Physics

We discuss the "hot hand" paradox within the framework of the backward Kolmogorov equation. We use this approach to understand the apparently paradoxical features of the statistics of fixed-length sequences of heads and tails upon repeated fair coin flips. In particular, we compute the average waiting time for the appearance of specific sequences. For sequences of length 2, the average time until the appearance of the sequence HH (heads-heads) equals 6, while the waiting time for the sequence HT (heads-tails) equals 4. These results require a few simple calculational steps by the Kolmogorov approach. We also give complete results for sequences of lengths 3, 4, and 5; the extension to longer sequences is straightforward (albeit more tedious). Finally, we compute the waiting times T nH for an arbitrary length sequences of all heads and T n(HT) for the sequence of alternating heads and tails. For large n , T 2nH ∼3 T n(HT) .

We consider how an advanced civilization might build a radiator to send gravitational waves signals by using small black holes. Micro black holes on the scale of centimeters but with masses of asteroids to planets are manipulated with a super advanced instrumentality, possibly with very large electromagnetic fields. The machine envisioned emits gravitational waves in the GHz frequency range. If the source to receiver distance is a characteristic length in the galaxy, up to 10000 light years, the masses involved are at least planetary in magnitude. To provide the energy for this system we posit a very advanced civilization that has a Kerr black hole at its disposal and can extract energy by way of super-radiance. Background gravitational radiation sets a limit on the dimensionless amplitude that can be measured at interstellar distance using a LIGO like detector.

We explore the gravitational dynamics of falling through planetary interiors. Two trajectory classes are considered: a straight cord between two surface points, and the brachistochrone path that minimizes the falling time between two points. The times taken to fall along these paths, and the shapes of the brachistochrone paths, are examined for the Moon, Mars, Earth, Saturn, and the Sun, based on models of their interiors. A toy model of the internal structure, a power-law gravitational field, characterizes the dynamics with one parameter, the exponent of the power-law, with values from -2 for a point-mass to +1 for a uniform sphere. Smaller celestial bodies behave like a uniform sphere, while larger bodies begin to approximate point-masses, consistent with an effective exponent describing their interior gravity.

We present an accurate two-dimensional mathematical model for steak cooking based on Flory-Rehner theory. The model treats meat as a poroelastic medium saturated with fluid. Heat from cooking induces protein matrix deformation and moisture loss, leading to shrinkage. Numerical simulations indicate good agreement with multiple sources of experimental data. Moreover, this work presents a new and computationally non-expensive method to account for shrinkage.

We use a feed-forward artificial neural network with back-propagation through a single hidden layer to predict Barry Cottonfield's likely reply to this author's invitation to the "Once Upon a Daydream" junior prom at the Conard High School gymnasium back in 1997. To examine the network's ability to generalize to such a situation beyond specific training scenarios, we use a L2 regularization term in the cost function and examine performance over a range of regularization strengths. In addition, we examine the nonsensical decision-making strategies that emerge in Barry at times when he has recently engaged in a fight with his annoying kid sister Janice. To simulate Barry's inability to learn efficiently from large mistakes (an observation well documented by his algebra teacher during sophomore year), we choose a simple quadratic form for the cost function, so that the weight update magnitude is not necessary correlated with the magnitude of output error. Network performance on test data indicates that this author would have received an 87.2 (1)% chance of "Yes" given a particular set of environmental input parameters. Most critically, the optimal method of question delivery is found to be Secret Note rather than Verbal Speech. There also exists mild evidence that wearing a burgundy mini-dress might have helped. The network performs comparably for all values of regularization strength, which suggests that the nature of noise in a high school hallway during passing time does not affect much of anything. We comment on possible biases inherent in the output, implications regarding the functionality of a real biological network, and future directions. Over-training is also discussed, although the linear algebra teacher assures us that in Barry's case this is not possible.

While dry Coulombic friction is an elementary topic in any standard introductory course in mechanics, the critical distinction between the kinetic and static friction forces is something that is both hard to teach and to learn. In this paper, I describe a geometric model of static friction that may help introductory students to both understand and apply the Coulomb static friction approximation.

We propose the use of specific dynamical processes and more in general of ideas from Physics to model the evolution in time of musical structures. We apply this approach to two ?tudes by F. Chopin, namely op.10 n.3 and op.25 n.1, proposing some original description based on concepts of symmetry breaking/restoration and quantum coherence, which could be useful for interpretation. In this analysis, we take advantage of colored musical scores, obtained by implementing Scriabin's color code for sounds to musical notation.

The fermi paradox uses an appeal to the mediocrity principle to make it seem counter-intuitive that humanity has not been contacted by extraterrestrial intelligence. A numerical, statistical analysis was conducted to determine whether this apparent loneliness is, in fact, unexpected. An inequality was derived to relate the frequency of life arising and developing technology on a suitable planet in the galaxy, the average length of time since the first broadcast of such a civilization, and a constant term. An analysis of the sphere reached thus far by human communication was also conducted, considering our local neighborhood and planets of particular interest. We clearly show that human communication has not reached a number of stars and planets adequate to expect an answer. These analyses both conclude that the Fermi paradox is not, in fact, unexpected. By the mediocrity principle and numerical modeling, it is actually unlikely that the Earth would have been reached by extraterrestrial communication at this point. We predict that under 1 percent of the galaxy has been reached at all thus far, and we do not anticipate to be reached until approximately half of the stars/planets have been reached. We offer a prediction that we should not expect this until at least 1,500 years in the future. Thus the Fermi paradox is not a shocking observation, and humanity may very well be contacted within our species' lifespan.

A formula is proposed to quantitatively estimate the signal emission rate of Communicating Extra-Terrestrial Intelligent civilizations (CETIs) in the Galaxy. I suggest that one possible type of CETI signal would be brief radio bursts similar to fast radio bursts (FRBs). A dedicated search for FRB-like artificial signals in the Galaxy for decades may pose a meaningful upper limit on the emission rate of these signals by CETIs. The Fermi-Hart paradox is answered in terms of not having enough observing times for this and other types of signals. Whether humans should send FRB-like signals in the far future is briefly discussed.

After a short review of basic biomechanics of Seoi Family and their characteristic, two fast survey of Seoi in judo books and in worldwide researches are performed. The lot of information collected around the world flow into the competitive application of this family (in Japanese view) or in the most energy convenient technical variation (in Biomechanical view) with the study of the last new solution or variation applied. An analysis of complementary tools utilized for each component of the Family to increase their effectiveness or refine their application to Ippon follow. Till to the new ways Chaotic applications based both on totally rotational application or reverse application of Seoi Lever System, with the conclusion at the end by a brief overview of Physical and Biomechanical framework connected to Seoi Family, with a more extended study of interaction ( Seoi application to throws). Conclusion is presented with a comparative evaluation of some remarkable properties all applicable competitive Seoi techniques useful both for coaches and teachers