Last week … Volume : -The volume of a solid object measures how much space it occupies. -The volume of irregularly shaped objects can be determined by their displacement of a liquid. Lecture demo: Displacement of water by a butterfly and a sponge. Density: -The density of a material is the mass per volume density = mass / volume

Position Context: Where are you? Where are the keys? Definition: -The position is the location in aposition coordinate systemcoordinate system, usually in two or more dimensions. Location in a coordinate system - The position of an object is the location of the center of the object. - The position of a person is a point between the eyes. Discussion: -Center means geometrical center or center of mass, … - Position vs. Time graphs; symbol for position: x, symbol for time: tPosition vs. Time Lecture demo: PendulumPendulum, Motion DetectorMotion Detector and Computer

Out-of-body experiences with video feedback Blanke O et al.Linking OBEs and self processing to mental own body imagery at the temporo-parietal junction. J Neurosci 25: (2006). - Subject sees video image of itself with 3D goggles - Two sticks, one strokes person's chest for two minutes, second stick moves just under the camera lenses, as if it were touching the virtual body. - Synchronous stroking => people reported the sense of being outside their own bodies, looking at themselves from a distance where the camera is located. - While people were experiencing the illusion, the experimenter pretended to smash the virtual body by waving a hammer just below the cameras. Immediately, the subjects registered a threat response as measured by sensors on their skin. They sweated and their pulses raced. Real system & similar virtual system & bi-directional instant. coupling = mixed reality

Experimental evidence for mixed reality states in physical systems Objective: Understand synchronization between virtual and real systems. Approach: - Couple a real dynamical system to its virtual counterpart with an instantaneous bi-direction coupling. - Measure the amplitudes of both systems and their phase difference, and then detect synchronization.

Experimental evidence for mixed reality states in physical inter-reality systems Results: - Experimental evidence for a phase transition from dual reality states to mixed reality states. - Phase diagram of the inter- reality system is in good agreement with the phase diagram of the simulated inter-reality system. Phase diagram of the inter-reality system: amplitude of the coupling versus the frequency ratio of the real and the virtual system. The phase boundary between mixed reality states (I) and dual reality states (II). The solid, dashed, and dotted lines indicate the critical points in the experiment, simulation, and analytic theory, respectively.

Mixed reality states in physical systems: Why are they important? Publication: The paper "Experimental evidence for mixed reality states in an inter-reality system" by Vadas Gintautas and Alfred Hubler, in Phys. Rev. E 75, (2007), was selected for the APS tip sheet: Virtual systems match their real counter parts with ever-increasing accuracy. - New hardware for instantaneous bi-directional coupling - In mixed reality states there is no clear boundary between the real and the virtual system. Mixed reality states can be used to analyze and control real systems with high precision. And then there is the possibility for time travel … by the virtual system. Photo: A. Hubler and V. Gintautas at the inter-reality system

Displacement and Distance Traveled Displacement Displacement Context: Where are we going? Definition: Displacement describes the change in Position Discussion: -Distance is the magnitude of the displacement - Velocity is the rate of change in position - Symbol for displacement: Δx

Velocity Velocity Context: Where are we going? Definition: -Velocity is the rate of change in position. -Velocity describes how fast something moves. Discussion: - Symbol for displacement: v = Δx / Δt where Δx is displacement and Δt is time lapsed - Units: mph, m/s, km/h -Velocity = 0 => object at rest - Motion with constant velocity: + frictionless horizontal motionfrictionless horizontal motion + sinking object in viscous fluidsinking object in viscous fluid + parachuteparachute + motion without push or pull -Speed is the magnitude of the velocity

Acceleration Context: A car accelerates. I am speeding up. Definition: -Acceleration how fast does fast change. -Acceleration the rate of change of the velocity. Discussion: -Symbol: a, Units: m/s 2 - Acceleration = 0 => velocity =constant -Motion with constant acceleration: free fall in vacuum, rollingfree fall in vacuumrolling down an inclinedown an incline, washers on a string, circular motion with const. speedwashers on a string

Position, velocity, acceleration - The position of an object is the location of the center of the object. - The position of a person is a point between the eyes. -Velocity is the rate of change in position. -Velocity describes how f ast something moves. -Acceleration describes how fast does fast change. - Acceleration describes how rapidly an object is speeding up. - Acceleration the rate of change of the velocity.