Search

We prove two partial regularity results for the scalar equation $u_t+u_{xxxx}+\partial_{xx}u_x^2=0$, a model of surface growth arising from the physical process of molecular epitaxy. We show that the set of space-time singularities has (upper) box-counting dimension no larger than $7/6$ and $1$-dimensional (parabolic) Hausdorff measure zero. These parallel the results available for the three-dimensional Navier--Stokes equations. In fact the mathematical theory of the surface growth model is known to share a number of striking similarities with the Navier--Stokes equations, and the partial regularity results are the next step towards understanding this remarkable similarity. As far as we know the surface growth model is the only lower-dimensional "mini-model" of the Navier--Stokes equations for which such an analogue of the partial regularity theory has been proved. In the course of our proof, which is inspired by the rescaling analysis of Lin (1998) and Ladyzhenskaya & Seregin (1999), we develop certain nonlinear parabolic Poincar\'e inequality, which is a concept of independent interest. We believe that similar inequalities could be applicable in other parabolic equations., Comment: 29 pages

In their 1968 paper Fujita and Watanabe considered the issue of uniqueness of the trivial solution of semilinear parabolic equations with respect to the class of bounded, non-negative solutions. In particular they showed that if the underlying ODE has non-unique solutions (as characterised via an Osgood-type condition) {\em and} the nonlinearity $f$ satisfies a concavity condition, then the parabolic PDE also inherits the non-uniqueness property. This concavity assumption has remained in place either implicitly or explicitly in all subsequent work in the literature relating to this and other, similar, non-uniqueness phenomena in parabolic equations. In this paper we provide an elementary proof of non-uniqueness for the PDE without any such concavity assumption on $f$. An important consequence of our result is that uniqueness of the trivial solution of the PDE is equivalent to uniqueness of the trivial solution of the corresponding ODE, which in turn is known to be equivalent to an Osgood-type integral condition on $f$.

This paper establishes the local-in-time existence and uniqueness of strong solutions in $H^{s}$ for $s > n/2$ to the viscous, non-resistive magnetohydrodynamics (MHD) equations in $\mathbb{R}^{n}$, $n=2, 3$, as well as for a related model where the advection terms are removed from the velocity equation. The uniform bounds required for proving existence are established by means of a new estimate, which is a partial generalisation of the commutator estimate of Kato & Ponce (Comm. Pure Appl. Math. 41(7), 891-907, 1988).

Current theoretical results for the three-dimensional Navier--Stokes equations only guarantee that solutions remain regular for all time when the initial enstrophy ($\|Du_0\|^2:=\int|{\rm curl} u_0|^2$) is sufficiently small, $\|Du_0\|^2\le\chi_0$. In fact, this smallness condition is such that the enstrophy is always non-increasing. In this paper we provide a numerical procedure that will verify regularity of solutions for any bounded set of initial conditions, $\|Du_0\|^2\le\chi_1$. Under the assumption that the equations are in fact regular we show that this procedure can be guaranteed to terminate after a finite time.

The Arkansas Future Ag Leaders tour is a 5-day professional development opportunity for undergraduate juniors and seniors enrolled in colleges of agriculture or pursuing agriculture-related majors across the state of Arkansas. Agriculture and agriculture-related professions are the largest employers in the state. This 1-week experience enhances students' leadership and employability skills, provides firsthand networking opportunities with potential employers, and highlights the vast resources, services, and careers available through Arkansas' agriculture industry. The call for applications goes out to all colleges with agriculture-related academic departments. Institutions with agriculture departments will be guaranteed a set number of seats if they designate participants by a specified date. Following the initial application deadline, the remaining unfilled seats will be open to any interested applicants, regardless of institutional affiliation. [ABSTRACT FROM AUTHOR]

The Soybean Science Challenge (SSC) continues to support Arkansas STEM (science, technology, engineering, and mathematics) educational goals and is aligned with the Next Generation Science Standards (NGSS), which engages junior high and high-school students in active learning and the co-creation of knowledge through support of classroombased lessons and applied student research. The SSC educates and engages junior high and high school science students and teachers in "real-world" Arkansas-specific soybean science education through original NGSS-aligned curriculum in 7E and GRC-3D format, and a continuum of educational methods, which include teacher workshops, online and virtual live stream education, virtual NGSS aligned mini-lessons for the science classroom, community gardens, personal mentoring, student-led research and corresponding award recognition, and partnerships with state and national educators, agencies and the popular media. Even as in-person instruction returned to a new normal postpandemic, the educational landscape looked different in 2022. The nature of the existing design and methodology of the SSC facilitated the launching of online Next Generation Science Standards (NGSS) Aligned Gathering Reasoning and Communicating (GRC)-3D and 7E lesson plans for teachers. An additional online course was added that included NGSS-aligned mini-lesson videos for the science classroom and additional virtual field trips to the list on the Soybean Science Challenge website. The Soybean Science Challenge was active in science fairs across the state, judging regional and state participants. In addition, the SSC is in its third year of the junior-level award at regional science fairs. Through the SSC, teachers now have access to many educational instructions that bring real-world agricultural critical thinking into the classroom and homes of students. The SSC has learned that Arkansas teachers and students benefit from these additional resources, and teachers and students from other states also benefit. [ABSTRACT FROM AUTHOR]

