scholarly journals Tree crowns grow into self-similar shapes controlled by gravity and light sensing

2018 ◽  
Vol 15 (142) ◽  
pp. 20170976 ◽  
Author(s):  
Laurent Duchemin ◽  
Christophe Eloy ◽  
Eric Badel ◽  
Bruno Moulia
Keyword(s):  
Tree Growth ◽  
Initial Conditions ◽  
Tree Crown ◽  
Tree Crowns ◽  
Light Sensing ◽  
The Core ◽  
Long Period ◽  
Self Similar ◽  
Similar Solutions ◽  
Front Model

Plants have developed different tropisms: in particular, they reorient the growth of their branches towards the light (phototropism) or upwards (gravitropism). How these tropisms affect the shape of a tree crown remains unanswered. We address this question by developing a propagating front model of tree growth. Being length-free, this model leads to self-similar solutions after a long period of time, which are independent of the initial conditions. Varying the intensities of each tropism, different self-similar shapes emerge, including singular ones. Interestingly, these shapes bear similarities to existing tree species. It is concluded that the core of specific crown shapes in trees relies on the balance between tropisms.

scholarly journals Analysis of the self-similar solutions of a generalized Burger's equation with nonlinear damping

2001 ◽  
Vol 7 (3) ◽  
pp. 253-282 ◽  
Author(s):  
Ch. Srinivasa Rao ◽  
P. L. Sachdev ◽  
Mythily Ramaswamy
Keyword(s):  
Initial Conditions ◽  
Nonlinear Damping ◽  
Nonlinear Ordinary Differential Equation ◽  
The Self ◽  
Similar Reduction ◽  
Generalized Burgers Equation ◽  
Different Types ◽  
Self Similar ◽  
Parameter Ranges ◽  
Similar Solutions

The nonlinear ordinary differential equation resulting from the self-similar reduction of a generalized Burgers equation with nonlinear damping is studied in some detail. Assuming initial conditions at the origin we observe a wide variety of solutions – (positive) single hump, unbounded or those with a finite zero. The existence and nonexistence of positive bounded solutions with different types of decay (exponential or algebraic) to zero at infinity for specific parameter ranges are proved.

Similarity solutions for viscous vortex cores

1992 ◽  
Vol 238 ◽  
pp. 487-507 ◽  
Author(s):  
Ernst W. Mayer ◽  
Kenneth G. Powell
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Axial Flow ◽  
Similarity Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
The Core ◽  
Axial Pressure Gradient ◽  
Self Similar ◽  
Similar Solutions

Results are presented for a class of self-similar solutions of the steady, axisymmetric Navier–Stokes equations, representing the flows in slender (quasi-cylindrical) vortices. Effects of vortex strength, axial gradients and compressibility are studied. The presence of viscosity is shown to couple the parameters describing the core growth rate and the external flow field, and numerical solutions show that the presence of an axial pressure gradient has a strong effect on the axial flow in the core. For the viscous compressible vortex, near-zero densities and pressures and low temperatures are seen on the vortex axis as the strength of the vortex increases. Compressibility is also shown to have a significant influence upon the distribution of vorticity in the vortex core.

Annular self-similar solutions in ideal magnetogasdynamics

2008 ◽  
Vol 74 (4) ◽  
pp. 531-554 ◽  
Author(s):  
R. M. LOCK ◽  
A. J. MESTEL
Keyword(s):  
Magnetic Field ◽  
Initial Value Problem ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
The Self ◽  
Initial Value ◽  
Azimuthal Magnetic Field ◽  
Self Similar ◽  
Similar Solutions ◽  
Z Pinch

AbstractWe consider the possibility of self-similar solutions describing the implosion of hollow cylindrical annuli driven by an azimuthal magnetic field, in essence a self-similar imploding liner z-pinch. We construct such solutions for gasdynamics, for ideal ‘β=0’ plasma and for ideal magnetogasdynamics (MGD). In the latter two cases some quantities are singular at the annular boundaries. Numerical solutions of the full ideal MGD initial value problem indicate that the self-similar solutions are not attractive for arbitrary initial conditions, possibly as a result of flux-freezing.

