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1-20 of 59 Search Results for
Convex geometry
Book Chapter
Series: AIPP Books, Methods
Published: March 2023
10.1063/9780735425743_005
EISBN: 978-0-7354-2574-3
ISBN: 978-0-7354-2572-9
... Quesada , I. and Grossmann , I. E. , “ An LP/NLP based branch and bound algorithm for convex MINLP optimization problems ,” Comput. Chem. Eng. 16 ( 10-11 ), 937 – 947 ( 1992 ). 10.1016/0098-1354(92)80028-8 Reddy , V. S. , Kaushik , S. C. , Ranjan , K. R. , and Tyagi , S...
Book Chapter
Series: AIPP Books, Principles
Published: March 2023
10.1063/9780735425590_004
EISBN: 978-0-7354-2559-0
ISBN: 978-0-7354-2556-9
... the substrate was bent toward the inside (concave like feature), it experienced more compression and hence the resistance dropped, as shown in Fig. 4.13(a) . In contrast, when it was bent outward (convex like feature), the resistance increased. This suggests that a small change in the curvature of the sample...
Book
Series: AIPP Books, Methods
Published: March 2023
10.1063/9780735425743
EISBN: 978-0-7354-2574-3
ISBN: 978-0-7354-2572-9
Book
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425477
EISBN: 978-0-7354-2547-7
ISBN: 978-0-7354-2544-6
Book
Series: AIPP Books, Principles
Published: March 2023
10.1063/9780735425590
EISBN: 978-0-7354-2559-0
ISBN: 978-0-7354-2556-9
Book Chapter
Series: AIPP Books, Principles
Published: February 2023
10.1063/9780735425033_002
EISBN: 978-0-7354-2503-3
ISBN: 978-0-7354-2500-2
... method is limited in boule length due to the free carrier absorption in the infrared causing problems in heat removal and a convex-to-concave interface inversion, which results in a corkscrew or spiral formation ( Baldini et al., 2018 ). EFG grown β-Ga2O3 crystals do...
Book Chapter
Series: AIPP Books, Perspectives
Published: December 2022
10.1063/9780735422537_003
EISBN: 978-0-7354-2253-7
ISBN: 978-0-7354-2251-3
... not necessarily convex surfaces in a three-dimensional space. For that, consider the polar cap of unit radius (see Fig. 3.3 ). The area is given by (3.4) S = ∫ 0 θ 2 π sin θ d θ = 2 π ( 1 − cos θ ) . Thus, ∫ R K d A = 1 × ( Area of S ) = 2 π ( 1 − cos...
Book
Series: AIPP Books, Perspectives
Published: December 2022
10.1063/9780735422537
EISBN: 978-0-7354-2253-7
ISBN: 978-0-7354-2251-3
Book Chapter
Series: AIPP Books, Principles
Published: August 2022
10.1063/9780735424876_010
EISBN: 978-0-7354-2487-6
ISBN: 978-0-7354-2484-5
... Gpoly2 is a concave angle (and, thus, ∠ 7 is not convex). Examples Geometric figures and their properties are found implicitly and explicitly throughout the natural sciences. One example where geometry explicitly appears is in the description of the movement of an object on an inclined...
Book Chapter
Series: AIPP Books, Principles
Published: August 2022
10.1063/9780735424876_011
EISBN: 978-0-7354-2487-6
ISBN: 978-0-7354-2484-5
... points. Triangles A triangle is a polygonal with three vertices (see Fig. 11.1 ). Note that a triangle is always a convex polygonal. FIG. 11.1 A triangle. Also shown are the three vertices: P1, P2, and P3; the three corresponding interior...
Book
Series: AIPP Books, Principles
Published: August 2022
10.1063/9780735424876
EISBN: 978-0-7354-2487-6
ISBN: 978-0-7354-2484-5
Book Chapter
Series: AIPP Books, Principles
Published: September 2022
10.1063/9780735425118_003
EISBN: 978-0-7354-2511-8
ISBN: 978-0-7354-2509-5
..., which form the loop, are subcritical (featuring concave segments) in the interval of 0 < λ < 0.0998. At 0.0998 < λ < 0.1018, the direct bifurcation is supercritical [with a convex Θ (Etotal) curve], while the reverse one is still subcritical. Both...
Book Chapter
Series: AIPP Books, Principles
Published: May 2022
10.1063/9780735424517_001
EISBN: 978-0-7354-2451-7
ISBN: 978-0-7354-2448-7
... provides a generalized formulation for light propagation through curved and planar surfaces. This is predominantly due to the fact that most of the optical elements involve spherical and planar interfaces. So, it seems imperative to understand spherical surfaces (both concave and convex). It is important...
Book Chapter
Series: AIPP Books, Perspectives
Published: July 2022
10.1063/9780735424715_005
EISBN: 978-0-7354-2471-5
ISBN: 978-0-7354-2469-2
... observations ( Skalak et al., 1981 ). The RBCs present a concave outer surface at the weak interaction, but a convex surface at the strong interaction. The contact surface between two adjacent RBCs is curved at both the weak and strong interactions, and the five RBCs exhibit the similar aggregation...
Book
Series: AIPP Books, Perspectives
Published: July 2022
10.1063/9780735424715
EISBN: 978-0-7354-2471-5
ISBN: 978-0-7354-2469-2
Book Chapter
Series: AIPP Books, Principles
Published: May 2022
10.1063/9780735424678_002
EISBN: 978-0-7354-2467-8
ISBN: 978-0-7354-2464-7
... dependent angular deflection δ θ = θ r − θ i ∝ d , where d is the radial offset from the principal axis of a lens. For a convex lens, these bent rays will intersect the principal axis at a distance f = d / tan δ θ ∼ d / δ θ = constant...
Book
Series: AIPP Books, Principles
Published: May 2022
10.1063/9780735424517
EISBN: 978-0-7354-2451-7
ISBN: 978-0-7354-2448-7
Book
Series: AIPP Books, Principles
Published: May 2022
10.1063/9780735424678
EISBN: 978-0-7354-2467-8
ISBN: 978-0-7354-2464-7
Book Chapter
Series: AIPP Books, Principles
Published: December 2021
10.1063/9780735422865_002
EISBN: 978-0-7354-2286-5
ISBN: 978-0-7354-2283-4
... of a convex polygon linking particles/atoms on the boundary. Equivalently, the domain can be defined as the convex hull inscribing the cloud of points. The RVE boundary Γμ is obtained as the envelope of the cloud of particles—the boundary of the convex hull. The particles are connected...
Book Chapter
Series: AIPP Books, Principles
Published: December 2021
10.1063/9780735422865_005
EISBN: 978-0-7354-2286-5
ISBN: 978-0-7354-2283-4
... on the beam ( Bruton, 2018 ). The configuration of the model can be simple or more complex, according to the level of accuracy required for the evaluation. A droplet of the fluid of concern is deposited on a surface that the fluid will not wet and on which the fluid creates a distinct convex droplet...
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