. Fluctuations and correlations in a diffusion-reaction system: Unified description of internal fluctuations and external noise. Phys Rev A 1992; 45:5492-5503. [PMID: 9907647 DOI: 10.1103/physreva.45.5492] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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Burschka MA, Doering CR, ben-Avraham D. Transition in the relaxation dynamics of a reversible diffusion-limited reaction. Phys Rev Lett 1989; 63:700-703. [PMID: 10041155 DOI: 10.1103/physrevlett.63.700] [Citation(s) in RCA: 28] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Doering CR, ben-Avraham D. Diffusion-limited coagulation in the presence of particle input: Exact results in one dimension. Phys Rev Lett 1989; 62:2563-2566. [PMID: 10040020 DOI: 10.1103/physrevlett.62.2563] [Citation(s) in RCA: 53] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Doering CR, ben-Avraham D. Interparticle distribution functions and rate equations for diffusion-limited reactions. Phys Rev A Gen Phys 1988; 38:3035-3042. [PMID: 9900720 DOI: 10.1103/physreva.38.3035] [Citation(s) in RCA: 183] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Doering CR, Gibbon JD, Holm DD, Nicolaenko B. Exact Lyapunov dimension of the universal attractor for the complex Ginzburg-Landau equation. Phys Rev Lett 1987; 59:2911-2914. [PMID: 10035685 DOI: 10.1103/physrevlett.59.2911] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Doering CR, Hagan PS, Levermore CD. Bistability driven by weakly colored Gaussian noise: The Fokker-Planck boundary layer and mean first-passage times. Phys Rev Lett 1987; 59:2129-2132. [PMID: 10035432 DOI: 10.1103/physrevlett.59.2129] [Citation(s) in RCA: 29] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Doering CR, Harvey PM. Optimal signal-to-noise in digital phase lock amplifiers. Appl Opt 1987; 26:633-642. [PMID: 20454190 DOI: 10.1364/ao.26.000633] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
We derive an expression for the optimal signal-to-noise ratio for linear phase lock amplifiers. In its digital form the optimal method can be implemented by real-time signal processing techniques. We analyze in detail the case of detector-noise-limited systems finding that the optimal technique can be used to eliminate effectively the detector's time constant from the set of parameters determining the overall efficiency. This has important implications for optical detection system design. We also report an experimental verification of the optimal method, thus establishing its practicality.
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Horsthemke W, Doering CR, Lefever R, Chi AS. Effect of external-field fluctuations on instabilities in nematic liquid crystals. Phys Rev A Gen Phys 1985; 31:1123-1135. [PMID: 9895593 DOI: 10.1103/physreva.31.1123] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Lombard HL, Doering CR. Classics in oncology. Cancer studies in Massachusetts. 2. Habits, characteristics and environment of individuals with and without cancer. CA Cancer J Clin 1980; 30:115-22. [PMID: 6768432 DOI: 10.3322/canjclin.30.2.115] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
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