(logo description)
We study the limiting dynamics of nonlinear spatially extended systems of type:
ψtt + ηψt + dV(φ)/dφ + dU(φx)/dφx = F(x,φ,φx,...)
We show that the limiting dynamics has a nontrivial conserved quantity H for F=0. We call this quantity structure since it is a measure for the maximum amplititude of the oscillations. We show that there is a structure work theorem:
H(x2) = H(x1) + Ix1 x2F(x)dx
Further we show that structure has an addition property. If a system with structure H1 is coupled to a systems with structure H2 the structure of the combined system is H1+H2 plus a boundary term which is negegible small if the coupling is small. We apply these finding to chemical wave patterns, solitary water waves, and de Broglie waves.
Davit Sivil and Alfred Hübler
In this experiment, we studied the relationship between low dimensional macroscopic models (with constraints and singularities) and the corresponding smooth microscopic models without constraints. We find that the macroscopic models accurately predict the statistical properties, and are well suited for prediction and control.
Joe Brewer and Alfred Hübler
 Fig. 1: Photo of experimental setup showing electrodes imersed in liquid nitrogen. An emulsion of superconduction particles has been placed between the electrodes. |
Ilya Prigogine’s work on minimum entropy production suggests that in many open systems the state of least resistance is an attractor. However, superconductivity appears to be outside this class of systems. In superconducting systems, when the current is increased, the magnetic field associated with the current eventually destroys superconductivity. This in turns leads to large increases in resistance and power consumption in the system.
In our experiment we show that a small current can induce superconductivity and thus reduce the resistance as predicted by Progogine’s theory. When the temperature is held to slightly above TC, superconducting fluctuations in the material are set up. When a small current is imposed on these superconduction fluctuations, they become electrically polarized, attract each other, and assemble themselves into a superconducting connection. We found this effect to be particularly strong when we applied an electric current between two locations within an emulsion of superconducting particles inliquid nitrogen. Initially there is a high resistance between the electrodes and the power consumption is large. However, due to the electric field, the superconduction particles assembled themselves into wires and eventually form a superconduction connection between the electrodes. At that point, the resistance and the power consumption drop to a very small value.
Marshall Kuypers and Alfred Hübler
 Fig. 2: Artistic rendition of the components of a digital quantum battery. |
Electromagnetic fields in vacuum store energy. Energy in lithium batteries, gasoline and hydrogen gas is stored in the electric field in the vacuum between the atoms. Energy in all types of capacitors is also stored in vacuum electric fields between oppositely charged electrodes.
Energy storage in chemical systems is limited by diffusion, fractal growth of electrodes and irreversible side reactions, and works only within a small temperature range. Hydrogen and hydrocarbons, such as gasoline, are commonly used for energy storage. Unfortunately, molecular hydrogen is difficult to handle and the energy retrieval from hydrogen and hydrocarbons in heat engines and fuel cells is slow and inefficient.
If the electric field in conventional capacitors exceeds E=3 x 106 V/m in air (6 x 107 V/m in Teflon) the capacitor discharges by arcing and the energy is lost. We show that nanoscale capacitors can hold fields of 109 V/m without arcing. This means they can hold the same energy density as chemical systems while charging and discharging a billion times faster and lasting for a decade of constant use. Further, they are fully operational from -273℃ to 500℃ and are constructed from non-toxic metals and carbon.
Alfred Hübler, Dave Lyon, Vishal Soni
[1] A. Hübler, O. Osuagwu, Digital quantum batteries: Energy and information storage in nano vacuum tube arrays, Complexity 15(5), 48-55 (2010) Abstract-1, Preprint-1
[2] A. Hübler, Digital Batteries, Complexity 14(3), 7-9(2008) Abstract-2, Preprint-2
 Fig. 4: A jumbo jets with replaceable batteries. |
Today aviation produces about 3% of the global CO2 emissions. If the amount of air travel keeps increasing at it's present rate of 5% per year, the carbon footprint of commercial aviation will more than double within the next 15 years.
