NOVELTY - The bio-electrochemical system (100) comprises a reactor including an anode (104), a cathode (108) and methanogenic microbes, first and second chambers, a power source to apply voltage to the anode and the cathode, a trickling filter disposed between the first chamber and the second chamber and configured to facilitate nitrification produced in the filter, and a membrane for separating the first chamber and the second chamber. The anode and the cathode are proximity in the reactor. The voltage facilitates exocellular electron transfer from the anode to the cathode.    USE - The bio-electrochemical system is useful: for generating methane from organic material for controlling elements including the measure of pH, biochemical oxygen demand, chemical oxygen demand, ammonia and other chemical species within the reactor such as an existing anaerobic digestion system for wastewater and solids treatment; in a fuel cell or a generator for generating electricity; and for reducing chemical oxygen demand and nitrogenous waste through denitrification (all claimed), where the wastewater includes animal manures or manure slurries, non-manure agricultural wastes, slaughterhouse waste or wastewater, food processing wastewater or slurries, beverage processing wastewaters including brewery wastewater or slurries, municipal wastewater, and septic system wastewater or grey-water building wastewater.    ADVANTAGE - The bio-electrochemical system is capable of economically and efficiently generating methane from organic material with enhanced production rate and high purity and without hydrogen thus easily treating the wastewater within the reactor.    DETAILED DESCRIPTION - The bio-electrochemical system (100) comprises a reactor including an anode (104), a cathode (108) and methanogenic microbes, first and second chambers, a power source to apply voltage to the anode and the cathode, a trickling filter disposed between the first chamber and the second chamber and configured to facilitate nitrification produced in the filter, and a membrane for separating the first chamber and the second chamber. The anode and the cathode are present in proximity in the reactor. The voltage facilitates exocellular electron transfer from the anode to the cathode and to the methanogenic microbes to initiate a reduction of hydrogen-2 oxidation. The organic materials are oxidized at the anode and cathode. A flow is created within the system to move material from the anode to the cathode to increase the rate of methane production. The first chamber has a tubular configuration, includes a first wall and a second wall defining an enclosed space such that the anode facilitates the oxidization of the microbes, and is disposed within a first membrane. The second chamber includes a first wall and a second wall defining an enclosed space such that the cathode is configured to facilitate the reduction of nitrates, oxygen or other oxidized species, and is disposed around the first membrane and enclosed by a tube member. The trickling filter is placed above the anode to facilitate flow through the anode and over the trickling filter. INDEPENDENT CLAIMS are included for:    (1) an electrode for a bio-electrochemical system;    (2) a system for the adaptive control of a bio-electrochemical system; and    (3) a fuel cell.    DESCRIPTION OF DRAWING(S) - The diagram shows plan view of a bio-electrochemical system.    Bio-electrochemical system (100)    Electrons (102)    Anode (104)    Circuit (106)    Cathode (108)    Barrier. (110)