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Results for “derivative discontinuity”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Theoretical and experimental characterization of coplanar waveguide discontinuities for filter applications

A full-wave analysis of shielded coplanar waveguide two-port discontinuities based on the solution of an appropriate surface integral equation in the space domain is presented. Frequency-dependent scattering parameters for open-end and short-end coplanar waveguide (CPW) stubs are computed using this method. The numerically derived results are compared with measurements performed in the frequency range 5-25 GHz and show very good agreement. From the scattering parameters, lumped-element equivalent circuits have been derived to model the discontinuities. The inductors and capacitors of these models have been represented by closed-form equations, as functions of the stub length, to compute the circuit element values for these discontinuities.

Dib, Nihad I.↗
DOE OSTI2020

A mass-transfer particle-tracking method for simulating transport with discontinuous diffusion coefficients

The problem of a spatially discontinuous diffusion coefficient (D(x)) is one that may be encountered in hydrogeologic systems due to natural geological features or as a consequence of numerical discretization of flow properties. To date, mass-transfer particle-tracking (MTPT) methods, a family of Lagrangian methods in which diffusion is jointly simulated by random walk and diffusive mass transfers, have been unable to solve this problem. This manuscript presents a new mass-transfer (MT) algorithm that enables MTPT methods to accurately solve the problem of discontinuous D(x). To achieve this, we derive a semi-analytical solution to the discontinuous D(x) problem by employing a predictor-corrector approach, and we use this semi-analytical solution as the weighting function in a reformulated MT algorithm. Furthermore, this semi-analytical solution is generalized for cases with multiple 1D interfaces as well as for 2D cases, including a 2 × 2 tiling of 4 subdomains that corresponds to a numerically-generated diffusion field. The solutions generated by this new mass-transfer algorithm closely agree with an analytical 1D solution or, in more complicated cases, trusted numerical results, demonstrating the success of our proposed approach.

42 ENGINEERING↗
DOE OSTI2024

Reinforcement induced microcracking during the conversion of polymer-derived ceramics

This study investigates the role of discontinuous reinforcement on the microcracking of a preceramic polymer matrix during polymer to ceramic conversion. The material system comprised a carbosilane-based, preceramic polymer reinforced with mullite particles. The preceramic resin slurry was formulated for photopolymerization on a digital light projection 3D printer. Micro X-ray computed tomography, using a synchrotron light source, monitored a printed composite part during pyrolysis. The conversion of the carbosilane matrix into Si(O)C generated microcracks in the matrix that radially extended from particles. The likelihood of microcrack formation positively correlated with particle size. The largest particles (>10 4 µm 3 volume or >60 µm side length) always abutted microcracks, while the matrix surrounding smaller particles (<5 µm) was free of microcracks. Numerical calculations showed the particles resist the shrinking matrix during its conversion. This created tensile stresses within the matrix. The driving force for microcrack growth was also analyzed with regard to the influence of matrix material parameters, particle form-factor and crack length. These results reveal the need to consider the form factor of discontinuous reinforcements, with regard to the material properties of the polymer-derived ceramic, in order to reduce or eliminate defects in the final part.

36 MATERIALS SCIENCE↗
NASA NTRS1999

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations That Arise from Nonlinear Two-Point Boundary Value Problems

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + definite integral of g(x, t)F(t,y(t))dt with limits between 0 and 1,0 less than or equal to x les than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integral equations arise, e.g., when one applied Green's function techniques to nonlinear two-point boundary value problems of the form y "(x) =f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and y(l) = y(sub l), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trepezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal rule, thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

Sidi, Avram↗
NASA NTRS1999

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations that Arise from Nonlinear Two-Point Boundary Value Problems

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + integral(0 to 1) g(x,t) F(t, y(t)) dt, 0 less than or equal to x less than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integrals equations arise, e.g., when one applies Green's function techniques to nonlinear two-point boundary value problems of the form U''(x) = f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and g(l) = y(sub 1), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trapezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