Recent work at the University of Illinois suggests that it is possible to fabricate a Digital Quantum Batteries (DQB) which holds at least as high an energy density as kerosene. In this paper we explore the design requirements of a electric jumbo jet powered by such a high density battery. We introduce and address the following design challenges:
(1) a DQB powered plane would need to be able to recharge quickly, perhaps even within minutes; (2) because the power density of DQBs is many orders of magnitude larger than that of kerosene, a DQB failure is potentially explosive; (3) these size and weight of DQBs must not have a negative impact on the aerodynamic stability and energy efficiency of the plane; (4) DQBs would have to be easily and efficiently recharged using a carbon neutral source of energy; (5) a DBQ powered plane must avoid high maintenance costs; (6) reducing noise emission;
We propose two designs to overcome these challenges: airplane image
 Fig. 5: A jumbo jet with energetic wall materials. |
Design 1: Jumbo jets with replaceable batteries
This design combines jumbo jet technology with fighter jet technology. Four missile shaped DQBs are attached to the bottom of the wings of a jumbo jet. The attachments are similar to missile attachments for fighter jets
Design 2: Jumbo jets with energetic wall materials
This design integrates mechanical stability and energy storage. We propose to fabricate DQBs in the shape of airplane hulls. They can store energy, but in addition provide thermal insulation and mechanical strength. DQB can be used as solar panels and can thus be recharged during flight.
Qi Chen and Alfred Hübler
 Fig. 6: A surfer catching a big wave. |
If a spherical object is floating in water where a wave is moving at a certain velocity, the spherical object may be able to reach the speed of the wave but will not be able to move faster than it. However, if a surfboard is moving perpendicular to this same wave, it will be able to move faster than the speed of the wave. A similar phenomenon occurs when electromagnetic waves accelerate particles. With this example we believe that it is possible to move faster than the speed of light in matter.
Joe Brewer and Alfred Hübler
[4] D. Farrell, A. Hübler, J. Brewer, I. Hübler, Acceleration beyond the wave speed in dissipative wave-particle systems, Complexity 15(5), 8-11 (2010) Abstract-4, Preprint-4
In the presence of an electric field, spherical conducting particles in a dielectric liquid assemble themselves into a dendritic tree form in order to dissipate charge. Several topological measures characterize such dendritic networks, including degree distributions, Strahler numbers, and total external pathlengths. Here, scaling laws relating these toplolgical measures to the number of nodes in the system are presented and shown to match diffusion limited aggregation(DLA) structures. Experimental bifurcation and stream-lingth ratios in this easily reproducible laboratory experiment are found to agree with DLA simulations and Horton’s Law for river networks. Certain scaling relations in transportation networks have previously been shown to originate from general features of networks. Here we find the experimental structures share properties with natural river networks.
Vishal Soni and Alfred Hübler
In this experiment, we studied the dynamics of an open one-dimensional discrete flow, in this case, a chain of moving point particles connected by ideal springs. These particles flow towards an inlet at constant velocity, pass into a region where they are free to move according to their nearest neighbor interactions, and then pass an outlet where they travel with a sinusoidally varying velocity. As the amplitude of the outlet oscillations is increased, we find that the resident time of particles in the chamber follows a bifurcating (Feigenbaum) route to chaos. This irregular dynamics may be related to the complex behavior of many particle discrete flows or is possibly a low-dimensional analogue of turbulence in continuous systems.
Austin Gerig and Alfred Hübler
 Fig. 7: Photo of experimental setup showing pendulum and computer simulation. |
In this experiment we create a mixed reality system by linking together both a real pendulum and a virtual one. To connect the two we have the real pendulum feed data into the computer the affects its virtual counterpart. The virtual in turn outputs to a motor that affects the movement of the real pendulum. When the frequencies of the pendulums are close to one another the pendulums are able to defy friction and keep swinging. This experiment helps us to understand more about mixed reality states.
