I propose that stiffness may be defined and quantified for nonlinear systems using Lyapunov exponents, and demonstrate the relationship that exists between stiffness and the fractal dimension of a strange attractor: that stiff chaos is thin chaos. What constitutes a stiff dynamical system? Stiffness is closely related to numerical methods [1]: the signature of stiffness in a problem is that, up...

We point out that the existence of post-inflationary phases stiffer than radiation leads to the production of stochastic gravitational waves (GW) backgrounds whose logarithmic energy spectra (in critical units) are typically “blue” at high frequencies. The maximal spectral slope (for present frequencies larger than 10 Hz) is of order one and it is related to the maximal sound velocity of the st...

Stiff-knee gait is characterized by diminished and delayed knee flexion during swing. Rectus femoris transfer surgery, a common treatment for stiff-knee gait, is often recommended when a patient exhibits prolonged activity of the rectus femoris muscle during swing. Treatment outcomes are inconsistent, in part, due to limited understanding of the biomechanical factors contributing to stiff-knee ...

It is well known that psychological stress affects health status. Stiff neck and shoulder in a broad sense is one of the major somatic complaints among Japanese. The objective was to determine how much perceived stress and stiff neck/shoulder are associated with health-related quality of life (HRQoL) by gender. Participants (n = 512) completed the Japanese version of Perceived Stress Scale, the...

Paraneoplastic Encephalomyelitis, Stiff Person Syndrome and Breast Carcinoma Paraneoplastic syndromes (PNS) are the rarest non-metastatic neurological complications of cancers in which no specific etiology can be identified. Among PNS, stiff person syndrome is characterized by “rock-hard” rigidity and painful spasms in distal limbs, most frequently legs, and abnormal foot and/or hand posture. G...

We first derive necessary and sufficient stiff order conditions, up to order four, for exponential splitting schemes applied to semilinear evolution equations. The main idea is to identify the local splitting error as a sum of quadrature errors. The order conditions of the quadrature rules then yield the stiff order conditions in an explicit fashion, similarly to that of Runge–Kutta schemes. Fu...

We consider the combustion equation as one of the candidates from the class of stiff ordinary differential equations. A solution over a length of time that is inversely proportional to δ > 0 (where δ > 0 is a small disturbance of the pre-ignition state) is sought. This problem has a transient at the midpoint of the integration interval. The solution changes from being non-stiff to stiff, and af...

The natural stiffness of DNA, which contributes to the interactions of the many proteins involved in its biological processing and packaging, also plays an important role in modern nanotechnology. Here we report new Monte-Carlo simulations of deformable DNA molecules of potential utility in understanding the behavior of the long, double-helical polymer in the tight confines of a cell and in the...

Ultrasound elastography, a technique used to assess mechanical properties of soft tissue is of major interest in the detection of breast cancer as it is stiffer than the surroundings. Techniques such as ultrasound quasi-static elastography have been developed to assess the strain distribution in soft tissues in two dimensions using a quasi-static compression. However, tumors can exhibit very he...