On space-like constant slope surfaces and Bertrand curves in Minkowski 3-space

In the present paper, we define the notions of Lorentzian Sabban frames and de Sitter evolutes of the unit speed space-like curves on de Sitter 2-space $\mathbb{S}^{2}_{1}$. In addition, we investigate the invariants and geometric properties of these curves. Afterwards, we show that space-like Bertrand curves and time-like Bertrand curves can be constructed from unit speed space-like curves on de Sitter 2-space $\mathbb{S}^{2}_{1}$ and hyperbolic space $\mathbb{H}^{2}$, respectively. We obtain the relations between Bertrand curves and helices. Also we show that pseudo-spherical Darboux images of Bertrand curves are equal to pseudo-spherical evolutes in Minkowski 3-space $\mathbb{R}^{3}_{1}$. Moreover we investigate the relations between Bertrand curves and space-like constant slope surfaces in $\mathbb{R}^{3}_{1}$. Finally, we give some examples to illustrate our main results.Comment: 16 pages, 4 figures. Accepted for publication in the Scientific Annals of "Al.I. Cuza" University of Ias

Time-like constant slope surfaces and space-like Bertrand curves in Minkowski 3-space

Defining Lorentzian Sabban frame of the unit speed time-like curves on de Sitter 2-space $\mathbb{S}^{2}_{1}$ and introducing space-like height function on the unit speed time-like curves on $\mathbb{S}^{2}_{1}$, the invariants of the unit speed time-like curves on $\mathbb{S}^{2}_{1}$ and geometric properties of de Sitter evolutes of the unit speed time-like curves on $\mathbb{S}^{2}_{1}$ are studied. A relation between space-like Bertrand curves and helices is obtained. De Sitter Darboux images of space-like Bertrand curves are equal to de Sitter evolutes. The relations between time-like constant slope surfaces lying in the space-like cone and space-like Bertrand curves in Minkowski 3-space $\mathbb{R}^{3}_{1}$ are obtained.Comment: 15 Pages, 2 Figures. Accepted for publication in the Proceedings of the National Academy of Sciences, India Section A: Physical Science

Acoustic Insulation Behavior of Composite Nonwoven

Multilayer or multicomponent composite nonwoven structures provide great advantages for many technical applications. Spunbond-meltblown-spunbond (SMS) type multilayer nonwovens have significant commercial success in terms of end-use versatility. SMS type composite nonwovens, which can be produced with both continuous and discontinuous production technologies, are evolving day by day. Bulky, fibrous, porous nonwoven structures are widely used as sound absorbers for a variety of applications for instant building and automotive insulations, machine insulations, etc. The fibers interlocking in nonwovens are the frictional elements and provide resistance to acoustic wave motion. As many researchers reported, the most effective factors on sound absorption properties of fibrous materials are fiber diameter, airflow resistance, material thickness, tortuosity, porosity, and fiber surface area. In this research chapter, the sound absorption performance of SMS type composite nonwovens in relation to air permeability and pore sizes has been determined. The results show that SMS type nonwovens perform sound insulation at high frequencies. Spunmelt nonwovens with the advantages of short production line will create various alternatives with varieties of layering and compete with commercially used other sound absorbers

Fiber Selection for the Production of Nonwovens

The most significant feature of nonwoven fabric is made directly from fibers in a continuous production line. While manufacturing nonwovens, some conventional textile operations, such as carding, drawing, roving, spinning, weaving or knitting, are partially or completely eliminated. For this reason the choice of fiber is very important for nonwoven manufacturers. The commonly used fibers include natural fibers (cotton, jute, flax, wool), synthetic fibers (polyester (PES), polypropylene (PP), polyamide, rayon), special fibers (glass, carbon, nanofiber, bi-component, superabsorbent fibers). Raw materials have not only delivered significant product improvements but also benefited people using these products by providing hygiene and comfort

Timelike Loxodromes on Lorentzian Helicoidal Surfaces in Minkowski N–Space

In this paper, we examine timelike loxodromes on three kinds of Lorentzian helicoidal surfaces in Minkowski n–space. First, we obtain the first order ordinary differential equations which determine timelike loxodromes on the Lorentzian helicoidal surfaces in E n 1 according to the causal characters of their meridian curves. Then, by finding general solutions, we get the explicit parametrizations of such timelike loxodromes. In particular, we investigate the timelike loxodromes on the three kinds of Lorentzian right helicoidal surfaces in E n 1 . Finally, we give an example to visualize the result