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The Omori-Utsu law shows the temporal power-law-like decrease of the frequency of earthquake aftershocks and, interestingly, is found in a variety of complex systems/phenomena exhibiting catastrophes. Now, it may be interpreted as a characteristic response of such systems to large events. Here, hierarchical dynamics with the fast and slow degrees of freedom is studied on the basis of the Fokker-Planck theory for the load-state distribution to formulate the law as a relaxation process, in which diffusion coefficient in the space of the load state is treated as a fluctuating slow variable. The evolution equation reduced from the full Fokker-Planck equation and its Green's function are analyzed for the subdynamics governing the load state as the fast degree of freedom. It is shown that the subsystem has the temporal translational invariance in the logarithmic time, not in the conventional time, and consequently the aging phenomenon appears.

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We developed a confocal microscopic method for a quantitative evaluation of the mixing performance of a three-dimensional microfluidic mixer. We fabricated a microfluidic baker's transformation (MBT) mixer as a three-dimensional passive-type mixer for the efficient mixing of solutions. Although the MBT mixer is one type of ideal mixers, it is hard to evaluate its mixing performance, since the MBT mixer is based on several cycles of complicated three-dimensional microchannel structures. We applied the method developed here to evaluate the mixing of water and a fluorescein isothiocyanate (FITC; diffusion coefficient, 4.9 × 10(-10) m(2) s(-1)) solution by the MBT mixer. This method enables us to capture vertical section images for the fluid distributions of FITC and water at different three-dimensional microchannel structures of the MBT device. These images are in good agreement with those of mixing images based on numerical simulations. The mixing ratio could be calculated by the fluorescence intensity at each pixel of the vertical section image; complete mixing is recognized by a mixing ratio of more than 90%. The mixing ratios are measured at different cycles of the MBT mixer by changing the flow rate; the mixing performance is evaluated by comparisons with the mixing ratio of the straight microchannel without the MBT mixer.

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We developed a new passive-type micromixer based on the baker's transformation and realized a fast mixing of a protein solution, which has lower diffusion constant. The baker's transformation is an ideal mixing method, but there is no report on the microfluidic baker's transformation (MBT), since it is required to fabricate the complicated three-dimensional (3D) structure to realize the MBT device. In this note, we successfully fabricate the MBT device by using precision diamond cutting of an oxygen-free copper substrate for the mould fabrication and PDMS replication. The MBT device with 10.4 mm mixing length enables us to achieve complete mixing of a FITC solution (D = 2.6 × 10(-10) m(2) s(-1)) within 51 ms and an IgG solution (D = 4.6 × 10(-11) m(2) s(-1)) within 306 ms. Its mixing speed is 70-fold higher for a FITC solution and 900-fold higher for an IgG solution than the mixing speed by the microchannel without MBT structures. The Péclet number to attain complete mixing in the MBT device is estimated to be 6.9 × 10(4).

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BACKGROUND: We have recently found that the median relative risk value (RRV) (0-1) of brain infarction estimated by protein-conjugated acrolein (PC-Acro), IL-6 and CRP together with age was in the order silent brain infarction (SBI) (0.80)>carotid atherosclerosis (CA) (0.76)>white matter hyperintensity (WMH) (0.46)>control (0.14). We clarified how metabolic disorders [hypertension (HT), hyperlipidemia (HL) and hyperglycemia (HG)] are correlated with RRV. METHODS: The levels of PC-Acro, IL-6 and CRP in plasma were measured by ELISA. SBI and WMH were evaluated by MRI, and CA was evaluated by duplex carotid ultrasonography. RESULTS: The median RRV of metabolic disorders was in the order HT+HG (0.84)>HT+HL (0.73)>HT (0.65)≈HG (0.65)>HL (0.61)>HL+HG (0.48)>no metabolic disorder (0.24)>normal (0.11). Correlation with SBI was in the order HT+HG (52%)>HT+HL (42%)>HT (40%)>HG (34%)≈HL(33%)>HL+HG (14%)≈no metabolic disorder (14%). CONCLUSION: The results indicate that HT is the most strongly associated factor with SBI among metabolic disorders and that the seriousness of metabolic disorder estimated by RRV was well correlated with SBI.

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OBJECTIVE: We found previously that the measurement of plasma levels of protein-conjugated acrolein (PC-Acro) together with IL-6 and CRP can be used to identify silent brain infarction (SBI) with high sensitivity and specificity. The aim of this study was to clarify how three biochemical markers are correlated to SBI, carotid atherosclerosis (CA) and white matter hyperintensity (WMH). METHODS: The levels of PC-Acro, IL-6 and CRP in plasma were measured by ELISA. SBI and WMH were evaluated by MRI, and CA was evaluated by duplex carotid ultrasonography. RESULTS: A total of 790 apparently healthy volunteers were classified into 260 control, 214 SBI, 263 CA and 245 WMH subjects, which included 187 subjects with two or three pathologies. When the combined measurements of PC-Acro, IL-6 and CRP were evaluated together with age, using a receiver operating characteristic curve and artificial neural networks, the relative risk value (RRV), an indicator of tissue damage, was in the order SBI with CA (0.90)>SBI (0.80)>CA (0.76)>WMH with CA (0.65)>WMH (0.46)>control (0.14). RRV was also correlated with severity in each group of SBI, CA and WMH. CONCLUSION: The RRV supports the idea that the degree of risk to develop a stroke is in the order SBI>CA>WMH.

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To characterize the dynamical features of seismicity as a complex phenomenon, the seismic data are mapped to a growing random graph, which is a small-world scale-free network. Here, hierarchical and mixing properties of such a network are studied. The clustering coefficient is found to exhibit asymptotic power-law decay with respect to connectivity, showing hierarchical organization. This structure is supported by not only main shocks but also small shocks, and may have its origin in the combined effect of vertex fitness and deactivation by stress release at faults. The nearest-neighbor average connectivity and the Pearson correlation coefficient are also calculated. It is found that the earthquake network has assortative mixing. This is a main difference of the earthquake network from the Internet with disassortative mixing. Physical implications of these results are discussed.

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The cumulative probability distribution of sparseness time interval in the Internet is studied by the method of data analysis. Round-trip time between a local host and a destination host through ten odd routers is measured using the ping command, i.e., doing an echo experiment. The data are found to be well described by q-exponential distributions, which maximize the Tsallis entropy indexed by q less or larger than unity, showing a scale-invariant feature of the system. The network is observed to itinerate over a series of the nonequilibrium stationary states characterized by Tsallis statistics.