The Soybean Science Challenge (SSC) continues to support Arkansas STEM (science, technology, engineering, and mathematics) educational goals. It aligns with the Next Generation Science Standards (NGSS). Junior high and highschool students are engaged in active learning and the co-creation of knowledge through the support of classroombased lessons and applied student research. The SSC educates and engages junior high and high school science students and teachers in 'real-world' Arkansas-specific soybean science education through an original NGSS-aligned curriculum in 7E and GRC-3D format and a continuum of educational methods, which include: teacher workshops, online and virtual live stream education, virtual NGSS aligned mini-lessons for the science classroom, community gardens, personal mentoring, student-led research and corresponding award recognition, and partnerships with state and national educators, agencies and the popular media. The COVID19 global pandemic continued to alter the educational landscape in 2021, despite increased in-person instruction. The Soybean Science Challenge (SSC), by nature of its existing design and methodology, launched online Next Generation Science Standards (NGSS) aligned Gathering Reasoning and Communicating (GRC)-3D and 7E lesson plans for teachers. An online course was added, including NGSS-aligned mini-lesson videos for the science classroom, and additional virtual field trips were added to the list on the Soybean Science Challenge website. The Challenge also sponsored the Arkansas Science Teacher Association Conference in October 2021, and the SSC Coordinator Diedre Young conducted a workshop on bringing agriculturally based lessons into the science classroom. The Soybean Science Challenge was also active in science fairs across the state, judging participants at both the regional and state levels. The SSC is in its second year of the junior level award at regional science fairs. Through the SSC, teachers now have access to a plethora of educational instructions that bring real-world agricultural critical thinking into the classroom and students' homes. The SSC has learned that not only do Arkansas teachers and students benefit from these additional resources but teachers and students from other states benefit as well. In 2021, the SSC program reached over 3,000 students and teachers through in-person, digital, virtual, and print methods. [ABSTRACT FROM AUTHOR]

The Soybean Science Challenge (SSC) continues to support Arkansas STEM (science, technology, engineering, and mathematics) educational goals, is aligned with the Next Generation Science Standards (NGSS and engages junior high and high school students in active learning and the co-creation of knowledge through support of classroom-based lessons and applied student research. The SSC educates and engages junior high and high school science students and teachers in ‘real-world’ Arkansas specific soybean science education through original NGSS aligned curriculum in 7E and Gathering Reasoning and Communicating (GRC)-3D format and a continuum of educational methods which include: teacher workshops, online and virtual education, NGSS aligned mini-lessons for science classrooms, community gardens, personal mentoring, student-led research and corresponding award recognition, and partnerships with state and national educators, agencies, and the popular media. The COVID-19 global pandemic altered the educational landscape in 2020 and continues to do so. The new educational environment has seen an increase in virtual classrooms, online courses, and interactions with Zoom©. The Soybean Science Challenge (SSC), by nature of its existing design and methodology, was and is amid these methods by launching online Next Generation Science Standards (NGSS) aligned Gathering Reasoning and Communicating (GRC)-3D and 7E lesson plans for teachers, adding an online course, adding NGSS aligned mini-lesson videos for the science classroom, and adding virtual field trips to the list on the Soybean Science Challenge website. The Challenge also sponsored the virtual Arkansas Science Teacher Association Conference, and the SSC Coordinator taught virtual workshops on bringing agriculturally based lessons into science classrooms. The Soybean Science Challenge virtually judged participants at both the regional and state level, and SSC added a junior level award at regional science fairs. Through the SSC, teachers now have access to a plethora of educational instructions that bring real-world agricultural critical thinking both into the classroom and the homes of students. [ABSTRACT FROM AUTHOR]

Results of an experimental investigation of the oxidation protection afforded to Ti-14Al-21Nb and Ti-14Al-23Nb-2V titanium aluminides and Ti-17Mo-3Al-3Nb titanium alloy by aluminum-boron-silicon and boron-silicon coatings are presented. These coatings are applied by a combination of physical vapor deposition (PVD) and chemical vapor deposition (CVD) processes. The former is for the application of aluminum, and the latter is for codeposition of boron and silicon. Coating thickness is in the range of 2 to 7 microns, and coating weights are 0.6 to 2.0 mg/sq cm. Oxidation testing was performed in air at temperatures to 1255 K in both static and hypersonic flow environments. The degree of oxidation protection provided by the coatings is determined from weight change measurements made during the testing and post test compositional analyses. Temperature-dependent total normal emittance data are also presented for four coating/substrate combinations. Both types of coatings provided excellent oxidation protection for the exposure conditions of this investigation. Total normal emittances were greater than 0.80 in all cases.

CVD coatings of boron-oxygen-silicon and aluminum-boron-oxygen and silicon compositions were applied to alpha 2 and gamma titanium-aluminide alloys, and tested under simulated earth reentry conditions to evaluate oxidation protection, recombination effifiency and total emittance under cyclic exposures between temperatures of 300 and 1255 K. The degree of oxidation protection afforded to the alloys was evaluated from the amount of specimen weight gain after a 100 hour exposure to air at atmospheric pressure and at a temperature of 1255 K. Data are presented for two types of coatings, a monolithic and a multilayer, which have recombination efficiencies from 0.005 to 0.020 after ten one-half hour long simulated reentry cycles. Total normal emittance was 0.80 or greater and weight gain was less than 10 g/sq m both coating types. Compositional and morphological changes resulting from the exposures are discussed in relation to time-dependent variations in recombination efficiency.