Determination of a Strain Energy Density Function for the Tricuspid Valve Leaflets Using Constant Invariant-Based Mechanical Characterizations

The tricuspid valve (TV) regulates the blood flow within the right side of the heart. Despite recent improvements in understanding TV mechanical and microstructural properties, limited attention has been devoted to developments of TV-specific constitutive models. The objective of this work is to use the first-of-its-kind experimental data from constant invariant-based mechanical characterizations to determine a suitable invariant-based strain energy density function (SEDF). Six specimens for each TV leaflet are characterized using constant invariant mechanical testing. The data is then fit with three candidate SEDF forms: (i) a polynomial model as the transversely isotropic version of the Mooney-Rivlin model, (ii) an exponential model, and (iii) a combined polynomial-exponential model. Similar fitting capabilities were found for the exponential and polynomial forms (R2=0.92-0.99 vs. 0.91-0.97) compared to the combined polynomial-exponential SEDF (R2=0.65-0.95). Furthermore, the polynomial form had larger Pearson's correlation coefficients than the exponential form (0.51 vs. 0.30), indicating a more well-defined search space. Finally, the exponential and combined polynomial-exponential forms had notably smaller but more eccentric model parameter's confidence regions than the polynomial form. Further evaluations of invariant decoupling revealed that the decoupling of the invariant terms within the exponential SEDF leads to a less satisfactory performance. From these results, we conclude that the exponential form is better suited for the TV leaflets due to its superb fitting capabilities and smaller parameter's confidence regions.

Cooperative games with additive multiple attributes

This paper studies cooperative games in which players have multiple attributes. Such games are applicable to situations in which each player has a finite number of independent additive attributes in cooperative games and the payoffs of coalitions are endogenous functions of these attributes. The additive attributes cooperative game, which is a special case of the multiattribute cooperative game, is studied with respect to the core, the conditions for existence and boundedness and methods of transformation regarding a general cooperative game. A coalitional polynomial form is also proposed to discuss the structure of coalition. Moreover, a Shapley-like solution called the efficient resource (ER) solution for additive attributes cooperative games is studied via the axiomatical method, and the ER solution of two additive attribute games with equivalent total resources coincides with the Shapley value. Finally, some examples of additive attribute games are given.

Analysis of a Regulated Cascode Cross Couple Power Amplifier

The input impedance of a regulated cascode cross couple amplifier is derived. The frequency response of the input impedance polynomial form can be plotted with MATLAB. From the polynomial form of the input impedance of the proposed circuit, it can be transformed by substitute complex frequency s with jω into the polynomial form equation. After that, this function can be grouped into a symbolic real and a symbolic imaginary form. The next step in derivation is to multiply this function with a complex conjugate function of the symbolic complex form of the input impedance. The last step is to plot a real and an imaginary part as a function of the input frequency so that the power amplifier can be matching with the various matching circuit according to the condition of the maximum power transfer.

Uniform Energy Decay Rates for the Fuzzy Viscoelastic Model with a Nonlinear Source

This paper considers the fuzzy viscoelastic model with a nonlinear source u t t + L u + ∫ 0 t g t − ζ Δ u ζ d ζ − u γ u − η Δ u t = 0 in a bounded field Ω. Under weak assumptions of the function g t , with the aid of Mathematica software, the computational technique is used to construct the auxiliary functionals and precise priori estimates. As time goes to infinity, we prove that the solution is global and energy decays to zero in two different ways: the exponential form and the polynomial form.

New pancake series for π

In [1], Dalzell proved that $\pi = \frac{{22}}{7} - \int_0^1 {\frac{{{t^4}{{(1 - t)}^4}}}{{1 + {t^2}}}}$ . He then used this equation to derive a new series converging to π. In [2], Backhouse studied the general case of integrals of the form $\int_0^1 {\frac{{{t^m}{{(1 - t)}^m}}}{{1 + {t^2}}}dt}$ and derived conditions on m and n so that they could be used to evaluate π. As a sequel, he derived accurate rational approximations of π. This work was extended in [3] where new rational approximations of π are obtained. Some related integrals of the forms $\int_0^1 {\frac{{{t^m}{{(1 - t)}^m}}}{{1 + {t^2}}}P(t)\,dt}$ and $\int_0^1 {\frac{{{t^m}{{(1 - t)}^m}}}{{\sqrt {1 - {t^2}} }}P(t)dt}$ with P(t) being of polynomial form are also investigated. In [4] the author gives more new approximations and new series for the case m = n = 4k. In [5] new series for π are obtained with the integral $\int_0^a {\frac{{{t^{12m}}{{(a - t)}^{12m}}}}{{1 + {t^2}}}dt}$ where $a = 2 - \sqrt 3$ . The general problem of improving the convergence speed of the arctan series by transformation of the argument has also been considered in [6, 7]. In the present work the author considers an alternative form for the denominators in integrals. As a result, new series are obtained for multiples of π by some algebraic numbers.

Conservation laws and Darboux transformations for a 3-coupled integrable lattice equations

In this paper, we firstly establish infinitely many conservation laws of the 3-coupled integrable lattice equations by using the Riccati method. Comparing with the results obtained by Sahadevan and Balakrishnan, we not only get infinite conserved densities of the polynomial form, but also some conserved densities of logarithmic form. Secondly, Darboux transformation for the system is derived with the help of the Lax pair and gauge transformation. Finally, we obtain the exact solutions of the system with the obtained Darboux transformation, and present the soliton solutions and their figures with properly parameters.

Minimal Model for Sprag-Slip Oscillation as Catastrophe-Type Behavior

The infinite spragging force can be produced by a spring inclined with a constant angle in a frictional sliding system. The ensuing oscillation is called the sprag-slip oscillation. This sprag-slip oscillation is re-examined by using the minimal nonlinear dynamic model with the variable angle of the inclined spring. Nonlinear equilibrium equation is converted into the novel polynomial form. This simple but more realistic sprag model shows that the infinite spragging force is not realistic and the catastrophic static deformation in the steady-sliding state can occur. It indicates that the ‘sprag’, termed by Spurr, can be described by this catastrophic characteristic of the frictional sliding system.