THEORY AND PRACTICE OF AEROSOL SCIENCE
... behaviour for simple fluids, although their quantitative accuracy is unclear. Early work indicated a significant difference between these two approaches, but more recent calculations for the cut-off LennardJones fluid showed that the SGA gave values for the planar surface tension that agreed with co ...
... behaviour for simple fluids, although their quantitative accuracy is unclear. Early work indicated a significant difference between these two approaches, but more recent calculations for the cut-off LennardJones fluid showed that the SGA gave values for the planar surface tension that agreed with co ...
Solving Multi-Step Equations (Pages 142–148)
... Next, undo the subtraction by adding 3 to each side. 2x 3 3 36 3 2x 39 ...
... Next, undo the subtraction by adding 3 to each side. 2x 3 3 36 3 2x 39 ...
WORKSHEET: ONE-PARAMETER BIFURCATIONS Here we discuss
... value of the one parameter equation dy/dt = fµ (y). Definition: A bifurcation value for a differential equation dy/dt = fµ (y) is a value µ0 for µ where the phase lines for µ near µ0 differ for µ > µ0 and µ < µ0 . Problem: Find the bifurcation points for the differential equation with one parameter ...
... value of the one parameter equation dy/dt = fµ (y). Definition: A bifurcation value for a differential equation dy/dt = fµ (y) is a value µ0 for µ where the phase lines for µ near µ0 differ for µ > µ0 and µ < µ0 . Problem: Find the bifurcation points for the differential equation with one parameter ...
9 Scientific models and mathematical equations
... This is the general equation of a straight line, where m and c represent constants (m is the gradient of the line and c is the intercept). Substituting different numerical values for m and c gives different straight lines; for example, y 2x 1 represents one particular straight line, and y 3x 2 ...
... This is the general equation of a straight line, where m and c represent constants (m is the gradient of the line and c is the intercept). Substituting different numerical values for m and c gives different straight lines; for example, y 2x 1 represents one particular straight line, and y 3x 2 ...
Interaction of debris flow with rigid and flexible barriers
... JTC1 Workshop on Advances in Landslide Understanding Choi CE, Ng CWW, Au-Yeung, SCH & Goodwin G (2015b) Froude scaling of landslide debris in flume modelling. Landslides 12(6), 1197-1206. Cui P, Zeng C, & Lei Y (2015) Experimental analysis on the impact force of viscous debris flow. Earth Surface Pr ...
... JTC1 Workshop on Advances in Landslide Understanding Choi CE, Ng CWW, Au-Yeung, SCH & Goodwin G (2015b) Froude scaling of landslide debris in flume modelling. Landslides 12(6), 1197-1206. Cui P, Zeng C, & Lei Y (2015) Experimental analysis on the impact force of viscous debris flow. Earth Surface Pr ...
Linear Diophantine Equations
... are clearly the same as the integer solutions to the original one. We can easily find ONE solution to the reduced equation by the Euclidean algorithm, which gives integers s, t such that As + Bt = 1. Then multiply both sides by C to get A(sC) + B(tC) = C. This shows that x0 = sC, y0 = tC is a soluti ...
... are clearly the same as the integer solutions to the original one. We can easily find ONE solution to the reduced equation by the Euclidean algorithm, which gives integers s, t such that As + Bt = 1. Then multiply both sides by C to get A(sC) + B(tC) = C. This shows that x0 = sC, y0 = tC is a soluti ...
On the greatest prime factor of sides of a Heron triangle
... where x 1 , . . . , x s ∈ S is called an S-unit equation. If i∈I ai x i = 0 for all non-empty subsets I ⊂ {1, . . . , s}, then the S-unit equation (1) is called non-degenerate. The most important result about S-unit equations is the following finiteness theorem (see, for example, [3]). Theorem 2. T ...
... where x 1 , . . . , x s ∈ S is called an S-unit equation. If i∈I ai x i = 0 for all non-empty subsets I ⊂ {1, . . . , s}, then the S-unit equation (1) is called non-degenerate. The most important result about S-unit equations is the following finiteness theorem (see, for example, [3]). Theorem 2. T ...
JDEP384hLecture18.pdf
... If the system has a unique solution (which is the only kind of system we are dealing with), then the coe cient matrix is invertible, which is equivalent to having nonzero determinant. Verify this with the above example. A more reliable indicator of potential problems (sensitive matrix, nearly singul ...
... If the system has a unique solution (which is the only kind of system we are dealing with), then the coe cient matrix is invertible, which is equivalent to having nonzero determinant. Verify this with the above example. A more reliable indicator of potential problems (sensitive matrix, nearly singul ...
inverse scattering of buried inhomogeneous dielectric material
... Ⅲ. NUMERICAL RESULTS In this section, we report some numerical results obtained by computer simulations using the method described in the Section Ⅱ. Let us consider an inhomogeneous dielectric cylinders coated on a conductor buried at a depth of a = 0.1m in a lossless half space, as shown in Fig. 1 ...
... Ⅲ. NUMERICAL RESULTS In this section, we report some numerical results obtained by computer simulations using the method described in the Section Ⅱ. Let us consider an inhomogeneous dielectric cylinders coated on a conductor buried at a depth of a = 0.1m in a lossless half space, as shown in Fig. 1 ...
Introduction to Mechanical Vibrations
... (4) their response characteristics can be obtained from the form of system equations without a detailed solution (5) a closed-form solution is often possible (6) numerical analysis techniques are well developed, and (7) they serve as a basis for understanding more complex non-linear system behaviour ...
... (4) their response characteristics can be obtained from the form of system equations without a detailed solution (5) a closed-form solution is often possible (6) numerical analysis techniques are well developed, and (7) they serve as a basis for understanding more complex non-linear system behaviour ...
Mathematical Research and Modeling for the Army
... have the luxury of possessing data on the mature or aged item, as is often assumed. The models of minimal repair currently in use are not adequate in many instances. Composite materials, like ceramics, have high tensile strength and can withstand high temperatures but are typically brittle, which le ...
... have the luxury of possessing data on the mature or aged item, as is often assumed. The models of minimal repair currently in use are not adequate in many instances. Composite materials, like ceramics, have high tensile strength and can withstand high temperatures but are typically brittle, which le ...
5 more than a number “n”
... 26 cartons and had 3 cans left over. How many cans were in each carton? Let x = cans per carton (cans per carton)(# cartons) = total cans ...
... 26 cartons and had 3 cans left over. How many cans were in each carton? Let x = cans per carton (cans per carton)(# cartons) = total cans ...
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.