Brandan Pflugmacher and Alfred Hübler
[5] V. Gintautas, A. Hübler, Experimental evidence for mixed reality states in an interreality system digital wire image Reprint-5
[6] G. Gintautas, A. Hübler, A simple low-cost, data-logging pendulum built from a computer mouse Reprint-6, Newpaper-article-6
Dynamical systems are often studied using maps; functions that determine the next state from the current state:
yn+1 = f(yn)
The map f "maps" the current state vector to the next one. We are most interested in nonlinear maps, specifically maps that result in chaotic dynamics (e.g. logistic map, Bournoulli shift). We study the effects of adding forcing:
xn+1 = f(xn) + Fn
We are interested in what patterns of forcing (subject to various constraints) cause this system to have a dynamical trajectory that is the most different from the original unforced trajectory, i.e. the greatest response. Relevant tools are the calculus of variations, difference equations, symbolic dynamics, and numerical modeling.
Glenn Foster and Alfred Hübler
We study the diffraction patterns of one-dimensional quasi-periodic scatterers from quasi-periodic pulse trains. We find a single sharp diffraction peak when the dynamics of the incident wave matches the arrangement of the scatterers, that is, when the pulse train and the scatterers are in resonance. The maximum diffraction angle and the resonant pulse train determine the positions of the scatterers. These results may provide a methodology for identifying quasicrystals with a very large signal to noise ratio.
Jian Xu and Alfred Hübler
 Fig. 8: Diagram of network pathways. |
We are investigating propagation on networks (small-world graphs, lattices, trees, random graphs, scale free graphs, socal neworks) and robustness of networks. This includes behavior like disease/viral infection on social and computer networks and cascade failures in electronic and physical systems. This has been an area of intense research in the last few years by numerous researchers (notably Barabasi, Watts, Strogatz, et. al.) with lots of interesting applications of percolation theory, statistical mechanics, graph theory, and of course, computer simulation.
Glenn Foster and Jian Xu
 Fig. 9: Diagram showing hypothetical nodes and branches in root system. |
An iterated function system is used to generate fractal ramified graph networks of absorbers, which are optimized for desalination performance. The diffusion equation is solved for the boundary case of constant pressure difference at the absorbers and a constant ambient salt concentration far rom the absorbers. We use a linearized form of the solution to obtain optimal shapes for each of the first nine generations G = 2, . . . , 10, subject to the onstraints that total length of the network and total area of the absorbers are kept constant as functions of generation G. Total water production rate increases parabolically as a function of generation, with a maximum at G = 7. Total water production rate is shown to be approximately linearly related to the power consumed, for a fixed generation. Optimal branching ratios obey a decaying power law which asymptotes to r = .510 for large G, and optimal branching angle obeys an increasing exponential law which asymptotes to 1.17 radians. We show that asymetric graphs are less efficient then symmetric graphs. The problem can be specified by three dimensionless parameters: a dimensionless membrane resistance, a dimensionless scaling factor denoting absorber size to pipe system ratio, and a dimensionless applied pressure. The optimal geometry does not depend strongly on the dimensionless parameters, but the optimal water production does. The optimal generation is found to increase with the scaling parameter. We conclude by outlining a research program to develop a theory of geometric optimization as applied to absorbing networks.
Martin Singleton and Alfred Hübler
We study the dissipative wave particle dynamics driven by band filtered noise. We show that particles have prefered locations if the main wavelength of the noise is comparable with the dimensions of the systems. We study transitions between the attractor locations.
Davit Sivil, Jacqueline Mentzel, and Alfred Hübler
[7] D. Sivil, A. Hübler, Quantized motion of a particle pushed around by waves, Complexity 15(2), 10-12(2009) Abstract-7, Preprint-7
We study the the divergence of neighboring trajectories in multi-dimensional chaotic dynamical systems. We find that in general maximum divergence is not related to the largest Liapunov exponent, except in special cases. We show that common numerical methods for computing the largest Liapunov exponent, determine the maximum divergence instead. We explore the possibility of periodic dynamics with positive Liapunov exponents, and chaotic dynamics where the largest Liapunov exponent is negative.