Sidi, Avram↗
NASA NTRS1994

Fourth order difference methods for hyperbolic IBVP's

Fourth order difference approximations of initial-boundary value problems for hyperbolic partial differential equations are considered. We use the method of lines approach with both explicit and compact implicit difference operators in space. The explicit operator satisfies an energy estimate leading to strict stability. For the implicit operator we develop boundary conditions and give a complete proof of strong stability using the Laplace transform technique. We also present numerical experiments for the linear advection equation and Burgers' equation with discontinuities in the solution or in its derivative. The first equation is used for modeling contact discontinuities in fluid dynamics, the second one for modeling shocks and rarefaction waves. The time discretization is done with a third order Runge-Kutta TVD method. For solutions with discontinuities in the solution itself we add a filter based on second order viscosity. In case of the non-linear Burger's equation we use a flux splitting technique that results in an energy estimate for certain different approximations, in which case also an entropy condition is fulfilled. In particular we shall demonstrate that the unsplit conservative form produces a non-physical shock instead of the physically correct rarefaction wave. In the numerical experiments we compare our fourth order methods with a standard second order one and with a third order TVD-method. The results show that the fourth order methods are the only ones that give good results for all the considered test problems.

Gustafsson, Bertil↗
DOE OSTI2020

Structural features of solid-solid phase transitions and lattice dynamics in U 3 O 8

Triuranium octoxide (U 3 O 8 ) undergoes an orthorhombic to hexagonal structural phase transition near Ts=305°C, and a separate nonstructural phase transition at Tc=210°C. The later transition has previously been associated with temperature-induced fluctuations in the uranium oxidation state. A discontinuity in the slope of electrical conductivity versus temperature measurement at 210°C has supported this idea. The orthorhombic phase has three crystallographic sites in two distinct oxidation configurations [2 U(V) and 1 U(VI)], whereas the hexagonal phase has one distinct uranium site. High-resolution x-ray diffraction measurements eliminate the possibility of superlattice Bragg reflections to less than 0.2 e - scattering power and U 3 O 8 is not metallic; consequently, the presence of oxidation fluctuations is required for charge balancing. Interestingly, the order-to-disorder transition occurs at a much lower temperature than the structural transition. Using temperature-dependent x-ray diffraction and Raman spectroscopy, we show anisotropic lattice expansion in the in-plane b and c lattice constants. A specific discontinuity in the temperature derivatives of the b and c lattice constants are the first reported structural signatures of the order-to-disorder transition, suggestive of a change in local U–O coordination. Phonon frequencies of U 3 O 8 measured by Raman spectroscopy show significant temperature-dependent dynamics. Redshifting of several modes between 40 and 300°C cannot be explained by unit cell expansion alone because the unit cell volume decreases in this region. Instead, we show that phonon frequencies are highly correlated with the anisotropic lattice expansion/contraction along specific crystallographic directions.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A flexible linear diffusion acceleration to k-eigenvalue neutron transport with SN discontinuous finite element method

In this paper, we derive a flexible linear diffusion acceleration (LDA) for k-eigenvalue neutron transport discretized with discontinuous finite element method (DFEM) and discrete ordinates(SN). This LDA is based on our two pieces of previous works: the flexible non linear diffusion acceleration (NDA) for DFEM-SN and LDA for k-eigenvalue neutron transport using pre-conditioned Jacobian-free Newton-Krylov with self-adjoint angular flux (SAAF), continuous finite element method(CFEM), and SN. We point out the differences between LDA and NDA for DFEM-SN and the difference between DFEM-SN and SAAF-CFEM-SN for LDA. Numerical tests are presented to compare the convergence behaviour of NDA and LDA. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1993

A priori error estimates for an hp-version of the discontinuous Galerkin method for hyperbolic conservation laws

A priori error estimates are derived for hp-versions of the finite element method for discontinuous Galerkin approximations of a model class of linear, scalar, first-order hyperbolic conservation laws. These estimates are derived in a mesh dependent norm in which the coefficients depend upon both the local mesh size h(sub K) and a number p(sub k) which can be identified with the spectral order of the local approximations over each element.

Bey, Kim S.↗
NASA NTRS1976

A nonlinear finite-element analysis of wings in steady incompressible flows with wake roll-up

The problem of lifting surfaces and complex aircraft configurations in steady incompressible flow is considered. For lifting surfaces the problem is formulated in terms of an integral equation relating the potential discontinuity on wing and wake to the normal derivative of the potential on the lifting surface. For complex configurations the problem is formulated in terms of an integral equation relating the potential to its normal derivative on the surface of the aircraft. The integral equation is approximated by a system of linear algebraic equations obtained by dividing the surfaces into small quadrilateral elements and by assuming the potential (or the potential discontinuity) and its normal derivative to be constant within each element. The wake geometry is obtained by iteration by satisfying the condition that the velocity be tangent to the surface of the wake and that the potential discontinuity be constant along the streamlines.

