Hutchinsonianism and the Newtonian Enlightenment

Abstract. Historians of science have labeled followers of the 18th cosmologist John Hutchinson (1674– 1737) as anti‐Newtonian. While Hutchinson was clearly anti‐Newtonian, this was not the case with later followers like George Horne and William Jones. Horne and Jones sought a rapprochement between Newton and Hutchinson; in their hands, interpretations of Newton's works were refashioned to support Hutchinson's biblically based cosmos and Trinitarian natural philosophy. Newton's thought could be used by conservative Anglican Churchmen to battle religious heterodoxy. This raises problems for traditional Enlightenment historiography which views Newtonianism as a set of ideas which supported and reinforced emerging modern forms of political and religious thought.     

Computing the Kantorovich Distance for Images

Computing the Kantorovich distance for images is equivalent to solving a very large transportation problem. The cost-function of this transportation problem depends on which distance-function one uses to measure distances between pixels.In this paper we present an algorithm, with a computational complexity of roughly order (N2), where N is equal to the number of pixels in the two images, in case the underlying distance-function is the L1-metric, an approximation of the L2-metric or the square of the L2-metric; a standard algorithm would have a computational complexity of order (N3). The algorithm is based on the classical primal-dual algorithm.The algorithm also gives rise to a transportation plan from one image to the other and we also show how this transportation plan can be used for interpolation and possibly also for compression and discrimination.     

Linearized Crank–Nicolson method for solving the nonlinear fractional diffusion equation with multi-delay

This paper is concerned with numerical solution of the nonlinear fractional diffusion equation with multi-delay. The studied model plays a significant role in population ecology. A linearized Crank–Nicolson method for such problem is proposed by combing the Crank–Nicolson approximation in time with the fractional centred difference formula in space. Using the discrete energy method, the suggested scheme is proved to be uniquely solvable, stable and convergent with second-order accuracy in both space and time for sufficiently small space and time increments. Several numerical experiments for solving the delay fractional Hutchinson equation and two real problems in population dynamics are provided to verify our theoretical results.     

Investigation on constraint effect of reactor pressure vessel under pressurized thermal shock

In recent years, the integrity of reactor pressure vessels (RPVs) under pressurized thermal shock (PTS) accident has been treated as one of the most critical issues. Under PTS condition, the combination of thermal stress due to a steep temperature gradient and mechanical stress due to internal pressure causes considerable tensile stress inside the RPV wall. As a result, cracks on the inner surface of RPVs can experience elastic-plastic behavior that can be explained using the J-integral. In such a case, however, the J-integral may possibly lose its validity due to the constraint effect. The degree of constraint effect is influenced by the loading mode, the crack geometry and the material properties. In this paper, three-dimensional finite element analyses are performed for various surface cracks to investigate the effect of clad thickness and crack geometry on the constraint effect. A total of 36 crack geometries are analyzed and results are presented by the two-parameter characterization based on the J-integral and the Q-stress.     

Improved digital signature protocol using iterated function systems

In this paper, a novel digital signature protocol is proposed. It is based on the iterated function system attractor, which is regarded as an emerging method. The idea behind our proposed method is based on selecting a known fractal set and then finding the attractor of the affine transformation functions. The attractor is then used in the encryption and decryption of a hash function to ensure the protection of the document from eavesdropping and integrity during the transmission. The properties and software implementation of the proposed protocol are discussed in detail. A comparison is made with the Rivest, Shamir, and Adleman cryptosystems, which shows that it performs better.