Joe Muka and Alfred Hübler
 Fig. 10: Petri dish showing ball-bearings in an electrical field forming connections. |
In this work, we measure the time of the congregations and connection of particles between two points of connection and its relation to the increase of voltage. We also study the time interval between which a connection is formed at one point and reformed in another. This will give us clues as to how the neural connections of the brain works and ways to control connections. We vary our methods to find the best way to control the results of these experiments and bring the standard deviation of our trials to a minimum. When there exists a field or charge in an area of particles, the ball bearings rearrange themselves to be in the path of the charge. As the distance of the path grows longer, the charge between the two points of connection will become weaker. Eventually, it will be no longer strong enough to sustain the connection and the particles will be unable to form a path with each other. The ability of association of the particles not only depend on the distance, but also the strength of the voltage. These two factors are the main control of the experiment.
Joy Chao and Alfred Hübler
 Fig. 11: Petri dish with glass beads in an electrical field. |
Conducting particles placed between two electrodes tend to assemble themselves into particle “wires” when a voltage is applied. In the presence of multiple input and output electrodes, these particles assemble themselves into wire networks. The layout of these networks depend on the charging of the electrodes. Sperl et al. has shown that these types of particle networks “remember” which electrodes were charged--in effect, a kind of learning. Thus, these systems are hardware implementations of a neural net.
Our experiments have shown, however, that these networks have many symmetries and that particles often have imperfect memory because they get stuck in meta-stable states. Noise helps to break these symmetries and therefore facilitates learning. However, if the noise in the system is too large, it destroys wires and the system forgets. In this project we try to determine the optimal amount of noise which helps a system to learn but does not make it to forget.
Marshall Kuypers and Alfred Hübler
[8] M. S. Singleton, A. Hübler, Learning Rate and attractor size of the single-layer perceptron Reprint-8
[9] M. Sperl, A. Changl, N. Weber, A. Hübler, Hebbian Learning in the Agglomerations of Conduction Particles, Phys.Rev.E. 59, 3165-3165 (1999),Abstract-9, Reprint-9
In this experiment, we studied the migration patterns of yeast cells in environments with and without ultraviolet light. We also examined the effect ultraviolet light has on the cell cycle of an individual yeast cell, and whether these affects persist from generation to generation.
The synchronization of yeast cells growth plays a huge role in understanding the process of eukaryotic cell division and of the molecular components of the cell which guide this process. Having such knowledge could improve our understanding of human cancer. In a synchronized yeast cell population, the cells divide almost completely in unison. With these controlled cell divisions, the cycle can be observed and understood to a greater extent, and this can, in turn, be useful in determining effective ways of annihilating cancer cells in humans.
Mihaela Marinova and Alfred Hübler
[10] V. Gintautas, A. Hübler, Resonant forcing of nonlinear systems of differential equations
[11] J. Xu, A. Hübler, Detecting quasiperiodic structures with double diffraction
[12] A. Hübler, Homeopathic dynamical systems
[13] V. Gintautas, G. Foster, A. Hübler, Resonant forcing of select degrees of freedom of multidimensional chaotic map dynamics
[14] A. Hübler, G. Foster, K. C. Phelp, Managing chaos: Thinking out of the box, Complexity 12(3), 10-13 (2007) Abstract-14, Preprint-14
We are converting wind energy into electrical energy via a system containing no (mechanical) moving parts. We do this by allowing the wind to move moist air through a wire screen. As the water droplets in the moist air move through the screen they become electrically charged. As the wind continues to push these charged droplets through a second screen, the droplets lose their charge. This charge is stored on a black cylinder and can be used to power a heater, computer, engine or other similar devices.
This wind electricity convertor is convenient because it produces no noise and is not harmful to the environment. Other energy convertors, such as wind turbine farms, produces loud noise and is often harmful to birds flying into the moving blades.
Matthias Gempel and Alfred Hübler