Suciu, E. O.↗
NASA NTRS1993

Characterization of Asymmetric Coplanar Waveguide Discontinuities

A general technique to characterize asymmetric coplanar waveguide (CPW) discontinuities with air bridges where both the fundamental coplanar and slotline modes may be excited together is presented. First, the CPW discontinuity without air bridges is analyzed using the space-domain integral equation (SDIE) approach. Second, the parameters (phase, amplitude, and wavelength) of the coplanar and slotline modes are extracted from an amplitude modulated-like standing wave existing in the CPW feeding lines. Then a 2n x 2n generalized scattering matrix of the n-port discontinuity without air bridges is derived which includes the occurring mode conversion. Finally, this generalized scattering matrix is reduced to an n x n matrix by enforcing suitable conditions at the ports which correspond to the excited slotline mode. For the purpose of illustration, the method is applied to a shielded asymmetric short-end CPW shunt stub, the scattering parameters of which are compared with those of a symmetric one. Experiments are performed on both discontinuities and the results are in good agreement with theoretical data. The advantages of using air bridges in CPW circuits as opposed to bond wires are also discussed.

Dib, Nihad I.↗
NASA NTRS1989

Cosmic rays at fluid discontinuities

Cosmic-ray transport near discontinuities in the background fluid velocity is considered. Matching conditions for the cosmic-ray distribution are derived for both shear and compressive (shock) discontinuities, keeping terms to second order in the ratio of fluid speed to energetic-particle speed. Acceleration is found at shear discontinuities, which is not present in the first-order theory, and a modification of the matching condition at shocks. If there is no particle source concentrated at a shock, the new condition reduces to that obtained from first-order theory. Monte Carlo simulations show good agreement with the theory.

Jokipii, J. R.↗
DOE OSTI2026

Assessment of the hydromechanical higher-order MPM for the simulation of geotechnical problems

The Material Point Method (MPM) has been increasingly used to simulate large strain deformations. Linear interpolation functions are commonly used to perform the spatial integration. It is well-known that the discontinuities in the interpolation function derivatives induce shock-like artifacts known as ‘cell-crossing’ error. These errors compound with volumetric locking errors when used with hydromechanical formulations for porous media, where different velocity fields are used for each phase. The capabilities of higher-order MPM frameworks have not been explored for real-scale geotechnical problems. As such, this paper aims to assess, validate, and further discuss a higher-order B-spline MPM (BS-MPM) framework. First, the BS-MPM framework is verified against the large-strain oedometer consolidation problem. Second, the framework is validated against a real-scale slope failure experiment triggered by pore water pressure recharge. Landslide features that are captured using the higher-order framework are specifically highlighted, and results (e.g., pore water pressure and deformation) are validated with field measurements. A generally convergent numerical solution is observed when using cubic interpolation functions. Third, a footing penetration problem is simulated using the multi-patch BS-MPM. Trends are examined with respect to penetration velocity and variation in hydraulic conductivity. The BS-MPM framework ultimately presents a stabilized numerical solution that captures plausible hydromechanical interaction trends important in geotechnical engineering applications.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Strong magnetoelastic coupling in Mn 3 X ( X = Ge , Sn)

Here we measure the full elastic tensors of Mn 3 Ge and Mn 3 Sn as a function of temperature through their respective antiferromagnetic phase transitions. Large discontinuities in the bulk moduli at the Néel transitions indicate strong magnetoelastic coupling in both compounds. Strikingly, the discontinuities are nearly a factor of 10 larger in Mn 3 Ge than in Mn 3 Sn. We use the magnitudes of the discontinuities to calculate the pressure derivatives of the Néel temperature, which are 39 K/GPa 14.3 K/GPa for Mn 3 Ge and Mn 3 Sn, respectively. We measured the in-plane shear modulus c 66 , which couples strongly to the magnetic order, in magnetic fields up to 18 T and found quantitatively similar behavior in both compounds. Recent measurements have demonstrated strong piezomagnetism in Mn 3 Sn : Our results suggest that Mn 3 Ge may be an even better candidate for this effect.

36 MATERIALS SCIENCE↗