Experimental demonstration of the supersonic
... it becomes tremendously complicated for all but its most simple applications. For example, the appearance of more exotic forms such as polygones [4], through variations of the surface tension [5] or when the liquid flows over microtextured surfaces [6], has been studied experimentally but a solid un ...
... it becomes tremendously complicated for all but its most simple applications. For example, the appearance of more exotic forms such as polygones [4], through variations of the surface tension [5] or when the liquid flows over microtextured surfaces [6], has been studied experimentally but a solid un ...
10/14 - The Mathematical Institute, University of Oxford, Eprints Archive
... molecule of C dissociates. Whenever new molecules of A and B are introduced to the system, we have to initiate their positions. Since the algorithm considers all molecules as points, it would make sense to place them at the position where the complex C was just before the reaction (1.5) occurred, i. ...
... molecule of C dissociates. Whenever new molecules of A and B are introduced to the system, we have to initiate their positions. Since the algorithm considers all molecules as points, it would make sense to place them at the position where the complex C was just before the reaction (1.5) occurred, i. ...
Complex numbers - Beaufort Secondary College
... and solids formed from combinations of prisms. Describe translations, reflections in an axis, and rotations of multiples of 90° on the Cartesian plane using coordinates. Identify line and rotational symmetries. Identify corresponding, alternate and co- interior angles when two straight lines are cro ...
... and solids formed from combinations of prisms. Describe translations, reflections in an axis, and rotations of multiples of 90° on the Cartesian plane using coordinates. Identify line and rotational symmetries. Identify corresponding, alternate and co- interior angles when two straight lines are cro ...
chapter 5 open-channel flow
... surface is momentarily deformed in some small area by a deforming force of some sort—by the force of the wind, or by your agitating the water with your hand—the force of gravity acts to try to restore the free surface to its original planar condition. Provided that the viscosity of the liquid is not ...
... surface is momentarily deformed in some small area by a deforming force of some sort—by the force of the wind, or by your agitating the water with your hand—the force of gravity acts to try to restore the free surface to its original planar condition. Provided that the viscosity of the liquid is not ...
Seven common errors in finding exact solutions of
... method, that allows us to look for the solitary wave solutions and rational solutions for the exact solvable nonlinear differential equations [7, 8]. As to nonintegrable nonlinear evolution equations we cannot point out the best method to look for the exact solutions of nonlinear differential equati ...
... method, that allows us to look for the solitary wave solutions and rational solutions for the exact solvable nonlinear differential equations [7, 8]. As to nonintegrable nonlinear evolution equations we cannot point out the best method to look for the exact solutions of nonlinear differential equati ...
New algorithm for the discrete logarithm problem on elliptic curves
... that is polynomial in n. The assumption was proved correct in numerous experiments with MAGMA, see Section 4.5.1. We were able to solve (5) for t = m and therefore (4) for m as 5, 6 and some n on a common computer. For n, m as in [19, 28], the solution is up to 50 times faster and takes up to 10 tim ...
... that is polynomial in n. The assumption was proved correct in numerous experiments with MAGMA, see Section 4.5.1. We were able to solve (5) for t = m and therefore (4) for m as 5, 6 and some n on a common computer. For n, m as in [19, 28], the solution is up to 50 times faster and takes up to 10 tim ...
Lecture 1 Describing Inverse Problems
... we cannot use this vector as a new guess for the solution. So, we compute the change in the solution and add as much of this vector as possible to the solution mS without causing the solution to become infeasible. We therefore replace mS with the new guess mS + α δm, where is the largest choice that ...
... we cannot use this vector as a new guess for the solution. So, we compute the change in the solution and add as much of this vector as possible to the solution mS without causing the solution to become infeasible. We therefore replace mS with the new guess mS + α δm, where is the largest choice that ...
Problems - Stanford University
... 3. Page 110, equation 7.70 is not normalized because it does not include the integral over angles. The equation gives the correct unnormalized radial distribution, which shows the relative probability of finding an electron in a thin spherical shell a distance r from the nucleus. Note that the norma ...
... 3. Page 110, equation 7.70 is not normalized because it does not include the integral over angles. The equation gives the correct unnormalized radial distribution, which shows the relative probability of finding an electron in a thin spherical shell a distance r from the nucleus. Note that the norma ...
Effective slip on textured superhydrophobic surfaces
... drop on this surface reaches a terminal velocity of about 16 cm/ s, compared with 25 cm/ s for the 15 m and 26 cm/ s for the 8 m surfaces. Experiments with 1:1 and 2:1 ZnCl2:water solutions show similar results, but with decreasing terminal velocities. The theoretical terminal velocity of the wate ...
... drop on this surface reaches a terminal velocity of about 16 cm/ s, compared with 25 cm/ s for the 15 m and 26 cm/ s for the 8 m surfaces. Experiments with 1:1 and 2:1 ZnCl2:water solutions show similar results, but with decreasing terminal velocities. The theoretical terminal velocity of the wate ...
Nondegeneracy of the Lump Solution to the KP-I Equation
... Theorem 1 has long been conjectured to be true. See the remark after Lemma 7 in [30] concerning the spectral property and its relation to stability. We also expect that the linearized operator around Q has exactly one negative eigenvalue. But we have not been able to prove this. The rigidity result, ...
... Theorem 1 has long been conjectured to be true. See the remark after Lemma 7 in [30] concerning the spectral property and its relation to stability. We also expect that the linearized operator around Q has exactly one negative eigenvalue. But we have not been able to prove this. The rigidity result, ...
Stochastic flows associated to coalescent processes II: Stochastic
... There is a simple procedure to construct a random exchangeable partition from a bridge B, which is a variant of Kingman’s paintbox process. Let R = {B(r), r ∈ [0, 1]}cl be the closed range of B, so Rc = [0, 1]\R is a random open set which has a canonical decomposition into disjoint open intervals, c ...
... There is a simple procedure to construct a random exchangeable partition from a bridge B, which is a variant of Kingman’s paintbox process. Let R = {B(r), r ∈ [0, 1]}cl be the closed range of B, so Rc = [0, 1]\R is a random open set which has a canonical decomposition into disjoint open intervals, c ...
The Motion of a Pair of Charged Particles
... for Xc the position closest to D/2 in a given trajectory – that’s what led to ∆T = .0005 [? ]. While it is clear from Figure 4 that the four cases we have considered have quantitatively different values for T ∗ , we are not claiming particularly high accuracy for T ∗ . The accuracy is, however, goo ...
... for Xc the position closest to D/2 in a given trajectory – that’s what led to ∆T = .0005 [? ]. While it is clear from Figure 4 that the four cases we have considered have quantitatively different values for T ∗ , we are not claiming particularly high accuracy for T ∗ . The accuracy is, however, goo ...
Computational fluid dynamics
Computational fluid dynamics, usually abbreviated as CFD, is a branch of fluid mechanics that uses numerical analysis and algorithms to solve and analyze problems that involve fluid flows. Computers are used to perform the calculations required to simulate the interaction of liquids and gases with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved. Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulent flows. Initial experimental validation of such software is performed using a wind tunnel with the final validation coming in full-scale testing, e.g. flight tests.