Расчеты сверхзвукового пограничного слоя в полной и локально автомодельной постановках

2020 ◽  
Author(s):  
Y.N. Grigoryev ◽  
A.G. Gorobchuk ◽  
I.V. Ershov
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Initial Conditions ◽  
Plane Boundary ◽  
Transfer Coefficients ◽  
Vibrationally Excited ◽  
Limit Values ◽  
Various Boundary Conditions ◽  
Self Similar ◽  
Similar Solutions

The article considers the possibility of using locally self-similar solutions of a stationary boundary layer in linear stability problems. These solutions are compared with various boundary conditions for a vibrationally excited gas with finite-difference calculations of the corresponding flows. The initial system of equations for a plane boundary layer of a vibrationally excited gas was obtained from the complete equations of two-temperature relaxation aerodynamics. The relaxation of vibrational modes of gas molecules is described in the framework of the LandauTeller equation. Transfer coefficients depend on the static flow temperature. It is shown that in all considered cases the convergence of profiles of hydrodynamic variables to some limit values takes place for the longitudinal coordinate 8 . . . 15. In parallel, the same flows were calculated using the full formulation based on the finite-difference KrankNicholson type scheme. It is shown that for all considered boundary and initial conditions the limiting locally self-similar profiles coincide with the profiles calculated within the full formulation. The obtained result substantiates the use of locally self-similar solutions in problems of the linear theory of stability of boundary layer flows of vibrationally excited gas. Проведены расчеты течения в плоском пограничном слое сжимаемого колебательно возбужденного газа в локально автомодельной постановке для ряда характерных условий внешнего потока и теплообмена на границе. Показано, что во всех рассмотренных случаях имеет место сходимость профилей гидродинамических переменных к некоторым предельным значениям для продольной координаты x> 8 . . . 15. Параллельно те же течения рассчитывались в полной постановке на основе конечно-разностной схемы типа Кранка-Николсон. Показано, что для всех рассмотренных граничных и начальных условий предельные локально автомодельные профили совпадают с профилями, рассчитанными в полной постановке. Это позволяет обоснованно использовать легко рассчитываемые локально автомодельные профили в задачах линейной теории устойчивости.

Freely draining gravity currents in porous media: Dipole self-similar solutions with and without capillary retention

2007 ◽  
Vol 18 (3) ◽  
pp. 337-362 ◽  
Author(s):  
JOCHONIA S. MATHUNJWA ◽  
ANDREW J. HOGG
Keyword(s):  
Unsaturated Flow ◽  
Multiple Scales ◽  
Initial Conditions ◽  
The Self ◽  
Similar Solution ◽  
Self Similar Solution ◽  
Theoretical Predictions ◽  
Analytic Expressions ◽  
Self Similar ◽  
Similar Solutions

We analyse the two-dimensional, gravitationally-driven spreading of fluid through a porous medium overlying a horizontal impermeable boundary from which fluid can drain freely at one end. Under the assumption that none of the intruding fluid is retained within the pores in the trail of the current, the motion of the current is described by the dipole self-similar solution of the first kind derived by Barenblatt and Zel'dovich (1957). We show that small perturbations of arbitrary shape imposed on this solution decay in time, indicating that the self-similar solution is linearly stable. We use the connection between the perturbation eigenfunctions and symmetry transformations of the self-similar solution to demonstrate that variables can always be specified in terms of which the rate of decay of the perturbations is maximised. Unsaturated flow can be modelled by assuming that a constant fraction of the fluid is retained within the pores by capillary action in the trail of the current. It has been shown (Barenblatt and Zel'dovich, 1998; Ingerman and Shvets, 1999) that in this case, the motion of the current is described by a self-similar solution of the second kind characterised by an anomalous exponent. We derive leading-order analytic expressions for the anomalous exponent and the self-similar quantities valid for small values of the fraction of fluid retained using direct asymptotic analysis and by using a novel application of the method of multiple scales. The latter offers a number of advantages and permits the evolution of the current to be clearly connected with its initial conditions in a way not possible with conventional approaches. We demonstrate that the theoretical predictions provided by these expressions are in excellent agreement with results from the numerical integration of the governing equations.

Serial Homology as a Challenge to Evolutionary Theory

2017 ◽  
Author(s):  
Stéphane Schmitt
Keyword(s):  
Biological Sciences ◽  
Evolutionary Theory ◽  
Serial Homology ◽  
The Core ◽  
Long Period ◽  
Colonial Theory ◽  
Experimental Approaches ◽  
Evo Devo ◽  
The 19Th Century ◽  
Development And Evolution

The problem of the repeated parts of organisms was at the center of the biological sciences as early as the first decades of the 19th century. Some concepts and theories (e.g., serial homology, unity of plan, or colonial theory) introduced in order to explain the similarity as well as the differences between the repeated structures of an organism were reused throughout the 19th and the 20th century, in spite of the fundamental changes during this long period that saw the diffusion of the evolutionary theory, the rise of experimental approaches, and the emergence of new fields and disciplines. Interestingly, this conceptual heritage was at the core of any attempt to unify the problems of inheritance, development, and evolution, in particular in the last decades, with the rise of “evo-devo.” This chapter examines the conditions of this theoretical continuity and the challenges it brings out for the current evolutionary sciences.

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